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Theories of investor behavior and their application to segmentation and predictive modelling of retail… Franjic, Nicole Marija 2001

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Theories of Investor Behavior and Their Application to Segmentation and Predictive Modeling of Retail Clients at Phillips, Hager & North by Nicole Marija Franjic BCom, University of Alberta, 1999 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE (BUSINESS ADMINISTRATION) in THE FACULTY OF GRADUATE STUDIES FACULTY OF COMMERCE AND BUSINESS ADMINISTRATION We accept this thesis as conforming to the^squired standard THE UNIVERSITY OF BRITISH COLUMBIA November 2001 © Nicole Marija Franjic, 2001 UBC Special Collections - Thesis Authorisation Form Page 1 of 1 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department o The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada Date pec 3 y 2 o O l http://www.library.ubc.ca/spcoll/thesauth.html 12/3/2001 ABSTRACT Behavioural theories of finance and economics have received little academic attention until recently. Nevertheless, behavioural theories of investor behaviour can be directly applied to categorization of investors and prediction of future behaviour. The purpose of characterizing and predicting future behaviour is to ensure allocation of appropriate corporate resources to meet the needs of clients as effectively as possible. This research specifically focuses on segmentation and predictive modeling of retail clients at Phillips, Hager & North Investment Management Ltd. Segmentation is undertaken through cluster analysis of investors based on transactional and performance data. Subsequent logistic regression and seemingly unrelated regression models are developed to determine if investment personality - through Know-Your-Client (KYC) information - and demographics have an explanatory and predictive relationship with future investor behaviour. © Nicole Marija Franjic ii ABSTRACT ii TABLE OF CONTENTS iii LIST OF TABLES v LIST OF FIGURES vi ACKNOWLEDGEMENTS. vii 1.0 INTRODUCTION. 1 1.1 Background 3 1.1.1 PH&N Corporate Structure - Advisory Services 3 1.2 Competitive Environment 4 1.2.1 Mutual Fund Industry 5 1.3 Regulatory Environment 5 2.0 INVESTOR BEHA VIOUR 7 2.1 Traditional View of Investor Behaviour 7 2.1.1 Finance Overview 7 2.1.2 Markowitz Model and Portfolio Selection 8 2.1.3 Rational Expectations and Economic Theory 10 2.1.4 Limitations of the Traditional View of Investor Behaviour 11 2.2 Behavioural View of Investor Behaviour 11 2.2.1 Traditional versus Behavioural View 11 2.2.2 Behavioural Finance 12 Investor Overconfidence 13 Cognitive Dissonance and Limitations 14 2.2.3 Behavioural Economics 17 Loss Aversion 17 2.3 Dynamic Portfolio Theory 18 3.0 DATA 20 3.1 Data Collection 20 3.2 Transaction and Market Value History 21 3.3 Portfolio Performance 23 3.4 Know-Your-Client (KYC) and Demographic Information 24 3.4.1 Descriptive Analysis of Demographic and Know-Your-Client Information 25 3.5 Technical Methodology 28 3.5.1 Cluster Analysis 28 3.5.2 Logistic Regression 31 Dichotomous Logistic Regression 31 Polytomous Logistic Regression 36 3.5.3 Seemingly Unrelated Regression (SUR) 37 4.0 RESUL TS FROM SEGMENTA TION AND PREDICTIVE MODELS. 40 4.1 Cluster Analysis 40 © Nicole Marija Franjic iii 4.2 ANOVA and Cross-tab Analysis of Clusters 46 4.3 Logistic Regression 50 4.3.1 Dichotomous Logistic Regression 50 Interpretation of Parameter Estimates for Clusters 51 Model Accuracy 54 4.3.2 Polytomous Logistic Regression 57 4.4 Seemingly Unrelated Regression (SUR) 60 5.0 APPLICA TION AND AREAS FOR FURTHER INVESTIGA TION. 66 5.1 Model Refinement and Improvement 66 5.2 Extension of Research and Areas for Further Investigation 68 6.0 CONCLUSION 69 REFERENCES. 74 APPENDICES. 76 © Nicole Marija Franjic iv LIST OF TABLES Number Table Name Page 3.1 R2 Test for Multicollinearity 35 4.1 Cluster Sizes as a Function of the Number of Clusters 42 4.2 Trading Behaviour and Performance of Clusters, Non-Standardized 43 4.3 Results of Cross-Tabs and ANOVA for Predictors on Clusters 47 4.4 Occupation with Highest Comparative Percentage Between Clusters 47 4.5 Occupation with Lowest Comparative Percentage Between Clusters 48 4.6 Comparative Percentage of Clients Within Each Cluster - Investment Knowledge 48 4.7 Comparative Percentage of Clients Within Clusters - Risk Tolerance 49 4.8 Analysis of Cutoff Values for "Buy-and-hold" Cluster 55 4.9 Optimal Cutoff Values, by Cluster 56 4.10 Occupational Categories 58 4.11 Pseudo-R2 Measures 59 4.12 Analysis of OLS Equation Results 61 4.13 Seemingly Unrelated Regression Error Covariance Matrix 62 4.14 OLS and SUR Parameter Estimates 63 1.1 List of PH&N Funds 77 1.2 Indices Used in Calculation of Normalized Client Returns 77 1.3 Occupation Categories 78 1.4 Nominal Variables 78 111.1 "Buy-and-hold" Parameter Estimates 80 111.2 "Loss Averse" Parameter Estimates 81 111.3 "Market Timer" Parameter Estimates 82 111.4 "Overconfident" Parameter Estimates 83 111.5 "Novice" Parameter Estimates 84 111.6 Analysis of Cutoff Values for "Loss Averse" Cluster 85 111.7 Analysis of Cutoff Values for "Market Timer" Cluster 85 111.8 Analysis of Cutoff Values for "Overconfident/DCA" Cluster 85 111.9 Analysis of Cutoff Values for "Novice" Cluster 86 © Nicole Marija Franjic v LIST OF FIGURES Number Figure Name Page I. 1 Hierarchy of Advisory Services at PH&N 4 2.1 Efficient Frontier and Portfolio Selection 8 2.2 Optimal Portfolio Selection 9 3.1 Age Distribution of Retail Client Sample at PH&N 23 & 3.2 Investment Knowledge for Retail Client Sample 27 4.1 Pattern for Standardized Cluster Means Across Variables 43 II. 1 PH&N Investment Profile Form 78 © Nicole Marija Franjic vi ACKNOWLEDGEMENTS I would like to thank the University of British Columbia and the Centre for Operations Excellence for their resources and support. In particular, I would like to thank Paul Hiom, Dr. Murray Carlson, Dr. Jonathan Berkowitz, and Dr. Martin Puterman for their advice and guidance. In addition, I would like to thank Phillips, Hager & North for access to their database and resources and for making this research possible. I would specifically like to thank Ron Matthews, James Darke, and Harinder Dail for their support and constant willingness to provide any information or resources necessary to successfully complete this research. I would also like to thank my family and friends for their overwhelming support throughout this entire process. I would like to thank my parents - Ana and Nikola Franjic - for always encouraging me in my endeavours and my sister - Vera Franjic - for her insight and guidance during the writing process. I would also like to thank my niece - Izidora Franjic -for keeping life in perspective, as only a child can. In addition, I would like to thank my friends - Sheelah Turner, Kathryn Kolbuch, Sarah Colby, and Ellen Fowler - for their technical advice on my research as well as their constant friendship and support. © Nicole Marija Franjic vii 1.0 INTRODUCTION To deliver exceptional service to clients, financial services firms must understand how and why their clients - and investors in general - behave the way they do. The underlying assumption in understanding investor behaviour is that investor characteristics and past trading behaviour provide insights into future behaviour. The purpose of characterizing and predicting future behaviour is to ensure allocation of appropriate corporate resources to meet the needs of clients as effectively as possible. Understanding investor behaviour in this research is undertaken by segmentation of retail clients at Phillips, Hager & North (PH&N) based on transaction activity, portfolio market value, and portfolio performance. Segmentation enables categorization of clients who invest at PH&N into similar groups, which facilitates an understanding of the general trading behaviour and investment philosophies of PH&N clients. Analysis of segments can also uncover different personality characteristics of clients within the behavioural segments created. These different personality characteristics are used in predictive modeling - such as logistic regression - to predict segment membership, which is a proxy for future behaviour. In addition, a seemingly unrelated regression model is used to predict future trading behaviour directly. The research undertaken here provides evidence that different behaviours exist at PH&N and that certain demographics and measures of investment personality appear to exhibit a predictive relationship with future investor behaviour. Investment personality is difficult to measure but if effectively collected, it can be an important predictor of future trading behaviour. Recently, legislation has been introduced requiring investment advisory firms to collect information from clients, which is intended to measure a client's investment personality. The need for client information is referred to as "Know-Your-Client" (KYC). Although collection of KYC information is standard in the investment industry, each Canadian province determines the guidelines that must be followed regarding the types of information to collect. Nevertheless, the collection of KYC information serves two main purposes. First, knowing a client's KYC information protects an investment firm from fraudulent client practices because an advisor can ensure every trade done by and for a client remains within the client's investment objectives. Second, knowing a client's investment personality - through KYC information - can assist advisors in providing the most suitable advice. © Nicole Marija Franjic 1 In the past, KYC information was only taken when a client first invested with a firm and even then it was on a voluntary basis. With the number of investors in the market increasing, legislation now requires KYC information to be collected from every client upon initial investment. In addition, firms must update KYC information annually or whenever major changes occur in the client's life - such as marriage, birth of children, or change in occupation. Consequently, with increased interest in investing and additional regulatory constraints, it is increasingly important for investment firms to understand their clients. This understanding will assist investment firms to comply with legislation and provide better client service. Nevertheless, in order to segment clients and analyze predictive models in the most efficient manner, investor behaviour must be understood on a conceptual level. Significant research has been undertaken in both traditional and behavioural finance and economics. It is important to understand where these theories began, what they entail, and how they pertain to investor behaviour in general. Chapter 2 discusses the similarities and differences of traditional and behavioural theories of investor behaviour. The data used in this research includes transaction, market value, performance, demographic, and client investment personality information. In addition, segmentation and predictive modeling of retail clients at PH&N involves cluster analysis, dichotomous and polytomous logistic regressions, and seemingly unrelated regression. Data definitions and descriptive statistics as well as methodology, technical formulations, and diagnostic methods of the analytic models are presented in Chapter 3. Segmentation and predictive models are analyzed in Chapter 4. This chapter examines the relationship between transactional behaviour, portfolio performance, and investor personality. The results indicate certain explanatory relationships appear to exist between investor behaviour and investor personality. Refinements and improvements that could be made to the segmentation and predictive models developed in this research are described in Chapter 5. In addition, areas for future investigation that are intended to further extend the results uncovered are also discussed. Finally, a summary of the findings and research undertaken are presented in Chapter 6. There is also a practical benefit to be gained by applying these methods and results to the Retail client base at PH&N. To fully understand the contribution of these theories and © Nicole Marija Franjic 2 subsequent analyses, background on PH&N and the financial services industry - with particular attention to the trading of mutual funds - is discussed next. 1.1 Background Phillips, Hager & North Investment Management Ltd. (PH&N) is a financial services firm that administers its own mutual funds and provides advisory services to institutional and private clients. Founded in 1964 by Art Phillips, Bob Hager, and Rudy North, PH&N is now an employee-owned firm. PH&N has offices in Vancouver, Calgary, and Toronto with over $35 billion in assets under management. In its early years, PH&N primarily managed pension plans for institutional investors; however, their service and fund performance led to expansion in their client base that now includes private clients as well. PH&N quickly realized positive word-of-mouth was an effective strategy for attracting new clients. Even today PH&N chooses to preserve this unconventional marketing strategy; a strategy that has allowed them to attract a client base of high net worth investors. In addition, PH&N has a reputation for conservative investment strategies, steady returns, and low fees on its mutual funds. As Tom Bradley, President and CEO of PH&N, was quoted in the National Post, "the investment process is a marathon, not a sprint".1 This long-term view of investing permeates through the company. 1.1.1 PH&N Corporate Structure - Advisory Services PH&N advises both institutional and private clients. The latter are further divided into discretionary and non-discretionary (Retail) clients. Discretionary clients have a Portfolio Manager who regularly makes decisions regarding client investments whereas a non-discretionary client can seek advice but investment decisions rest solely with the client. In addition, a minimum initial investment amount was established in 1999. This minimum value is $500,000 for discretionary clients and $25,000 for non-discretionary clients. Within the Retail department, there is a further distinction between client types. If a client has an internal account within PH&N, this client can be assigned to an Investment Advisor or left unassigned. In addition, clients can invest in PH&N mutual funds through other financial service providers - such as a brokerage or other financial advice firm. The latter clients are referred to as nominee clients. This project focuses on the former types of © Nicole Marija Franjic 3 clients; those who have internal PH&N accounts and whose primary relationship is within PH&N. The hierarchy of advisory services at PH&N is illustrated in Figure 1.1. FIGURE 1.1 HIERARCHY OF ADVISORY SERVICES A T PH&N PH&N Institutional clients Private clients Discretionary Non-discretionary clients clients r Assigned Unassigned Nominee clients clients clients 1.2 Competitive Environment As the investment industry has grown and diversified, so has the nature of financial services. Where individuals were once investing spectators, the rise of financial services and advisory firms has brought investing to the masses. Banks are no longer the exclusive point of financial contact for individuals; investors specifically want firms who specialize in money management and growth. PH&N is regarded as one of these specialty firms. Companies such as PH&N are known as "wealth management" agents. While banks provide a plethora of services - from depository and borrowing services to investment advice - wealth management firms cater specifically to managing investments and growing an investor's portfolio. Several Canadian banks have already developed wealth management divisions. These banks have developed new offers intended to provide superior service to those who have high net worth and growth potential. Although banks have more resources, their size may be an impediment in the wealth management niche. Understanding a client's needs and delivering quality services are paramount in wealth management; therefore, banks may find their size and myriad service offers limit their ability to fulfill the needs of this client segment well. Despite this new competition, PH&N © Nicole Marija Franjic 4 still has a key advantage - an established reputation for providing superior service and portfolios that generate consistent returns. To understand obstacles faced by PH&N in the changing investment environment, it is important to analyze trends in the mutual fund industry as well as relevant mutual fund legislation. Specifically, the increasing popularity of mutual funds as well as regulatory requirements will be examined. The regulatory requirements create administrative difficulties but they also enable firms to explore client investment personality more easily. 1.2.1 Mutual Fund Industry Over the past decade, mutual funds have become extremely popular with investors. Mutual funds are dissimilar from regular investment securities in that they pool the monetary contributions of numerous investors and purchase a variety of securities and security types. Instead of purchasing shares of the fund on an exchange, investors purchase units of the funds directly from the company that issues and manages the fund. The mutual fund industry in Canada has grown considerably in the past decade. There were approximately 32.8 million unitholder accounts totaling C$24.9 billion in 1990.2 By August 2001 unitholder accounts grew to 52.2 million totaling C$411.1 billion3 - a growth of over 59% and 1,550% respectively. In addition, the value of assets in mutual funds as of March 31, 2001 in 38 countries worldwide was over U$l l trillion - where the United States and Canada accounted for approximately 60% and 2% of this total respectively.4 The growth of mutual funds is attributed primarily to the level of diversification they allow that cannot be achieved by the average investor with limited financial resources. Mutual funds enable investors to invest in a wide variety of securities across the different asset classes - money market, fixed income, and equity. This level of diversification is rarely possible for the average investor because the hundreds of securities included in a mutual fund would have to be individually purchased - a costly alternative. 1.3 Regulatory Environment Within Canada, there is no federal regulatory body controlling securities and mutual funds; legislation is done by commissions at the provincial level. In contrast, the United States has a federal regulatory body known as the Securities Exchange Commission (SEC). These regulatory bodies are responsible for ensuring both investors and investment advisory firms are protected against fraudulent practices. © Nicole Marija Franjic 5 Although there are no federal regulatory bodies in Canada, there are numerous organizations responsible for ensuring proper registration, conduct, and education of all individuals and firms undertaking securities trading and advising. One of the key educational bodies in Canada is the Canadian Securities Institute (CSI). An individual cannot trade securities or advise clients on investment issues without completion of required courses. Education of their professionals is a substantial cost and responsibility for investment firms such as PH&N. In addition to education of their professional, collection of KYC information from clients is a major undertaking for most investment firms. Due to the large number of clients, investment firms will be required to expend significant monetary and human resources to ensure the investment personality of every client within the firm is documented and regularly updated. © Nicole Marija Franjic 6 2.0 INVESTOR BEHAVIOUR Concepts of behaviour have generally fallen into the realm of the social sciences while investment theories have been within the domain of finance and economics. These disciplines are often regarded as mutually exclusive. While the study of investor behaviour is not a new phenomenon, only in recent decades has the integration of qualitative methods from the social sciences and quantitative techniques from finance and economics become more prevalent in application to modern investor theory. Nonetheless, there is still no definition or theory for investor behaviour supported by all disciplines. The traditional view of investor behaviour is rooted in the idea that investors are inherently rational and sophisticated beings. In contrast to this, behavioural theories contend that people are inherently irrational and do not always act in their own best interests. While both views have merit, the reality is that human behaviour and interactions are complex and no one theory will ever be able to fully explain or predict what every investor will do. Regardless, the traditional and behavioural approaches have both contributed significantly to understanding why investors behave the way they do. 2.1 Traditional View of Investor Behaviour5 2.1.1 Finance Overview Early in the twentieth century, Benjamin Graham's theory of fundamental analysis in security selection permeated through the investment industry. The idea underlying fundamental analysis is that the future direction of a security's price can be determined through careful analysis of the issuing firm's financial statements. Another theory related to price determination is technical analysis. While fundamental analysis looks for information in a firm's financial statements, technical analysis attempts to find predictable patterns in the past prices of a security. Modern academic investment theory has shifted away from these analysis techniques and towards theories of efficient markets and efficient portfolios. Financial theories in the latter half of the twentieth century began hypothesizing that financial markets exhibit some sort of efficiency. The basic supposition of financial market efficiency is that financial markets quickly and efficiently incorporate new and relevant information about a security. Consequently, an investor cannot "on the average, ...make abnormal profits by using this set of information to formulate buying and selling decisions."6 © Nicole Marija Franjic 7 Of course it is nearly impossible for a market to be perfectly efficient - even with increased access to information through the Internet. Related to the theory of efficient markets is the random walk hypothesis. The random walk hypothesis asserts future price changes of a security are independent from past prices; therefore, stock price movements are unpredictable. As a result, one cannot use historical performance to predict future performance. The random walk hypothesis also depends on the concept that investors accurately interpret and apply available information. Opponents of the efficient markets and random walk hypotheses posit that it is not logical to assume all investors are sophisticated and can accurately apply information gathered. Due to cognitive limitations, time constraints faced by investors, and difficulty of obtaining information, it is improbable - even with the level of competition in the market -that the price of all securities will, at all times, reflect company information and historical price performance. 2.1.2 Markowitz Model and Portfolio Selection In 1952, Harry M. Markowitz introduced a portfolio selection model based on the postulation that investors will select portfolios where expected returns are maximized and portfolio risk7 is minimized. The group of portfolios where returns are maximized for a given level of risk is called the efficient set or the mean-variance efficient frontier. Figure 2.1 provides an example of the efficient frontier. FIGURE 2.1 EFFICIENT FRONTIER A W i C ^ F O L I O SELECTION!, ~ Expected return Efficient C A Low Risk High © Nicole Marija Franjic 8 As can be seen in Figure 2.1, portfolios A, B, and C are on the efficient frontier. Consequently, portfolios A, B, and C would be considered efficient because they maximize expected returns for a given level of risk. Portfolio D is inefficient because portfolio A offers less risk for the same level of expected return. Similarly, portfolio E is inefficient because portfolio C offers a greater expected return for the same level of risk. Once the efficient set is identified, investors must determine the set of portfolios where they are indifferent to the expected returns at a given level of risk. The portfolios to which they are indifferent are graphed as indifference curves against the efficient frontier. The optimal portfolio is then determined by selecting the investor's indifference curve that is tangent to the efficient frontier. Figure 2.2 illustrates the optimal portfolio in relation to the indifference curve that is tangent to the efficient frontier. jiilglia OJR$IM AL PQCTFOUO SELECTION ~ According to the Markowitz model, there is one optimal portfolio for risky assets and another optimal portfolio for risk-free assets. Consequently, an investor will maximize total expected returns by combining the optimal risky and risk-free portfolios. This combination will create the investor's optimal overall portfolio. Similar to the efficient markets and random walk hypotheses, the Markowitz model also depends on certain assumptions about investors. First, it is assumed investors will always prefer portfolios with higher expected returns; this is referred to as the assumption of nonsatiation8. In addition, the Markowitz model assumes investors are risk averse; an investor will always choose the less risky portfolio against comparable expected returns. © Nicole Marija Franjic 9 Through diversification between two types of assets - risky and risk-free - an investor can optimize his expected portfolio returns for a given level of risk or risk-aversion. The portfolio selection model developed by Markowitz has generally been adopted as the method by which rational investors select their portfolios. While it is possible that professional analysts and investment managers have the knowledge and capability to compute expected returns and risk, it is doubtful the typical investor possesses similar knowledge. In addition, some theorists argue not only do investors lack the competencies to perform the calculations necessary in the Markowitz model but they also assert that investors are inherently irrational. Consequently, the basic tenets of modern portfolio theory inappropriately rely on the quantitative capabilities and rationality of investors. Nevertheless, based on the Markowitz model, mutual fund investors would be expected to divide their portfolio between several funds, based on risk tolerance. The money market fund represents the portfolio of risk-free assets while a combination of domestic and foreign bond and equity index funds represent the portfolio of risky assets -or the relevant market portfolios. As a result, it is expected investors choose their optimal portfolios by dividing their investments between the money market, bond index, and equity index funds where returns are maximized for a given level of risk tolerance. Consequently, investors following the Markowitz model would also be expected to have returns that are very similar to market portfolios. 2.1.3 Rational Expectations and Economic Theory A common theme underlying most traditional financial theories is that investors exhibit rational behaviour; however, what does this rationality entail? There are many economic theories that attempt to define the concept of rationality. One of the basic theories of the neo-classical economic approach is the rational expectations hypothesis. This hypothesis states that people collect information, form expectations based on this information, and then act upon the expectations formed. This hypothesis simply states people rationally consider their alternatives and then react according to what they expect will happen in the future. Due to the informed actions of rational people and the resulting competitive marketplace, the rational expectations hypothesis alleges people cannot expect to systematically outperform the market. © Nicole Marija Franjic 10 The rational expectations hypothesis does not assume all people exhibit rational behaviour at all times. Instead, the hypothesis "claims that on the average expectations are rational".9 In addition, the hypothesis does not exclude erroneous expectations to be formed and acted upon; however, it assumes people learn from their mistakes and, on average, form correct expectations. Consequently, given people make informed expectations, the majority of people will exhibit rational behaviour most of the time. 2.1.4 Limitations of the Traditional View of Investor Behaviour The traditional methods in finance and economics have imparted an invaluable understanding of how markets and economies should function; however, these quantitative methods may not be the most suitable for predicting how Investors will behave in these markets. Even when given mathematical tools to assist them, people invariably use judgment or intuition to make decisions. For example, many of the companies ethical funds avoid are very profitable; however, investors use their values and morals rather than quantitative analysis when choosing not to invest in these companies. Traditional theories are also ill-equipped to explain stock market anomalies. These anomalies encompass myriad market events, including market crashes and speculative bubbles. The latter phenomenon is particularly interesting, primarily due to the recent rise and fall of hi-technology securities. Traditional theories cannot explain why the technology firms were trading at prices far exceeding their intrinsic values. Why? Behavioural researchers assert it is because traditional theories do not acknowledge that investor irrationality can affect market prices. In response to the limitations of traditional methods, the relatively new field of behavioural studies has gained wider acceptance. These behavioural theories question the efficient and rational premises of classic finance and economic theory. 2.2 Behavioural View of Investor Behaviour 2.2.1 Traditional versus Behavioural View Traditional and behavioural theories in finance and economics attempt to explain how investors affect market and economic movements; however, they differ considerably in their underlying beliefs and approaches. The basic tenet of traditional theories is the expectation that markets are efficient because investors are rational and use all information © Nicole Marija Franjic 11 at their disposal before making a decision. Conversely, behavioural theories believe markets are inefficient because investors are inherently irrational and allow emotions to overwhelm their decisions rather than relevant facts and logic. Behavioural theories assert the inherent uncertainty of the investment environment causes investors to prefer simpler, more intuitive methods of analysis. Amos and Kahneman studied the application of heuristics to uncertain and complex choices. They illustrate "that people rely on a limited number of heuristic principles which reduce the complex tasks of assessing probabilities...to simpler judgmental operations." 1 0 Heuristics are less accurate and can often result in incorrect investment decisions. Consequently, behavioural theories allege markets cannot be efficient if the investors of whom the markets are composed do not rationally assess the probabilities and outcomes of their investment choices. Nevertheless, it is not the intention of behavioural theories to negate the insights uncovered by traditional theories. Instead, behavioural theories attempt to rectify oversights in traditional tenets by integrating theories of human behaviour from the social sciences. Although many of the conclusions reached in both behavioural finance and behavioural economics are complementary, their respective classical disciplines contain fundamental differences. Consequently, the research and findings of behavioural finance and behavioural economics shall be addressed separately. 2.2.2 Behavioural Finance Behavioural finance is the application of psychological principles and financial theories to investor behaviour. Behavioural finance studies how investors use emotions and past experiences rather than quantitative methods to make investment decisions. This qualitative method of decision-making often results in poor investment choices and inferior portfolio performance. Many behavioural researchers assert investment errors occur because humans are irrational when faced with uncertainty and making monetary decisions in general. This innate human flaw results in systematic and repeated patterns of investment mistakes. As Fuller states, "these mental mistakes can cause investors to form biased expectations regarding the future", 1 1 which can create exploitable market opportunities. Although numerous areas of research have been undertaken in behavioural finance, investor overconfidence as well as cognitive dissonance and limitations shall be discussed. © Nicole Marija Franjic 12 Investor Overconfidence Classical theories of finance have imbued investors with the idea that possession of pertinent information enables a certain degree of success in investing. Unfortunately, this attitude has created an investing paradox; information has not created an efficient market of rational investors but rather, an inefficient market of irrational and overconfident investors. Investor overconfidence is perhaps one of the most prominent and studied phenomena in behavioural finance, often because of this paradox. Overconfidence specifically relates to how individuals overestimate their knowledge and abilities by taking into consideration investor psychological attitudes and how investors act on these beliefs. Psychology has undertaken numerous studies examining the effects of confidence levels on human decision making. Of particular interest are those studies that investigate how access to information increases confidence. A study by Oskamp of psychological professionals and students 1 2 postulates that as "judges" are given more information about an individual, levels of confidence with decisions about the individual will increase but the accuracy of judgments will not. In all instances, the confidence of the judges - measured as the percentage of decisions believed to be correct - exceeds the accuracy of their decisions - the percentage of actual correct decisions. In addition, as the judges are given more information, the accuracy of their decisions do not change significantly but their confidence rises considerably. This study provides evidence that people often erroneously believe having more information helps them to better understand a situation; therefore, they are more confident the decisions they make are correct. Considerable related research has also been studied in investor behaviour. Odean has contributed significantly to understanding how investor overconfidence affects behaviour and performance. In one study, he tests the theory that investors who are overconfident will trade excessively and improperly. By examining 10,000 discount brokerage accounts over an eight-year period, he concludes that the securities investors buy consistently underperform those they sell. In addition, when investors are "most likely to be trading solely to improve performance..., performance gets worse." 1 3 Odean also concludes investor overconfidence cannot completely account for the excessive trading and poor performance. Although people may have access to relevant information, investors seem to be "systematically misinterpreting information available to them." 1 4 Consequently, investors seem to mistakenly believe that possession of information is equivalent to possessing the © Nicole Marija Franjic 13 knowledge to accurately use that information. This erroneous assumption is refuted through evidence of the poor portfolio returns for these investors. In a subsequent and related study, Odean and Barber analyze 66,645 households with discount brokerage accounts. They assert "high levels of trading can be at least partly explained by a simple behavioural bias: People are overconfident, and overconfidence leads to too much trading."15 In addition, they specifically address the flaws in the rational expectation framework. This rational model states investors who trade frequently must achieve higher gross returns to effect net returns similar to those of less frequent traders. Odean and Barber's evidence proves this does not occur; the gross returns of frequent traders in their study are not significantly different from those of infrequent traders. Investor overconfidence has considerable ramifications for the investment industry. Evidence shows that "overconfidence does not decline over time...[because] people generally remember failures very differently from successes."16 Similarly, misinterpretation of information and actions based on these misunderstandings can cause market prices to be incorrect. Consequently, if people react on beliefs based on overconfidence or misperceptions, the market cannot be efficient because investors are not rational. Based on these theories, overconfident mutual fund investors are expected to buy, sell, and switch between funds frequently. In addition, it would be expected these trades would be highly correlated with press releases, pertinent newspaper articles, or whenever information regarding a company or fund is disseminated. Furthermore, based on the aggressive and potentially erroneous trading, portfolio returns for these investors are not expected to exceed the market average. Cognitive Dissonance and Limitations Cognitive dissonance was first studied in psychology and theorizes that people become uncomfortable when event outcomes conflict with decisions made. This theory asserts people tend to alter their beliefs to justify past actions. Although this concept was popularized in psychology, it has obvious applications to the study of investor behaviour. There are several behavioural finance theories that support and elaborate on the concept of cognitive dissonance; many of these relate to how investors integrate new information with previous beliefs. Statman and Fisher describe how people use confirmation bias to deceive themselves into believing their ideas and actions are correct; investors © Nicole Marija Franjic 14 "focus on information that is consistent with their beliefs while neglecting inconsistent information".17 Related to the concept of overconfidence, investors also have a tendency to overweight or underweight information as it pertains to their prior beliefs. Prendergast and Stole examine how investors attempt to reduce the anxiety surrounding conflicting evidence through biases known as the base rate fallacy and sunk cost fallacy.18 The former is related to overconfidence, where individuals believe the information they hold is more important than the information they do not hold - their responses to new information are exaggerated. The latter highlights the nature of conservative individuals who do not react to the introduction of new information for fear of taking the wrong action. The evidence presented here is that "cognitive dissonance reduction considers individuals as rationalizing beings rather than rational beings".19 Goetzmann and Peles analyze how these cognitive biases affect an investor's recollection of past fund performance. They provide evidence supporting greater monetary inflow into "winning funds" than outflow from "losing funds".20 Through a mutual fund questionnaire, a study of two types of investors is compared. Each group is asked to estimate the past performance of 57 mutual funds. The group considered more knowledgeable about investing overestimated actual return by 3.40%. The less knowledgeable group overestimated actual fund return by 6.22%. Although the more informed group overestimated actual returns by almost half the amount of the latter group, both results indicate recollection of past performance is positively skewed. Consequently, if people view past performance being higher than it actually was, they are more likely to stay in this fund even after it becomes a "losing fund". In addition, not only do people alter their beliefs about past events but they also exhibit regret for incorrect past choices. Feelings of regret can result in self-deception or even regret avoidance. Investors - as people in general - do not like to admit they are wrong. Consequently, they tend to deceive themselves by believing their knowledge or abilities contribute to their investment successes but chance or bad luck results in investment failures. This deception prevents feelings of regret for past mistakes; however, it also prevents investors from learning from their mistakes. Conversely, regret avoidance can result when an investor acknowledges past mistakes. This avoidance can paralyze investors; they will not make a decision for fear it will be a wrong one. Both these © Nicole Marija Franjic 15 attitudes can result in investors remaining in poorly performing funds and not taking advantage of funds performing well. Investors do not only alter their beliefs to reduce psychological discomfort but many researchers believe they also have inherent cognitive limitations that impede their ability to make prudent investment choices. In addition, it has been suggested that people require a cause and effect relationship. Since the investment market is chaotic and unpredictable, many theorists postulate investors do not have the cognitive ability to process all information necessary to make an effective investment choice. Consequently, investors must depend on certain heuristics to make decisions. Furthermore, as Fuller describes, "people evaluate the probability of an uncertain future...by the degree to which it is similar to recently observed events".21 By comparing similarities of the decision to be made with previously known information, people reduce the amount of information to be analyzed; however, they also reduce the accuracy of the conclusion reached. The theory of cognitive dissonance and hypothesized cognitive limitations challenges the essence of the efficient markets hypothesis. If people have a natural propensity towards belief alteration and self-deception as well as being innately limited in cognitive abilities, it cannot be inferred that all investors are rational. Indeed, it cannot be inferred that the majority of investors are rational. As a result, this reliance on intuition and heuristics creates market inefficiencies. The theories of cognitive dissonance and inherent cognitive limitations would be manifested in mutual fund traders through moderate trading, on average, and inferior portfolio returns compared to the market average. The level of trading is not necessarily representative of these people because some may trade frequently, based on beliefs that information they hold is correct. Conversely, another group may trade infrequently because they believe they cannot process the necessary amount of information and are paralyzed from trading at all. Consequently, these investors - as a group - would be moderate traders, but the standard deviation of trades within the group would be large. Nevertheless, the trading behaviours would result in poor returns for this group as a whole. It is the high variability of trades and poor returns that would primarily categorize these investors. © Nicole Marija Franjic 16 2.2.3 Behavioural Economics Similar to behavioural finance, behavioural economics attempts to explain how the cognitive limitations of investors affect their actual decision-making process. One of the key principles underlying behavioural economics is the idea of bounded rationality. The classical theory of rational behaviour assumes "an ideal world [where] every individual behave[s] like a rational Bayesian, optimally learning about the economic environment".22 Conversely, bounded rationality recognizes that "limited cognitive abilities constrain human problem solving";23 therefore, investors make the best decisions possible within their cognitive constraints. Investor perception of losses and actions taken in response to potential losses will be the focus of the discussion on behavioural economics. Loss A version Traditional theories assert investors are risk averse; they will choose the portfolio with the least risk when given a choice of portfolios with similar returns. Behavioural economics contends people are not risk averse but rather, they are loss averse. There are two similar theories that illustrate loss aversion in investors. The first theory is referred to as disposition effect. This theory states investors use a benchmark value - often a security's purchase price - against which they value whether they should hold or sell a security owned. Investors are more likely to sella security that is trading above the benchmark value and more likely to hold a security that is trading below the benchmark value. This occurs because loss averse investors are unwilling to accept a tangible loss. In a 1998 study, Odean illustrates this aversion through "evidence that individual investors tend to hold their losers and sell their winning investments."24 The second theory is known as myopic loss aversion. Benartzi and Thaler define this form of loss aversion as the "tendency for individuals to be more sensitive to reductions in their levels of well-being than to increases",25 especially when they are evaluating investments over a short time horizon. As a result, investors are more upset by losses than they are content by equivalent gains. In general, myopic loss aversion refers to the inability of investors to take a long-term view of their investments; therefore, they become distressed and overreact to short-term fluctuations. Kahneman and Tversky illustrate how this fear of tangible loss and myopic view can also create risk-taking behaviour from investors who would ordinarily be risk averse. Their © Nicole Marija Franjic 17 research involves assigning probabilities to certain scenarios, or prospects. Each prospect is either positive - where the outcome would be a gain - or negative, where the outcome would be a loss. They find "the preference between negative prospects is the mirror image of the preference between positive prospects."26 Consequently, this relationship "implies that risk aversion in the positive domain is accompanied by risk seeking in the negative domain".27 Traditional economic utility theory states investors will choose the option with the highest expected value. The conclusions reached by Kahneman and Tversky in their 1979 study are contrary to this theory. Their conclusions illustrate how investors may choose a prospect with a lower expected value if the probability of loss is not certain. This conclusion demonstrates the inherent optimism of investors; they overweight the occurrence of positive outcomes and underweight the occurrence of negative outcomes. Loss averse mutual fund investors would be expected to trade infrequently, with buys exceeding sells or switching between funds. These investors would have a greater propensity to hold onto funds than sell or switch between funds since they do not like to realize tangible losses. As a result, loss averse investors would also be expected to have returns below the market average due to the inability of these investors to sell funds performing poorly. 2.3 Dynamic Portfolio Theory The traditional view of portfolio theory, as developed by Markowitz, has three main concepts. The primary underlying concept is that security prices follow a random walk; therefore, they are unpredictable. In addition, investors are only concerned with maximizing expected returns for a given level of risk. As a result, an investor's optimal portfolio is comprised of only two asset types, risk-free fixed income assets and risky assets that mimic market performance. In contrast, dynamic portfolio theories believe returns can be somewhat predictable when taking a long-term view of investing. This new portfolio theory also expands on traditional theories by stating investors are not only concerned with risk minimization and return maximization but are also interested in hedging their risk exposure to macroeconomic factors. As Cochrane illustrates in a 1999 paper, the mean-variance efficient frontier becomes "the multi-factor efficient frontier...[and] the market return is no longer on the © Nicole Marija Franjic 18 mean-variance frontier".28 Indifference curves of investors also expand beyond the two-factor dimension of risk and return and become multi-dimensional based on additional factors taken into consideration. Cochrane asserts the idea of long-term predictable returns expands portfolio theory in three ways. Of paramount importance is the investment horizon; long-term predictability of returns is less helpful for short-term investors. In addition, this predictability creates market timing opportunities as well as the ability to hedge exposure to economic risks, such as fluctuating interest rates and reinvestment risk. Despite the new concepts dynamic portfolio theory introduces, these concepts must be used with discretion. As Cochrane cautions, the new portfolio theory is based on the assumption that only a limited number of investors will be interested in factors beyond risk and return. As a result, he asserts "the average investor must hold the market portfolio. Thus, multiple factors and return predictability cannot have any portfolio implications for the average investor."29 In addition, investors who are concerned with multiple factors must be exposed to several different risks so they will be investing in different assets at different prices and at different times. These investors cannot hold the same market beliefs and types of risks or the opportunities present in dynamic portfolio theory will disappear. If the average investor must still hold the market, mutual fund investors following the rules of dynamic portfolio theory would be expected to represent a very small proportion of total investors within a firm. Given these investors would be timing the market in an attempt to reduce the risk exposure to numerous factors they would primarily be switching between funds. If done correctly, efficient market timers following dynamic portfolio theories would be expected to have higher long-term returns. Nevertheless, short-term fluctuations or poor market timing may result in short-term returns that are lower than the market average. © Nicole Marija Franjic 19 3.0 DATA Concepts of investor behaviour are investigated through segmentation and predictive modeling of assigned and unassigned retail clients at PH&N. Segmentation is performed through cluster analysis while the predictive models include logistic regression and seemingly unrelated regression. In addition, modeling of retail clients at PH&N is further divided into two groups - new or existing PH&N clients. Current PH&N clients already have a measurable history through past trades and historical portfolio performance at PH&N. Conversely, PH&N has no similar measures for new clients since they have neither invested assets nor trading history at PH&N. Consequently, information available to predict future behaviour for new clients is much more limited and subjective in nature - it is restricted to basic demographics, KYC responses, and the monetary amount initially invested at PH&N. Despite the large amount of data available for existing clients, several necessary types of data are difficult to collect. In addition, these clients already have an existing relationship with PH&N and possibly an Investment Advisor at PH&N. Consequently, Advisors may not readily accept a model's results because they feel they already know their clients. Similarly, clients who have a history at PH&N may be reluctant to try new approaches because they already have established strategies. Conversely, analysis of new clients would be more amenable to Advisors as they would appreciate any information about new clients that might help them advise these clients better. As well, new clients would be more receptive to ideas by Advisors as they do not have established strategies with PH&N. For these reasons, segmentation and predictive modeling focuses on new PH&N clients. 3.1 Data Collection All data in this analysis is from PH&N's data warehouse. The data warehouse integrates data from several software applications at PH&N that contain the history of transactions, funds held, and portfolio market value for clients. Individual records pertaining to transactions, market value and performance for each client within each of these databases are subsequently merged into one flat file. The sample size and period under study includes 3,037 clients who joined PH&N between January 1, 1985 and December 31, 1999 and who have complete KYC and demographic information. Only the transaction, performance, and market value history for the first year after joining PH&N for each client is examined. Only the first year of trading is analyzed because the first year © Nicole Marija Franjic 20 after joining a new financial services firm is when new clients generally establish and reveal their investment strategies. By knowing how clients will trade during the first year enables PH&N to more effectively advise clients and to deter clients from trading inappropriately from the moment they join PH&N. To analyze this behaviour, several types of transaction, performance, and market value data are included in this analysis and are most pertinent for segmentation and predictive modeling. This data is described in the proceeding sections. 3.2 Transaction and Market Value History Of all transaction types analyzed, there are six types of transactions that can occur and are client-initiated. It is important to exclude any transactions that are not client-initiated because these are not representative of trading behaviour. The following list describes all data in the analysis based on transaction and market value history. a) Buy- the total number of transactions during the first year of trading with PH&N where the client is purchasing units of PH&N mutual funds. This involves an increase in the market value of the client's PH&N portfolio through addition of new money. b) Sell- the total number of transactions during the first year of trading with PH&N where the client is selling units of PH&N mutual funds. This involves a decrease in the market value of the client's PH&N portfolio through withdrawal of existing money. c) Switch-In or Switch-Out - the total number of transactions during the first year of trading with PH&N where the client is switching money already within a PH&N portfolio between two or more PH&N mutual funds. These transactions are equivalent; therefore, only one of side of this transaction type needs to be included in any analysis. d) Transfer-In or Transfer-Out - the total number of transactions during the first year of trading with PH&N where the client is transferring between two or more PH&N mutual funds, transferring money into PH&N, or transferring money out of PH&N into another financial services firm. As shown, this transaction type is multi-faceted. In general, these transactions are not a large percentage of total transactions and have a similar structure to switches; therefore, only one of transfers-in or transfers-out is counted. e) Total Transactions - sum of the total number of transactions of each type above for each client during the first year with PH&N. f) Number of Trade Days - as an alternate measure for total transactions, the number of days on which a client had transactions during the first year after opening an internal © Nicole Marija Franjic 21 PH&N account was also calculated. By using the number of days, especially in conjunction with total transactions, it is anticipated investors are not incorrectly classified as aggressive because of multiple transaction events - such as portfolio re-balancing. g) Transaction Origin - this refers to whether the transaction was manual or automatic. Manual transactions occur when the client contacts PH&N directly to trade a mutual fund. Although generally sporadic in nature, a client can initiate a transaction request at regular intervals as well. Conversely, an automatic transaction is electronically processed at regular intervals, most commonly on a specific day each month. h) DCA Transactions - this transaction, known as Dollar-Cost Averaging (DCA), is a subset of both the switch transaction type and the automatic transaction origin. DCA transactions indicate investors are electronically switching between the same funds at regular intervals. DCA transactions are used primarily, but not exclusively, by investors who are slowly moving towards their ultimate investment strategy and asset mix but are somewhat apprehensive about investing in security markets. Consequently, DCA transactions are considered similar to buy transactions by PH&N, especially when clients are switching from money market funds to other funds. i) Manual Switches - excessive manual switching generally signifies aggressive behaviour or market timing. Since PH&N is a conservative, buy-and-hold investment firm, excessive manual switching identifies clients whose philosophies differ from PH&N. j) December and January Switches - many investors alter their non-registered (non-RRSP) portfolios in the last month of a calendar year to minimize taxes paid on investments. In the first month of the following year the portfolio may once again be re-adjusted. Consequently, manual switches that occur in the last month or first month of the year may not represent aggressive behaviour but rather, a tax minimization strategy. k) Total Funds - this refers to the total number of different funds held, at any time, during the first year of trading after joining PH&N. During the period covering this study, seventeen different funds and two currency holding funds - Canadian and U.S. - were available to PH&N investors. The list of these funds is shown in Appendix I, Table LI. I) Initial, Ending, and Change In Market Values - measures of market value are useful in estimating not only the net worth of an investor but may also help determine the client's perception of PH&N's performance over the previous year. If the change in market © Nicole Marija Franjic 22 value is positive, the client may be investing regularly, transferring assets into PH&N, or realizing portfolio growth. Conversely, if the change in market value is negative, this may indicate the client is withdrawing funds from PH&N due to poor performance. 3.3 Portfolio Performance Portfolio performance is one of the key measures of investment success; however, there are numerous methods to calculate portfolio return. Unfortunately, this data is not readily available; calculation for each client included in the sample is necessary.30 Annualized return for the first year of trading after joining PH&N is calculated using an index value generated by an internal performance calculator in the twelfth month after account opening, less 100. Using this estimation method, the annualized return is almost equivalent to the actual annualized return, ±0.5%. Additionally, since clients do not join PH&N in the same year, estimated annualized returns reflect the prevailing market conditions of the year after account opening. As a result, these estimated annualized returns could not be compared to each other due to different market conditions. Consequently, annualized returns for the Toronto Stock Exchange (TSE) Total Return Index, Standard and Poor's (S&P) Total Return Index, and Scotia Universe Bond Index are used to normalize investor returns against market influences. The bond index is weighted at 40% and the equity indices are weighted at 60%. This weighting is used because this is the breakdown between fixed income and equity weightings for the PH&N Balanced fund, which is considered PH&N's internal benchmark for returns. Of the 60% equity weighting, the Canadian and U.S. equity indices are additionally weighted according to Canadian RRSP foreign content rules.31 The returns for these indices and the total weighted market returns from 1986 to 2000 are included in Appendix I, Table 1.2. Annualized market returns are then subtracted from estimated annualized client returns for the appropriate year to create a normalized annualized return variable for each client. Consequently, this normalized annualized return compares each client's portfolio return to the return that would be expected from a client holding the Markowitz efficient portfolio in the respective year. © Nicole Marija Franjic 23 3.4 Know-Your-Client (KYC) and Demographic Information In addition to transaction, market value, and performance data, the predictive models also use KYC and demographic information. Client ages and years in which they joined PH&N are discrete variables while other KYC and demographic information are categorical variables. This data includes: a) Investment Objective - investment objectives can be income, growth, or balanced. b) Investment Knowledge - a client's knowledge can be classified as none, minimal, limited, fair, good, or excellent. c) Risk Tolerance- a client's risk tolerance is classified as low, medium, or high. d) Income Range - clients choose five relatively broad categories for income range. This is based on client responses and thus, it is somewhat subjective. The choices for income range are on the Investment Profile form reproduced in Appendix II, Figure II.1. e) Net Worth Range- similar to income range, clients have a choice of six broad categories for net worth range. These ranges are also on the Investment Profile form reproduced in Appendix II, Figure II. 1. As well, the category in which a client is classified is based on client responses and does not include submitting financial statements. Consequently, the categorization is subjective, based on client willingness to divulge information or recollection of value of assets owned. f) Occupation - clients are allocated to one of sixteen possible occupation categories, including a retired category. All responses in the sample have been classified into one of these sixteen occupational categories. These categories are shown in Appendix I, Table 1.3. g) Age- the client's age in this analysis is the age of the client as of the December 31s t of the year after joining PH&N. h) Year Joined- the year representing when the client joined PH&N. i) Gender of client The different categories for each of the nominal variables and their assigned numerical values or the indicator variables created, which are used in subsequent analyses, are included in Appendix I, Table 1.4. The KYC information is collected from clients using PH&N's Investment Profile form, which is included in Appendix II, Figure II. 1. © Nicole Marija Franjic 24 3.4.1 Descriptive Analysis of Demographic and Know-Your-Client Information The primary predictor variable data for logistic regression and seemingly unrelated regression models includes demographic and KYC information from a sample of 3,037 assigned and unassigned retail clients at PH&N who joined PH&N between January 1, 1985 and December 31, 1999. PH&N knows nothing of client trading behavior when a client first invests with PH&N; demographic information - such as client age and gender - as well as KYC information are the only potential indicators of future behavior available to PH&N. As detailed above, PH&N collects two types of KYC information. Investment personality information includes investment objective, risk tolerance, and investment objective. Net worth potential encompasses information on estimated income, total net worth, and client occupation. Although this analysis is performed at the investor - not account - level, it should be noted that investors who share a joint account are included as separate investors in this analysis. Despite the potential difficulties this could create, these investors are included separately because they may hold more accounts - in addition to the shared joint account -that have further transaction activity, which should be analyzed independently. Nevertheless, of the sampled clients, the split between males and females is 50.8% and 49.2% respectively. In addition, 90.75% of these clients were still active at PH&N at the end of the year 2000 while 9.25% exited the assigned or unassigned status on or before December 31, 2000. Reasons for leaving the status are predominantly a result of the client leaving PH&N (57.65%); however, other reasons include switching to nominee client status (39.5%) or becoming discretionary clients at PH&N (2.85%). In the sample and during the sample period, the largest group (24.12%) of clients is between 35 and 44 years old with almost 86% of clients between 35 and 74 years old. In addition, only 0.5% of clients are under 25 years of age and 3% are over 74 years old. The age distribution of clients in the sample is shown in Figure 3.1. PH&N's Investment Profile form (Appendix II, Figure II. 1) includes three possible categorizations for investment objective. The growth investment objective is a frequent objective for pre-retired or younger clients who are growing their portfolios. This is generally a more aggressive and risky objective as it primarily invests in equity funds. The income investment objective is a frequent objective for retired clients who live on savings. These investors may require regular income to be generated from their investments. This © Nicole Marija Franjic 25 type of strategy generally holds fixed income securities or funds. The balanced investment objective is a multi-purpose objective between income and growth as it invests in a combination of fixed income and equity securities. Analysis of investment objective information indicates the most frequent investment objective is growth, with 53.01% of investors categorizing themselves as having this objective. The second most common objective is balanced at 40.57% while the least common objective is income at 6.42%. FIGURE 3.1 A G E DISTRIBUTION OF KYC RETAIL CLIENT SAMPLE A T PH&N 400 350 300 250 c S 200 0) 150 100 50 • Males • Females • Total < 25 25- 30- 35- 40- 45- 50- 55- 60- 65- 70- 75- >= 29 34 39 44 49 54 59 64 69 74 79 80 Age Range Financial theories generally use standard deviation as the measure of investment risk. Standard deviation is used because "it is an estimate of the likely divergence of an actual return from an expected return."32 Although financial theories analyze the risk of investments or risk tolerance of investors using this concept of standard deviation, it is unreasonable to assume the average investor does the same. On PH&N's Investment Profile form (Appendix II, Figure II. 1), risk tolerance is assessed by asking clients to consider how much volatility - or percentage decline in the value of their assets - they would be willing to comfortably accept. Low risk tolerance indicates a client would not be willing to accept more than a 10% decline in portfolio asset value and the client prefers long-term stability in return performance. Medium risk tolerance indicates a client would be willing to accept between a 10% and 15% decline in portfolio asset value. Finally, high © Nicole Marija Franjic 26 tolerance indicates a client would be willing to accept greater than 15% decline in portfolio asset value and can endure considerable portfolio fluctuations to achieve potentially higher long-term returns. In the sample of PH&N assigned and unassigned retail clients, 72.82% are classified as having a medium risk tolerance. The categories of high and low are similarly distributed at 15.76% and 11.42% respectively. In addition, medium risk tolerance is the most common for both males and females; however, the second most common category differs considerably between genders. 7% more males are categorized as having a high risk tolerance compared to females. Conversely, 6% more females are classified as having a low risk tolerance compared to males. There are five possible responses under Investment Knowledge - none, limited, minimal, fair, good, and excellent. Figure 3.2 illustrates the percentage of responses in each area. As can be seen, over half (57.06%) of clients respond they have good FIGURE 3.2 INVESTMENT KNOWLEDGE FOR RETAIL CLIENT SAMPLE Limited Good 57.06% knowledge of investments and investing. Unfortunately, client responses for investment knowledge are as subjective as investment objective and risk tolerance and may be more representative of perceived knowledge than actual knowledge. This becomes evident when examining the breakdown even further - by males and females. Approximately 66% of males categorize their investment knowledge as good whereas only 47% of females answer © Nicole Marija Franjic 27 similarly. Conversely, 35% of females categorize their investment knowledge as minimal whereas only 20% of males answer similarly. In addition, although all responses for excellent investment knowledge are low, males are twice as likely to respond their investment knowledge is excellent than are females. Estimated net worth potential is an important component of any KYC process. If a client is an aggressive investor but does not have the earning power or worth to support potentially significant declines in portfolio value, this aggressiveness can be potentially harmful to the investor. Consequently, by knowing the current and potential worth of a client, a firm is more capable of identifying and preventing potentially destructive behaviour. This net worth potential is assessed through client responses regarding income, net worth, and occupation. Although occupation is not a closed form question, a client's occupation is allocated to one of 16 different categories. These categories are shown in Appendix I, Table 1.3. 3.5 Techn ica l Methodology There are numerous statistical methods intended to describe characteristics of objects or to describe relationships between characteristics and behaviours. Application of several of these statistical methods is undertaken in this research. One group of models uses cluster analysis to identify distinct segments based on trading behaviours and then applies logistic regression models to predict segment membership whereas the seemingly unrelated regression model intends to predict trading behaviour directly. The technical details and formulations of these models shall be subsequently discussed. 3.5.1 Cluster Analysis The purpose of cluster analysis is to divide a population into distinct groups that are as similar as possible internally but as dissimilar as possible from the other groups created. This is accomplished by minimizing the variability within clusters while maximizing the variability between clusters. Computationally, this is achieved by measurement of distances between the characteristics or attributes of different objects. There are predominantly two techniques that can be used to create clusters, hierarchical and non-hierarchical methods. Hierarchical cluster methods group similar objects based on minimization of distance measurements after each iterative step. Once an object or cluster is joined in hierarchical clustering, the object or cluster remains in the same group. Consequently, hierarchical © Nicole Marija Franjic 28 methods track cluster membership and an object cannot become a member of another cluster unless the entire cluster to which it belongs is joined with another object or cluster. In addition, hierarchical methods can identify where the benefit of joining similar clusters or objects diminishes; therefore, the output from hierarchical clustering techniques can suggest the optimal number of clusters or groupings. Nevertheless, since hierarchical clustering records the membership of an object throughout the process, this method tends to be computationally intensive. As a result, it is suggested hierarchical clustering should not be used for analyses with more than a few hundred observations or objects. Although the basic purpose of all types of cluster analysis are the same, to create groups which are similar internally but as dissimilar as possible to other groups, non-hierarchical cluster techniques are computationally very different from hierarchical techniques. One of the most common non-hierarchical methods - and the method used in this research - is K-means clustering. Unlike hierarchical methods, in K-means clustering the user must choose the number of clusters (k) to create. Although clusters are also created through minimization of distance measurements, objects can move freely from one cluster to another throughout the process. Non-hierarchical methods do not track objects but record only the final cluster into which an object is assigned. Since the K-means method does not track cluster membership, this technique is computationally less intensive and more suited for analyses with a larger number of objects or observations. Another method providing useful information regarding similarities between objects is multidimensional scaling. This technique is primarily used to display multivariate data by minimizing the number of graphical dimensions so similarities can be identified and interpreted. This technique only displays individual objects to assist the researcher in identifying similar groups; multidimensional scaling does not create similar groups. Unfortunately, for very large data sets it is unlikely efficient groupings could be done through visual inspection. Refer to Johnson and Wichern (1999) for a more detailed discussion of multidimensional scaling and how it relates to cluster analysis. Of the possible models discussed, the K-means clustering method is chosen for two reasons. First, although the hierarchical technique would have been preferable due to the more systematic method for creating the optimal number of clusters, the sample of 3,037 PH&N clients in this analysis makes the hierarchical method infeasible. In addition, © Nicole Marija Franjic 29 multidimensional scaling is inappropriate for similar reasons and because creating similar groups is the desired outcome, not merely displaying information. The first step in cluster analysis is determining the objects to cluster and the attributes on which similarity and dissimilarity will be measured. Second, several scenarios are tested - by varying the number of (k) clusters created - to determine the number of clusters that appears to be most representative of the population. The most common distance measure, and the one used in this analysis, is Euclidean distance. Euclidean distance for two objects with n attributes, where x and y are vectors, is J(x,y) = V (x-y) ' (x-y) 1 ' ; where x = [xi, x2,...,xn]' and y = [y 1 # y 2 , . . . , y n ] ' Cluster analysis for this study uses SPSS statistical software. SPSS's K-means clustering algorithm uses Euclidean distance to determine the distance an object's attributes are from the cluster mean, which subsequently determines the object's membership in or removal from a cluster. If an object is added to or removed from a cluster, cluster means are recalculated and the process iterates until objects do not move between clusters from iteration n-1 to iteration n. In addition, the K-means algorithm in SPSS provides the option of computing an ANOVA table; however, use of ANOVA in K-means clustering is not for statistical purposes. Instead, the F ratios that SPSS computes are to provide insight into the relative importance of variables. As stated in the SPSS manual, "ANOVA tests...are not taken seriously as actual statistical tests since clusters are formed that maximally separate groups, but as indicators of which cluster variables are most important in the formation of clusters."33 The outcome of a cluster analysis should always be analyzed for validity. Unfortunately, because cluster analysis can be very subjective, validity techniques are also subjective. One of the key validation techniques is to compare the number of objects in the final clusters against initial expectations of final cluster membership. Another technique is to examine the final cluster means: Are these means different from each other and do they make sense in the context of the objects being clustered? In K-means clustering, these questions are often best answered by comparing the outcomes of different k cluster analyses to each other. Another validation technique is to present the final clusters to the © Nicole Marija Franjic 30 project's sponsors at PH&N and thus, allowing PH&N to determine cluster validity. For further discussion regarding validity and cluster analysis, refer to Romesburg (1990). 3.5.2 Logistic Regression After the clusters are determined to be sufficiently representative of PH&N retail clients, logistic regression is used to predict a client's cluster membership. Cluster membership is used as a proxy for future behaviour of clients because the clusters are created using client transaction, performance, and market value information, using the cluster analysis methods described in the previous section. In this analysis, logistic regression models are computed using SPSS statistical software. Another technique considered for predicting cluster membership is discriminant analysis; however the main restrictions of discriminant analysis are that the underlying predictor data must follow a normal distribution and have equal covariance matrices. In addition, discriminant analysis assumes a linear relationship exists and would attempt to find the linear combination of objects that belong to a cluster and objects that do not. Logistic regression does not have such restrictive assumptions. Logistic regression is based on the idea that the likelihood of an object belonging to a particular cluster falls on a continuum; a client has a probability of belonging to one cluster or another. Although use of a large sample in this analysis would most likely not impede the ability of using discriminant analysis, logistic regression is chosen because there are less restrictions and it is easier to interpret the output. For more on linear regression and discriminant analysis, refer to Kleinbaum et al. (1998) and Wichern and Johnson (1998) respectively. In this research, dichotomous and polytomous logistic models are developed. In the dichotomous models, the outcome Y=l signifies the client belongs to a specific cluster whereas the outcome Y=0 signifies the client does not belong to the cluster. Dichotomous models are applied to each of the k final clusters. In the polytomous model, the outcome variable, Y, pertains to the client's relevant cluster - a categorical variable. Dichotomous Logistic Regression Dichotomous logistic regression uses probability to assign an observation to the binary outcomes of 0 or 1. The probability of the outcome Y=l is expressed as P(Y=1) whereas the probability of the outcome Y=0 is P(Y=0) = [1 - P(Y=1)]. In a logistic © Nicole Marija Franjic 31 regression model these probabilities are often expressed in terms of odds or logits. The odds that Y=l is shown as Odds{Y = l) = i ^ l ^ ) (3.2) The logit form of the probability is the basis for analyzing the logistic regression model. The logit of Y is defined as the natural logarithm of the odds and is represented as logit [P(Y = l)] = In P(Y = l) 1 - P(Y = 1) (3.3) Nevertheless, a regression model expresses a relationship between the independent and dependent variables; therefore, the logit is transformed to a linear expression, which is similar to the equation for linear regression, by logit[P(7 = l)] = a+ X,. (3.4) 1=1 where a = model intercept, Pi = regression coefficients, and Xj = independent variables. Since the equation is now expressed in terms of the dependent and independent variables, conversion of the logit equation back to odds is done by exponentiation. From odds, the equation can finally be converted back to probability, with the resulting equation being e i=1 1 P(7 = l) = - — : — = l - — l + e i = l l + e (3-5) Since logit [P(Y)] varies from negative infinity to positive infinity, "the probabilities estimated for the probability form of the model [Equation 3.5] will not be less than zero or greater than l." 3 4 In addition, Menard (1995) states that "because the linear form of the model [Equation 3.4] has infinitely large or small values of the dependent variable, OLS cannot be used to estimate the parameters",35 the a and pi's. As a result, maximum likelihood is used to estimate the parameters of the model. Since the dependent variables, the Yi's, in a logistic regression are binary, they follow a Bernoulli (point-binomial) distribution. If the Yi's are independent, the likelihood function is calculated as the product © Nicole Marija Franjic 32 of the marginal distributions of the individual Yi's. As formulated in Kleinbaum et al. (1998), if Yj occurs with probability 0j, then the likelihood function is Z(Y; P) = flPW ;/?,) = n(/J,.) * (1 - A ) ( 3 . 6 ) /=i i=i where Y = [Y l f Y 2 , Y n] and (3 = [Pi, p2, pn]. Kleinbaum et al. (1998) state, if L(Y; p) is a likelihood function with parameters 8 = [pi, p2,..., pn], "[L(Y; p)] can informally be treated as the probability distribution of the multivariate variable Y." 3 5 To obtain the maximum likelihood estimate of p, L(Y;P) needs to be maximized; however, it is computationally easier to maximize In L(Y;P) than L(Y;p) directly. The parameter estimates (^) are then calculated by solving the set of simultaneous equations by "setting the partial derivative of [In L(Y;P)] with respect to each [Pi] equal to zero."37 Kleinbaum et al. (1998) express the solution to these equations in vector form by — — [ l n Z (Y ; P ) ] = 0 where i = l,...,n (3.7) 5 (A) Unfortunately, these equations are generally complex and require iterative processes to solve; therefore, they are often solved using statistical computer algorithms. In logistic regression, one of the most common tests of significance for independent variables is done through calculation and analysis of the Wald statistic. Statistical significance is important in regression analyses because it is "used to evaluate the... contribution of an independent variable to the explanation of a dependent variable."38 The Wald statistic can be calculated as standard error of bk (3.8) and follows a normal distribution. Using Equation 3.8, interpretation of the Wald statistic is similar to interpretation of the t-statistic for independent variables used in linear regression. As Menard (1995) states, a disadvantage of using the Wald statistic occurs when bk is large because there is a tendency for a Type II error to occur. In linear regression, the independent variables are selected by minimizing the SSE measure - or sum of squared errors. Independent variables that are not significant where the SSE is minimized should not be included in the model. In logistic regression, the log-likelihood measure is similar to the SSE in linear regression. The log-likelihood for logistic © Nicole Marija Franjic 33 regression is generally multiplied by -2 because -2*log-likelihood approximately follows a chi-square distribution. In addition, log-likelihood is negative but when multiplied by -2, it is positive; therefore, as -2*log-likelihood increases, the model becomes poorer at predicting outcomes, Yj's. Hosmer and Lemeshow describe this concept of -2*log-likelihood for logistic regression models as the deviance chi-square. As Menard (1995) illustrates, if there are N total cases where Y=l for n cases and Y=0 for m cases and n+m=N, then the deviance chi-square is D = -2 * {n \n[P(Y = 1)] + (N-n) ln[l - P(Y = 1)]} D = -2*{n \n[P(Y = 1)] + m ln[P(7 = 0)]} (3-9) Logistic regression also provides a measure that is analogous to the F ratio in linear regression and is calculated by subtracting the deviance chi-square with all independent variables included ( D M ) from the deviance chi-square with no independent variables included (D i ) . Hosmer and Lemeshow refer to this as G whereas Menard refers to this measure as the model chi-square. G, or the model chi-square, is calculated as (D i - D M ) by Menard (1995) or alternatively, Maximum likelihood for model with no predictors G = -2 In (3.10) Maximum likelihood for full model with predictors Other logistic regression goodness of fit measures are discussed in Menard (1995). Hosmer and Lemeshow have also developed a measure analogous to the R2 in linear regression models, referred to as R2L. This measure attempts to explain how much the full model with predictors improves the goodness of fit compared to the initial model with no predictors. R2L also ranges between 0 and 1. Calculation of R2L is shown in equation 3.11. D 2 Model Chi - Square (G) . .. KL = ; ; Deviance Chi - Square for model with no predictors (D,) Other measures of association are discussed in Menard (1995), such as the pseudo-R2. In addition, logistic regression models require a probability cutoff level above which an observation would be classified as Y=l and below which an observation would be classified as Y=0. Using this cutoff, the logistic regression model can then calculate the percentage of cases correctly classified. The percentage correctly classified is referred to by Urbanovich (1999) as the Correct Classification Rate (CCR). Additional references to the CCR are discussed in Urbanovich (1999). © Nicole Marija Franjic 34 Multicollinearity, when one or more independent variables are correlated, will cause the standard errors of independent variables to become large and lead to regression coefficients that are statistically insignificant. To verify the presence of little or no multicollinearity in a logistic regression, analysis of the correlation between independent variables and the R-squared values for several models is performed. The dependent variable in the tests for multicollinearity in this analysis is the cluster to which a client is assigned. In addition, the logistic regression models include ten independent variables. These variables are Year Joined, Gender, Investment Knowledge, Investment Objective, Risk Tolerance, Income range, Net Worth range, Initial Market Value, and Age. Based on these ten independent variables 45 correlation relationships are analyzed. There are only 7 pairs of variables that have a correlation with an absolute value greater than 0.3. Of these correlation relationships, the largest correlation is 0.48 and the mean correlation is 0.03. In addition, Table 3.1 shows the R2 values for the full model - which includes all ten independent variables listed above - and the R2 values for the individual models with each of the independent variables. In all cases, the R2 values are very low. Consequently, the correlation and R2 tests for multicollinearity indicate multicollinearity is not a significant problem in the logistic regression models in this analysis. — - — .TABLE 3.1 R TEST FOR MULTIC< 3 L U N E A i S « MODEL R 2 Full Year Joined Gender Occupation Investment Knowledge Investment Objective Risk Tolerance Income Worth Initial Market Value Age 0.0325 0.0070 0.0014 0.0087 0.0060 0.0000 0.0005 0.0023 0.0065 0.0016 0.0031 In addition, two further problems related to multicollinearity are complete separation and zero cells. With complete separation, the dependent variable is perfectly predicted. No model is perfect; therefore, this indicates model design problems. In addition, since perfect prediction rarely occurs in practical applications, this may indicate problems in the underlying data. Related to this is quasicomplete separation, where separation is less than complete. Regardless of the extent, separation tends to produce regression coefficients and © Nicole Marija Franjic 35 standard errors that are large. Zero cells can also create problems in a logistic regression. When there are nominal variables in a logistic regression, zero cells indicate an entire group of observations is assigned to one indicator category, 0 or 1. Although the overall model may not be affected by zero cell counts, they can create high standard errors, which may result in one of the independent variable indicators becoming statistically insignificant. Polytomous Logistic Regression A polytomous logistic regression model - also known as a multinomial logistic regression - is one that includes an outcome variable having more than two categories; the outcomes are nominal or ordinal instead of binary. Although a dichotomous model can be extended to become a polytomous model for both nominal and ordinal variables, only extension with nominal variables shall be discussed. The formulation for a nominal polytomous model is similar to creation of indicator variables in a linear regression model. For complete details regarding the formulation presented, refer to Menard (1995). Similar to a dichotomous logistic regression, in a polytomous logistic regression two outcome variables are created. The difference lies in the fact the first variable indicates membership in a reference category and the second variable indicates membership in any category besides the reference category. Let q0 denote the reference category and q denote all other categories. If there are Q total categories, following the method for creating indicator variables, Q-l equations must be calculated. Then, as Menard (1995) illustrates, the equation for all categories other than the reference category would be In addition, two probability equations must also be created - one for the reference category and one for all other categories. These equations respectively are fq(Xl,...,Xn) = e for q = l,..., Q - l (3.12) and for the reference category, q0l the equation would be fo(X1,X2,...,Xn) -1 (3.13) P(Y = q0\Xlt...,XH) = 1 for q = l,..., Q - l (3.14) © Nicole Marija Franjic 36 where q 0 = Q or q0 = 0, P(Y = q\Xl,...,XH) = 6 "' . for q = l,..., Q - 1 These equations as well as further descriptions and examples of polytomous (multinomial) logistic regression and its applications are illustrated in Menard (1995). 3.5.3 Seemingly Unrelated Regression (SUR) Although ordinary least squares (OLS) regression has limited application to predicting cluster membership, OLS can provide useful insight to the relationships between trading behaviour and portfolio performance directly. Unfortunately, the assumptions of OLS regression can be easily violated when solving a system of equations that may be related. In this analysis, the dependent variables of the equations are transactions, total funds held, and portfolio returns. While these equations may seem unrelated, behavioural theorists - such as Odean - have provided evidence of how behaviour affects portfolio performance. As a result, an econometric technique known as seemingly unrelated regression (SUR) can be applied, which compensates for the possibility that the error terms between a system of equations may be correlated. In 1962 Zellner proposed the SUR model, which was based on the OLS model. SUR computes the model's estimated parameters using a two-step generalized least squares estimator (GLS). The first step involves a a system of Nequations in the form, Y2 0 0 x2 0 . 0 . .. 0 " .. 0 'fix ' s2 = 0 0 x3 . .. 0 + 0 0 0 . •• xN_ PN. .SN. (3.16) where the Yj's are the dependent outcomes, the Xj's are the independent variables, the Pi's are the parameters, and the si's are the error terms. This can also be expressed in matrix © Nicole Marija Franjic 37 form as Y = X p + e where Y, p, and s are Nxl vectors and X is an NxM matrix. Additionally, if the error covariance matrix of this system is 11 er. 12 IN Z = E{e'e) = a 21 cr 22 cr cr a a (3.17) m N2 NN where a represents the covariance between equations i and j, then the second step is to compute the GLS estimator of the model's parameters, given by where <8> indicates a kronecker product of E"1 and I. This means if XT1 is an NxN matrix and I is an MxM matrix, then I"1 ® I is an (NM)x(NM) matrix.39 Unfortunately, the covariance matrix is often unknown and must be estimated, known as Z , prior to application of the GLS estimator. To estimate the covariance matrix, individual OLS regressions for each equation in the system are run and the residuals are computed for each equation. From the residuals, the estimated covariance can be computed using the formula in Equation 3.19. a is the estimated covariance of the residuals between equations / and j, ei and ej are the estimated residuals from the OLS regression for each of equations /'and j, and N is the total number of observations. Using only the IN total observations in the covariance estimation may be misleading; different equations in the system may have a different number of independent variables. Software packages - such as SAS - have algorithms that can compute the estimated covariance matrix, Z , and feed this matrix back into the SUR model to compute the GLS estimator. Due to the system of multiple equations, effective use of SUR occurs primarily with large samples. In addition, although many of the OLS assumptions still hold for SUR estimation, SUR requires two additional criteria - one of which must hold for SUR to be useful instead of simple application of OLS regression. First, the covariance between p = [ X ' ( S _ 1 ® I ) X ] " ' X ' ( S " 1 ® I)Y (3.18) (3.19) © Nicole Marija Franjic 38 equations must be different than zero. Second, the independent variables between equations must be different. If neither of these hold, SUR is equivalent to OLS regression. For further discussion of seemingly unrelated regression and additional models for a system of equations there are several web sites40 that can be consulted. In addition, the online SAS manual provides valuable information regarding computer application of these models. Numerous econometric texts also discuss the mathematics and economic applications of SUR. © Nicole Marija Franjic 39 4.0 RESULTS FROM SEGMENTATION AND PREDICTIVE MODELS Using the data and models discussed in the previous chapter, four different models are developed. The first model uses cluster analysis to segment clients based on trading behaviour and portfolio performance. Next, several dichotomous logistic regression models and polytomous logistic regression models are used to determine if cluster membership can be predicted. Cluster membership is important to predict because it can act as a proxy for future behaviour and it can also suggest what services and resources are most needed by the client. Finally, a seemingly unrelated regression model (SUR) is used to determine whether trading behaviour and performance can be predicted directly through client transactional and performance data. 4.1 Cluster Analysis The cluster analysis uses all transaction and performance data as well as change in market value during the first year after joining PH&N. The only trading data not included is the market value at the beginning and end of the first year of trading. Once the optimal number of clusters is determined, each cluster is analyzed further - using cross-tabs and ANOVA - to compare KYC and demographic differences between clusters. In a for-profit business environment, companies are often interested in determining whether their clients behave differently or exhibit distinct preferences towards their products or services. Knowing whether different behaviours or preferences exist enables companies to better serve their clients and increase revenues by creating products and services that specifically target the groups of clients most likely to respond favourably. As a result, such companies rarely undertake cluster analysis without the intention of using the results in a marketing strategy or new service offer. Nevertheless, the number of clusters created is as important as cluster characteristics. Concluding there is only one cluster - that is, all clients behave similarly - would not warrant expenditure on a marketing campaign. Conversely, having too many clusters would also be inefficient because marketing expenditures would be spread too thin or numerous services would need to be created, which may be unprofitable^ The primary reason for cluster analysis on retail clients at PH&N is to determine whether there are distinct groups of clients within PH&N who have different transaction activity, portfolio performance, and market values with PH&N.. If the cluster analysis reveals © Nicole Marija Franjic 40 there are differences between clients in these areas - trading, performance, and worth with PH&N - determining the number of clusters to create is also necessary. Although not directly indicated, it is implicitly assumed the number of clusters to create for PH&N retail clients would be between four and six. This assumption is based on segmentation studies previously investigated. The cluster analysis is performed on standardized data. Transaction data are simple counts, performance data are in percentages, and market values are in dollars. Consequently, standardization of each variable was done by converting each observation within each variable to a z-score; therefore, each variable has a mean of 0 and a standard deviation of 1. Once standardization is done, k-means clustering is used because the sample size is too large to use hierarchical clustering techniques. Using the k-means method, cluster analyses for 4 < k < 8 clusters are run, including more transaction, performance, and market value variables at each iteration. Inclusion or removal of variables is determined by relative F-statistic magnitudes, as discussed in section 3.5.1. After standardization and F-tests, all transaction and performance variables are included in the cluster analysis; however, which market value variables - if any - are still unclear. Consequently, three different cluster analyses are examined. The first analysis does not include market value information. The second only includes the market value at the end of the one-year period. Finally, the third analysis includes only the change in market value from the initial deposit amount to the market value at the end of the one-year period. Although change in market value may be considered a proxy for performance, change in market value encompasses more than performance. Performance is calculated net of cash inflows or outflows; however, change in market value includes cash flows as well as increases or decreases in market value due to positive or negative performance. Each of these three types of analysis are used to create k-means clusters where 4 < k < 8. After analyzing the three different options available, change in market value is the most practical variable to represent market value information in the model, for the following reasons. First, inclusion of some measure of market value in the clustering would provide more insight into client behaviour than mere transactions alone. Ending market value can only represent a client's worth with PH&N at a given time; however, change in market value can be an indicator for client perception of PH&N. If the change in market value is © Nicole Marija Franjic 41 negative this may indicate a negative perception, whereas if change in market value is positive this may indicate confidence in PH&N and a desire to continue investing. In addition, change in market value can attribute a monetary value to a client's portfolio performance. Nevertheless, it bears mentioning that of the 15 variables that are used to create the clusters, the relative F-statistic is lowest for change in market value. The cluster options for 4 < k < 8 when change in market value is used are shown in Table 4.1. TABLE 4.1 CLUSTER SIZES AS A FUNCTION OF THE NUMBER OF CLUSTERS i 4 Clusters 5 Clusters 6 Clusters 7 Clusters 8 Clusters 83 443 1,169 2,238 12 2,467 80 1,438 12 1,165 475 59 156 88 1,438 12 12 12 2 170 2,443 91 133 1 171 563 93 1 2 156 Of the 4 < k < 8 choices, with change in market value included in the analysis, k= 6 clusters is chosen to be representative of PH&N retail clients for two main reasons. First, for k = 4, 5, and 7 clusters, there is always one large cluster that accounts for over 70% of clients in the sample. This is an unacceptably high percentage of membership in only one cluster. Although the smaller clusters may exhibit behaviour that PH&N would like to address, the large cluster is overwhelming and makes it unrealistic for PH&N to devote any corporate resources to the needs of the smaller clusters. Second, although the structure of k= 8 clusters is similar to k= 6 clusters, two of the eight clusters have two members or less. These clusters are also too small to be substantial and it would be unreasonable to assume a marketing campaign or service offer would be targeted to such a small segment. Despite the choice of 6 clusters, cluster 4 is still too small to be viable; therefore, the trading behaviour of cluster 4 is compared against the other five clusters. Cluster 4 and cluster 5 exhibit the most similar patterns across the majority of variables; therefore, cluster 4 and cluster 5 are merged to create a total of k= 5 clusters. The pattern of means using standardized variables and the labels for each of the five clusters is illustrated in Figure 4.1. In addition, Table 4.2 displays the non-standardized trading behaviour and performance data for each cluster. © Nicole Marija Franjic 42 FIGURE 4.1 PATTERN FOR STANDARDIZED CLUSTER MEANS ACROSS VARIABLES TABLE 4.2 TRADING BEHAVIOUR A N D PERFORMANCE OF CLUSTERS, NON-STANDARDIZED Buy-and- Loss Market Overconfident/ hold Averse Timer DCA Novice Overall Total Funds 3.59 2.27 6.15 5.82 4.82 3.24 Number of Trade Days 3.53 2.52 8.00 14.18 12.27 4.14 Total Transactions 7.68 4.29 22.99 51.85 40.85 10.23 Total Buys 5.67 3.11 8.53 8.15 35.79 6.38 Total Sells 0.45 0.40 1.41 9.85 2.07 0.88 Total Switches 1.45 0.70 11.75 33.28 2.90 2.79 Total Transfers 0.11 0.08 1.31 0.58 0.09 0.17 Manual 6.32 3.62 19.45 9.83 19.83 6.59 Automatic 1.36 0.67 3.53 42.03 21.02 3.63 DCA Transactions1 0.27 0.17 1.05 30.21 0.92 1.31 Manual Switches 1.18 0.53 10.70 3.09 1.97 1.47 Tax Switches2 0.631 0.247 3.538 0.922 0.965 0.627 Estimated Return 18.14% 4.84% 9.94% 8.45% 10.88% 10.68% Normalized Return 10.46% -6.02% 0.92% -0.03% 1.61% 1.31% Sze of duster 1,169 1,438 156 103 171 3,037 ! Percentage of Total 38.49% 47.35% 5.14% 3.39% 5.63% 100.00% 1 DCA Transactions are a subset of the "Switch" transaction type and the "Automatic" transaction origin 2 Tax Switches relate specifically to "Manual Switches" that occur in December and January. © Nicole Marija Franjic 43 As can be seen in Figure 4.1, certain patterns seem to emerge in the clusters. These patterns can be directly applied to behavioural concepts discussed in Chapter 2. Cluster 1 is labeled the "Buy-and-hold" cluster and includes 1,169 clients representing 38.5% of the total sample. The "Buy-and-hold" cluster has z scores below average (zero) in almost all categories - except return, change in market value, and total number of funds. As seen in Table 4.2, the number of buys outnumber switches by almost four to one and sells by almost thirteen to one; however, these investors switch approximately once per year, which indicates portfolio re-balancing. Although the number of buys for this cluster are not as high as in some other clusters, moderation in buys in addition to the approximate one switch per year - implying portfolio re-balancing - suggests buy-and-hold tendencies. The "Buy-and-hold" cluster also exhibits the highest returns and studies have shown buy-and-hold investors generally have among the highest performance, particularly because of their ability to maintain long-term strategies during periods of short-term fluctuation. Cluster 2 is labeled "Loss Averse" and contains 1,438 clients representing approximately 47.4% of the total sample. Unfortunately, the z-score graphical representation in Figure 4.1 does not fully describe the trading behaviour of investors in the "Loss Averse" cluster; Table 4.2 contributes additional information. Figure 4.1 shows the "Loss Averse" cluster is consistently below average on all variables, and lowest on returns. In addition, it appears the number of buys and sells are approximately equal; however, this is only compared to the standardized average. From Table 4.2 it is clear the mean number of buys exceed the mean number of sells by approximately eight to one. Nevertheless, the "Loss Averse" cluster holds the fewest number of funds, has the fewest number of transactions - of which buys predominate - and has the lowest returns. Based on theories discussed in section, Cluster 2 seems to exhibit behaviour that indicates loss aversion. These investors do not take advantage of suitable market opportunities - by selling funds that may be performing poorly and re-balancing their portfolios to the appropriate asset mix - which is reflected in the poor returns of this cluster. Cluster 3 is labeled "Market Timer" and contains 156 clients representing 5.1% of the total sample. The "Market Timer" cluster has the highest standardized manual switches and potentially tax-related switches, but is only slightly above average on buys and sells. As seen in Table 4.2, manual switches outnumber buys 1.25:1 and outnumber sells 7.6:1. In © Nicole Marija Franjic 44 addition, both standardized and non-standardized annualized returns are slightly below average. As a result, the trading behaviour indicates market timing; however, the mediocre returns suggest short-term fluctuations or inappropriate market timing strategies. The fourth cluster is labeled "Overconfident/DCA" and contains 103 clients representing 3.4% of the total sample. The "Overconfident/DCA" cluster has the highest number of transactions, of which 58% are DCA transactions. As described in section 3.2, DCA (Dollar Cost Averaging) transactions are used when investors are switching between the same funds regularly. Investors switching from money market funds to equity or bond funds - in an effort to more slowly invest in more aggressive funds and achieve a desired investment strategy or asset mix - often use this transaction type. Nonetheless, this cluster also has the highest number of sells and is considerably higher than average on number of funds held, number of trading days, and manual switches. As well, both standardized and non-standardized mean returns are lower than their respective averages. Consequently, there seem to be two different - but potentially related - behaviours being exhibited by this group. First, these investors are trading frequently and have lower than average returns; therefore, based on research by Odean, this suggests overconfidence. Nevertheless, the unusually high number of DCA switches can be indicative of several different behaviours including risk aversion, market timing, or overconfidence. First, DCA transactions at PH&N are considered similar to buy transactions if a client is using DCA transactions to switch from money market to bond or equity funds. PH&N views clients who use DCA transactions in this manner as risk averse because DCA transactions allow these investors to enter equity and bond markets slowly. Regardless, clients can also use DCA transactions to switch between equity and bond funds on a regular basis. This latter behaviour is indicative of market timing or overconfidence if done excessively. Since the types of funds that clients are switching between are not analyzed in this research, the frequent non-DCA and DCA transactions result in the dual label of "Overconfident/DCA" for this cluster. Finally, cluster 5 is labeled "Novice" and contains 171 clients accounting for 5.6% of the total sample. The "Novice" cluster has the highest buy transactions but is average on other transactions. Nonetheless, the average number of trade days is approximately twelve. This suggests there are numerous trades on the same day, but only about once per month. There is also an approximately equal division between manual and automatic transactions. As well, return is average and only slightly higher than the overall normalized © Nicole Marija Franjic 45 mean return for all clients. An integrated view of all transaction types and change in market value suggests this group is not comfortable or experienced with investing. The "Buy-and-hold" and "Loss Averse" clusters appear to almost consistently follow opposite patterns across variables; as the z-score for one variable in one cluster increases, a corresponding decrease in the z-score occurs for the same variable in the other cluster. Although not as apparent, the "Market Timer" and "Novice" clusters seem to follow similar opposite patterns. Another interesting outcome resulting from this analysis is the distribution of ending market value between the clusters. Although ending market value is not used to create the clusters, there are considerable differences in the mean ending market values across clusters. The "Market Timer" and "Overconfident/DCA" clusters have the highest ending market values respectively while the "Loss Averse" cluster has the lowest ending market value. The "Novice" and "Buy-and-hold" clusters have ending market values that are very similar to the overall ending market value for all clients. Based on the findings from the cluster analysis of PH&N clients, it is clear there are several different segments within the assigned and unassigned retail client base exhibiting different trading behaviours. These behaviours range from infrequent to excessive trading with portfolio performance that generally reflects the skill - or lack thereof - as well as the level of loss or risk aversion of PH&N retail investors. The proceeding section shall analyze KYC information of clients within each of these clusters to examine whether differences in investor personality may be potential predictors of future behaviour. 4.2 ANOVA and Cross-tab Analysis of Clusters After creation and labeling of clusters, ANOVA and cross-tabulation of variables are analyzed based on KYC and demographic information. Since these variables are not included in forming the clusters, they are used to determine if personality or demographic differences exist between the groups, independent of variables used to form the clusters. The Pearson Chi-Square values, ANOVA F ratios, and the significance for each of these predictor variables are shown in Table 4.3. As can be seen, it appears only gender is not significant at the a = 0.05 level. This indicates there are significant differences between clusters on most of the KYC and demographic variables, which are later used to predict cluster membership in the logistic regression models. Occupation, Investment Knowledge, and Risk Tolerance will © Nicole Marija Franjic 46 subsequently be analyzed to demonstrate the different investment personalities present in the clusters. For these variables, the percentage of clients in a particular nominal category are examined and compared across clusters. It should be noted comparisons are by observation and not statistical testing of significance. In addition, comparison of the most or least common category overall for each of the variables is not analyzed because each variable contains at least one category that contains a disproportionate number of clients. For example, the retired occupation category contains 32.3% of all clients, 57% of clients categorize themselves as having good investment knowledge, and 73% of clients have medium risk tolerance. TABLE 4.3 RESULTS OF CROSS-TABS AND ANOVA FOR PREDICTORS ON CLUSTERS Predictor Variable Continuous or Nominal Pearson Chi-Square or ANOVA F value p-value Significant (ata=0.05) ? Knowledge Nominal 35.370 0.018 Yes Objective Nominal 63.249 0.000 Yes Risk Tolerance Nominal 37.263 0.000 Yes Income Nominal 35.660 0.003 Yes Worth Nominal 69.669 0.000 Yes Gender Nominal 6.098 0.192 No Occupation Nominal 151.975 0.000 Yes Age Discrete 20.197 0.000 Yes Initial Market Value Continuous 17.263 0.000 Yes Year Joined Discrete 5.638 0.000 Yes The results of the cross-tab analysis for highest and lowest comparative Occupations across clusters are presented in Tables 4.4 and 4.5 respectively. Of the sixteen categories, only Broker does not appear in either table because the total number of brokers is small and not every cluster has an investor in the Broker occupation. As can be seen, there are distinct occupational differences between the five clusters. TABLE 4.4 OCCUPATIONS WITH HIGHEST COMPARATIVE PERCENTAGE BETWEEN CLUSTERS Ouster Name Occupations with Highest Comparative Percentages Buy-and-hold Loss Averse Market Timer O e^rconfidenryrXA Novice Engineer, labourer homemaker, real estate professional, retired investors Business Analyst, Teacher Chartered Accountant, executive, Lawyer Administrator, computer professional, medical professional, sales professional, self-employed investors © Nicole Marija Franjic 47 TABLE 4.5 OCCUPATIONS WITH LOWEST COMPARATIVE PERCENTAGE BETWEEN CLUSTERS Cluster Name Occupations with Lowest Comparative Percentages Buy-and-hold Loss Averse Market Timer Overconfident/DCA Novice real estate professional Administrator, sales professional, self-employed investors Engineer, homemaker, Lawyer, medical professional Business Analyst, computer professional, labourer, Teacher Chartered Accountant, executive, retired investors Analysis of the investment knowledge variable also presents some interesting differences between clusters. The results of the cross-tabulation for investment knowledge within clusters are shown in Table 4.6. The "Novice" cluster has the highest comparative percentage of clients who categorize themselves as having minimal investment knowledge. Conversely, the "Market Timer" cluster has the highest comparative percentage of clients who categorize themselves as having excellent investment knowledge. Furthermore, the "Buy-and-hold" and "Loss Averse" clusters have the highest comparative percentages in the fair and good investment knowledge categories. These results are only somewhat consistent with the theories related to cognitive dissonance. While the "Market Timer" cluster has the highest comparative percentage classified as having excellent investment knowledge, the TABLE 4 .6 COMPARATIVE PERCENTAGE OF CLIENTS WITHIN EACH CLUSTER - INVESTMENT KNOWLEDGE Investment Knowledge "Buy-and- "Loss "Market "Overconfident/ Type hold" Averse" Timer" DCA" "Novice" TOTAL None 2.2% 2.0% 1.9% 2.9% 1.8% 2.1% Minimal 26.7% 25.9% 28.2% 36.9% 40.4% 27.5% Limited 2.1% 2.8% 0.6% 1.0% 2.9% 2.3% Fair 7.2% 7.2% 5.8% 2.9% 2.9% 6.8% Good 58.3% 57.4% 56.4% 53.4% 48.5% 57.0% Excellent 3.6% 4.7% 7.1% 2.9% 3.5% 4.2% TOTAL 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% "Overconfident/DCA" cluster surprisingly has the comparatively lowest percentage in this category. Based on theories of cognitive dissonance, these two clusters would be expected to have similar comparative percentages in the excellent investment knowledge category. The differences between clusters are somewhat less apparent for the risk tolerance variable. Since 73% of the total client sample is categorized as having medium risk tolerance, the comparative differences between clusters are less evident. Nevertheless, some clusters appear to exhibit comparatively higher percentages in one category. The © Nicole Marija Franjic 48 "Loss Averse" cluster has the highest comparative percentage of clients who categorize themselves as having low risk tolerance. Conversely, the "Buy-and-hold" cluster has the highest comparative percentage of people who categorize themselves as having high risk tolerance. Although medium risk tolerance is by far the most common, clients in the "Market Timer" cluster have the highest comparative percentage for this category. The results of the cross-tabulation for risk tolerance within clusters are illustrated in Table 4.7. T A B l l W ^ ^ Risk Tolerance Type "Buy-and-hold" "Loss Averse" "Market Timer" "Overconfident/ DCA" "Novice" T O T A L Low Medium High 9.0% 73.1% 17.9% 14.8% 71.1% 14.0% 6.4% 79.5% 14.1% 6.8% 76.7% 16.5% 7.0% 76.0% 17.0% 11.4% 72.8% 15.8% TOTAL 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% Despite examination of only three of the KYC variables, the other variables from the cross-tabulation and ANOVA analyses provide further useful information. The "Novice" cluster has the lowest mean age, they have the lowest initial amount deposited with PH&N, and they have the highest comparative percentage of clients who categorize themselves as having a growth investment objective. Although gender is not significant in the cross-tabulation, the "Novice" cluster is the only cluster exhibiting a noticeable difference in the proportion of males and females. Specifically, the "Novice" cluster contains 43% males and 57% females. Additionally, the "Loss Averse" cluster has the highest comparative percentage of people who categorize themselves as having an income investment objective and the "Overconfident/DCA" cluster has the highest mean initial amount deposited with PH&N. The analysis presented here seems to suggest KYC, demographics, and initial market value have a noticeable relationship with cluster attributes. This indicates investor demographics, personality, and philosophy influence trading behaviour. In particular, the "Buy-and-hold" cluster seems to be comprised of a comparatively high proportion of clients with fair and good investment knowledge and high risk tolerance while the "Loss Averse" cluster has a proportionately higher percentage of clients with fair investment knowledge, income investment objective, and low risk tolerance. The "Market Timer" cluster has a higher comparative proportion of clients who categorize themselves as having excellent investment knowledge and medium risk tolerance. In addition, the "Overconfident/DCA" © Nicole Marija Franjic 49 cluster has the highest mean amount initially invested with PH&N as well as a higher proportion of clients who are in professional occupations. Finally, the "Novice" cluster is the youngest and has the lowest mean amount initially deposited with PH&N. The "Novice" cluster also has the highest proportion of clients who categorize themselves as having minimal investment knowledge and a growth investment objective. Unfortunately, cluster analysis can only illustrate the different behaviours and attributes but it cannot explain w/n/ these investors trade the way they do. In addition, cluster analysis does not present any method of predicting in which cluster a new client may belong. Nonetheless, analysis of clusters provides evidence of behavioural differences based on transactions activity, portfolio performance, and market value. As well, comparison of KYC and demographic information across clusters seems to suggest investor personality may provide insight into predicting future trading behaviour. Whether investment personality - represented by KYC information - and demographics can predict cluster membership shall be examined in the next section on logistic regression. Similarly, investment personality and demographics are used to predict trading behaviour and performance in the section on seemingly unrelated regression. 4.3 Logistic Regression In the logistic regression analysis, the predictor variables include gender, age, year joined, initial deposit with PH&N upon account opening, and KYC information - investment personality and estimated net worth potential. In the dichotomous logistic regression models, the dependent variable is binary where 1 indicates the client belongs to the cluster and 0 indicates the client does not belong to the cluster. For example, when performing a dichotomous regression on the "Buy-and-hold" cluster, if a client is a member of the "Buy-and-hold" cluster the value of the dependent variable for this client would be 1. In contrast, if the client is not a member of the "Buy-and-hold" cluster, the value of the dependent variable for this client would be 0. This dichotomous analysis is performed for all k=5 clusters. Conversely, for the polytomous models the dependent variables are the categorical values pertaining to the cluster in which a client is a member. 4.3.1 Dichotomous Logistic Regression Dichotomous regression analyses are performed for each cluster separately. All model chi-square values are statistically significant for each of the five clusters, thus © Nicole Marija Franjic 50 indicating at least one parameter estimate is significantly different than zero. In addition, most pseudo-R2 measures are below 0.1 for each of the models. Once the overall significance of the models is confirmed, parameter estimates are analyzed. Due to the large number of variables and dichotomous models, parameter estimates are included in Appendix III, Tables III. 1 to III.5. There are no variables that are consistently significant across all clusters; however, one category from all variables except gender are significant in at least one cluster. As a result, no variables are excluded to ensure consistency of variables across clusters. Interpretation of Parameter Estimates for Clusters Analysis of parameter estimates from the dichotomous logistic regression models for each cluster provide further evidence that investment personality, through KYC information, and demographics can be useful to predict segment membership and thus, future trading behaviour. Although the significant parameters in each model are different, they remain consistent with previous results from cross-tabulation and ANOVA analyses. The parameter estimates for the "Buy-and-hold" cluster suggest investors with excellent investment knowledge are less likely to belong to this cluster compared to investors indicating they have good investment knowledge. As well, compared with clients having a balanced investment objective, clients indicating they have a growth investment objective are more likely to belong to this cluster whereas clients with an income investment objective are less likely to be members of this cluster. Nevertheless, clients with a low risk tolerance and who are employed as professionals in real estate are less likely to belong to the "Buy-and-hold" cluster compared to clients with a high risk tolerance and who are employed in occupations other than real estate. Furthermore, the negative sign associated with the parameter estimate of the year joined variable suggests members of the "Buy-and-hold" cluster are clients who have been with PH&N longer. Consequently, the parameter estimates for the "Buy-and-hold" cluster are consistent with buy-and-hold investors. These investors generally have fair to good investment knowledge with growth or balanced investment objectives. As well, the year joined variable may provide insight into why the returns of this cluster are much higher than other clusters. Specifically, markets in the past may have provided higher returns to investors; therefore, clients who joined PH&N longer ago would be more likely to have higher returns in their first year of trading. © Nicole Marija Franjic 51 Contrary to the results of the "Buy-and-hold" cluster, clients with an income investment objective are more likely to be members of the "Loss Averse" cluster than are clients with a growth objective. In addition, clients with a low risk tolerance and who employed as real estate professionals are more likely to belong to the "Loss Averse" cluster compared to clients with high or medium risk tolerance and who are in occupations other than real estate. The sign associated with the parameter estimate for age is positive; therefore, this suggests older clients are more likely to belong to the "Loss Averse" cluster than are younger clients. As well, the parameter estimates suggest members of the "Loss Averse" cluster have a positive relationship with year joined; they are more recent clients. Regardless, clients with minimal investment knowledge are less likely to belong to the "Loss Averse" cluster compared to clients with good investment knowledge. To summarize, members of the "Loss Averse" cluster are more likely to have an income investment objective, low risk tolerance, and good investment knowledge. In addition, they are more likely to be recent clients and are more likely to be employed in real estate than other occupations. Consequently, this analysis further supports the ANOVA and cross-tabulation evidence that this cluster is loss averse. As well, the "Loss Averse" cluster has the lowest returns and is positively associated with year joined. As a result, this evidence could further support the hypothesis that markets performed better in the past resulting in higher returns for clients who joined PH&N longer ago. The "Market Timer" cluster is quite different than either the "Buy-and-hold" or "Loss Averse" clusters; many of the significant variables pertain to occupations rather than investment personality. Nevertheless, clients with excellent investment knowledge are more likely to be members of the "Market Timer" cluster compared to clients with good or other investment knowledge. In addition, clients who are employed as computer professionals, Engineers, homemakers, Lawyers, or who are retired are less likely to be members of this cluster. In particular, Lawyers, homemakers, and computer professionals are least likely to be members of this cluster compared to other occupations. This is consistent with the results for the "Market Timer" cluster illustrated in Table 4.5. Analysis of the "Overconfident/DCA" cluster provides some interesting - and possibly conflicting - evidence regarding the investment personality and demographics of this cluster. First, clients with minimal investment knowledge are more likely to belong to the "Overconfident/DCA" cluster compared to clients with good investment knowledge. This is © Nicole Marija Franjic 52 consistent with investors who perform DCA transactions - these investors are slowly increasing their knowledge and comfort with equity markets by investing at regular intervals. Nevertheless, analysis of logistic regression parameter estimates indicates clients with low risk tolerance are /ess likely to belong to this cluster compared to clients with high risk tolerance. This contradicts the assumptions of investors who perform DCA transactions, investors who are perceived to be apprehensive of investing, and more consistent with overconfident investors. In addition, clients employed as Chartered Accountants, executives, Lawyers, sales professionals, or who are self-employed are more likely to belong to the "Overconfident/DCA" cluster. In particular, Lawyers, executives, and sales professionals are more likely to belong to the "Overconfident/DCA" cluster than other occupations. As a result, based on the contrasting investment personality and occupational evidence, the dual label of overconfident and DCA for this cluster seems most appropriate. Finally, the parameter estimates for the "Novice" cluster supports previous evidence that these clients are relatively new to investing and may be somewhat unsure of their knowledge and skills. Younger clients who have minimal investment knowledge and who are employed as computer professionals are more likely to belong to the "Novice" cluster than are older clients with good or other investment knowledge and who are employed in occupations that are not computer related. Although gender is not significant at the a=0.10 level, it would be significant at a slightly higher alpha of a=0.13. This is consistent with the results from the cross-tabulation; although gender was not significant, the "Novice" cluster exhibits the only noticeable difference in gender across clusters. In particular, parameter estimates suggest female clients are more likely to belong to this cluster than male clients. Based on the dichotomous logistic regression parameter estimates, there appears to be evidence to support the hypothesis that a relationship exists between investor behaviour, personality, and demographics. Consequently, this relationship can be applied to predicting cluster membership - a proxy for future investor behaviour. In addition, the negative relationship between year joined in the "Buy-and-hold" cluster and the positive relationship between year joined in the "Loss Averse", "Overconfident/DCA", and "Novice" clusters suggests the year in which a client joined PH&N may impact portfolio returns. In particular, the "Buy-and-hold" cluster has the highest returns while the "Loss Averse" cluster has the lowest returns. Further research could be undertaken to identify if the year joined does indeed impact a client's returns. © Nicole Marija Franjic 53 Furthermore, using these parameter estimates, probability estimates can be computed for each client in relation to each cluster. Due to the various interrelated variables in the model, graphing the estimated probability curves for the independent variables provide no useful information. Instead, the subsequent focus will be on the accuracy of prediction for the various dichotomous regression models. Model Accuracy Probability estimates for whether a client belongs to a cluster as well as detailed diagnostics are readily available from most applications capable of performing logistic regression - such as SPSS, which is used in this analysis. Nevertheless, one of the primary concerns for PH&N is the model's accuracy of prediction. In order to determine the model's accuracy of prediction, the probability a client will belong to any given cluster must first be determined from the parameter estimates. Then, as discussed in Urbanovich (1999), an appropriate cutoff point must be chosen. This cutoff point is used to distinguish whether a client will be classified as a member of the cluster (Y=l) or classified as not being a member of the cluster (Y=0). This cutoff point is chosen in relation to client probability estimates. Urbanovich (1999) discusses several methods to determine appropriate cutoff values. Given the disproportionate cluster membership, it would not be useful to use 0.5 as the cutoff point for all 5 dichotomous regressions. Based on the approaches discussed by Urbanovich (1999), the conversion factor and equal classification percentages methods will be examined for each cluster. Although the conversion factor method is specific to research conducted by Urbanovich for the Workers Compensation Board of British Columbia, the conversion factor method provides useful application to the logistic regression models for retail clients at PH&N. Application of the conversion factor method to this analysis uses the proportion of clients in the sample who should belong to the cluster as the cutoff value. For example, 1,169 clients (38.49%) are categorized as members of the "Buy-and-hold" cluster. As a result, the cutoff value using the conversion factor method would be 0.3849. The equal percentages method uses the cutoff value where the percentage of correctly classified clients who belong to the cluster (Y=l) equals the percentage of correctly classified clients who do not belong'to the cluster (Y=0). For a further description of these methods, refer to Urbanovich (1999); however, each of these two methods is meant to compensate for © Nicole Marija Franjic 54 unequal probabilities of membership or non-membership. Using these two methods, the accuracy of prediction of each of the 5 clusters shall be investigated. Approximately 38.49% of clients (1,169 of 3,037) are classified as "Buy-and-hold". Table 4.8 presents the accuracy of predicted membership or non-membership in the "Buy-and-hold" cluster at various cutoff values - including 0.3849, which represents the actual Non-membership Membership Cutoff Value correct (Y=0) correct (Y=l) Total Correct 0.3000 17.72% 90.16% 45.60% 0.3800 52.30% 59.79% 55.19% " 0.3849 54.71% '56.29% 55.32% 0.3850 "' 54.76% 56.20% "5532% 0.3900 57.44% 53.72% 56.00% 0.4000 62.37% 49.62% 57.46% 0.4200 71.36% 40.98% 59.66% 0.4400 78.00% 32.34% 60.42% 0.4600 84.26% 24.64% 61.31% 0.4800 90.26% 17.79% 62.36% 0.5000 94.65% 10.78% 62.36% 0.5100 95.99% 8.90%"" """ 62.46% 0.5200 " 96.79% " 7.01% 62.23% 0.6000 99.57% 1.20% 61.71% 0.7000 100.00% 0.90% 61.54% percentage of clients in the sample who belong to the cluster. As the cutoff value increases, the number of clients who are correctly classified as not being members of the "Buy-and-hold" cluster (Y=0) increases to 100%. Conversely, as the cutoff value decreases, the number of clients who are correctly classified as being members of the cluster (Y=l) increases. The cutoff value of 0.51 has the highest percentage of total clients correctly classified, primarily due to the large percentage of clients correctly predicted as non-members. Although the cutoff value of 0.3849 has a lower percentage of total clients correctly predicted, the percentage correctly predicted between members and non-members is more equal. Consequently, while the cutoff value of 0.51 has a higher total accuracy than the cutoff value of 0.3849, membership in the cluster when the cutoff is 0.51 is rarely predicted correctly. This is unacceptable because the model becomes almost completely homogeneous - almost all clients are predicted as being non-members of the cluster. After performing comparable analyses for the remaining four clusters, the results are similar. The optimal cutoff values for the "Loss Averse", "Overconfident/DCA", and "Novice" clusters are equivalent to the proportion of clients who are classified as belonging © Nicole Marija Franjic 55 to the cluster. Specifically, 47.34% of clients (1,438 of 3,037) belong to the "Loss Averse" cluster so the optimal cutoff is 0.4734. In addition, 3.39% of clients (103 of 3,037) belong to the "Overconfident/DCA" cluster and 5.63% of clients (171 of 3,037) belong to the "Novice" cluster so their optimal cutoff values were 0.0339 and 0.0563 respectively. As well, for all except the "Market Timer" cluster the two theories of conversion factor and equal classification percentages previously discussed converge to the same optimal cutoff value. Conversely, the optimal cutoff value for the "Market Timer" cluster follows the equal percentages theory. Although this cluster represents 5.14% of clients (156 of 3,037), the optimal cutoff for this cluster is 0.0575 - or where the predictive accuracy for membership is approximately equal to the predictive accuracy for non-membership. The accuracy tables for the "Loss Averse", "Market Timer", "Overconfident/DCA", and "Novice" clusters are included in Appendix III, Tables III.6 to III.9. The optimal cutoff values and predictive accuracy totals for clusters are illustrated in Table 4.9. TABLE 4.9 OPTIMAL Cl JTOFF VALUES EOF t EACH CLUSTER Cluster Cutoff Non-membership correct (Y=0) Membership correct (Y=l) Total Correct Buy-and-hold Loss Averse Market Timer Overconfident Novice 0.3849 0.4734 0.0575 0.0339 0.0563 54.71% 63.48% 65.36% 64.49% 67.52% 56.29% 53.89% 66.03% 63.11% 67.25% 55.32% 58.94% 65.39% 64.44% 67.50% Unfortunately, there are certain limitations and notes of caution that should be considered regarding the dichotomous models. Since each of these models is binary there can be only two outcomes, member or non-member. Consequently, the benchmark value of accuracy against which these models can be compared is 50%. Additionally, the models can be analogized to a coin toss, where either outcome has a 50% probability of occurring. If the total accuracy is considerably higher than 50%, the model is more useful than using a coin toss to determine membership or non-membership. From Table 4.9 it is clear the "Market Timer", "Overconfident/DCA", and "Novice" clusters are valuable and provide predictive power beyond using a simple coin toss. Conversely, the predictive accuracy of the "Buy-and-hold" cluster is only 55%. Overall, the models appear to be valuable and predict more accurately than would a simple coin toss model. Although the 5 dichotomous models should not be used in a stepwise fashion to arrive at total membership across clusters, it is important to examine the reason why this © Nicole Marija Franjic 56 cannot be done. Primarily, due to the less than perfect accuracy of the dichotomous models, the same client may be predicted to belong to more than one cluster. Using the optimal cutoff values for each model, there are no clients predicted to belong to all 5 clusters; however, 111 clients (3.7%) are predicted to belong to 4 clusters. Conversely, 1 client (0.03%) is not classified into any of the 5 clusters. In total, 2,156 clients (71.0%) are predicted to belong to more than 1 cluster. Nevertheless, 880 clients (29.0%) are predicted to belong to only 1 cluster. Despite the limitations of the five dichotomous models, they seem to provide at least some assistance in determining cluster membership and thus, future trading behaviour of a new client. Nevertheless, due to the inadequacies of the dichotomous models, a series of polytomous models are subsequently examined. 4.3.2 Polytomous Logistic Regression In the polytomous regression, the dependent variable is the cluster indicator value specifying in which cluster clients belong - the clusters being "Buy-and-hold", "Loss Averse", "Market Timer", "Overconfident/DCA", and "Novice". The independent variables are slightly different in each of the three polytomous models analyzed. The first model includes all 10 independent variables - age, initial deposit amount, income, net worth, investment knowledge, investment objective, risk tolerance, occupation, gender, and year joined. The second model excludes the occupation variable and the third model includes occupation but transforms the 16 individual occupations into 5 occupational categories. These occupational categories and the occupations included within are shown in Table 4.10. After analysis of the model chi-square, which tests the null hypothesis that all the regression coefficients are zero, the null hypothesis is rejected for all three models. Significance of parameter estimates is determined next by examining corresponding Wald statistics and p-values. Polytomous logistic regression's use of a reference category results in four predictive equations. Each equation compares the probability of membership in one category against membership in the reference category. The following equations are used in this analysis: 1) Probability of being a "Buy-and-hold investor" versus being a "Novice" investor 2) Probability of being a "Loss Averse" investor versus being a "Novice" investor 3) Probability of being a "Market Timer" investor versus being a "Novice" investor © Nicole Marija Franjic 57 4) Probability of being an "Overconfident/DCA" investor versus being a "Novice" investor 5) Reference category equation is the probability of being a "Novice" investor The "Market Timer" cluster consistently has the largest number of significant variables, where 5 of the 10 independent variables are significant. These 5 variables are age, initial market value, knowledge, and occupation (when relevant). Age and initial market value are the most common significant variables whereas risk tolerance, worth, and year joined are least common. In fact, the latter three variables are not significant in any model or cluster. MBLE 4.10' OCCUPATIONAL CATEGORIES • • ".' • "/SW Category Occupations Included Business Technical Sales Professionals Other Administrator, Broker Engineer, computer professional, Business Analyst sales professional, real estate professional Chartered Accountant, Medical Professional, Lawyer, executive, Teacher self-employed, retired, homemaker, labourer Although many of the variables are insignificant, knowing the parameter estimates allows computation of the probability of membership in any given cluster. Unfortunately, due to the numerous equations and possibilities, illustration of these probabilities will not be undertaken here. Additionally, due to the limitations of SPSS, probabilities could not be computed for this analysis. Despite this limitation, SPSS produces a classification table that displays model classification accuracy, which shall be examined later in this discussion. Although the limitations of SPSS are a constraint regarding computation of probabilities, there are alternative methods to compute probabilities in future analyses. Probability estimates for clients could be computed by applying the polytomous coefficients - which are outputs from SPSS - and the equations from section, using an Excel spreadsheet. Next, a comparison of the pseudo-R2 for each model is performed; however, the SPSS output includes 3 different measures for each model. The Cox and Snell as well as Nagelkerke measures attempt to examine the strength of the relationship between the predictor and outcome variables. Both measures use likelihood to develop their respective pseudo-R2 measurements; however, while the Cox and Snell measurement varies between 0 and 1, it will never actually reach 1. Consequently, Nagelkerke's measurement attempts to resolve this by dividing "the Cox and Snell R2 by its maximum in order to achieve a measure that ranges from 0 to l." 4 1 The third measure, known as McFadden's R2, is © Nicole Marija Franjic 58 analogous to Hosmer and Lemeshow's R2L. This is calculated as the model chi-square divided by the initial -2*log-likelihood (intercept only). Table 4.11 presents the different pseudo-R2 measures for each of the three models. ™ f e L t l i l ? P S E U D C ^ R 2 ' M ^ Model I Model 3 P s e u d o - R 2 Model 1 (Occupation (Occupational Measure (all variables) excluded) categories) Cox and Snell 0.118 0.095 0.102 Nagelkerke 0.132 0.106 0.113 McFadden 0.055 0.044 0.047 The pseudo-R2 measures are not very high, indicating a relatively weak association between predictor and outcome variables; however, the comparison of these three models presents some interesting information. The polytomous model that excludes occupation seems to have the weakest association compared to the other two models. Conversely, the model with occupation - not occupational categories - has the highest R2. This suggests occupation is at least somewhat important for predictive purposes. The polytomous logistic regression analysis is not discussed in extensive detail due to several considerable limitations. One of the key limitations is the structure of the equations and data used. The first model, which includes all predictor variables, could not present conclusive findings because it violates two assumptions - quasicomplete separation and a large number of cells with zero frequencies. As discussed in Chapter 3, these violations can cause parameter estimates to be overstated and misleading. Predictive accuracy ranges from 49.2% to 50.3%. Although this may seem better than mere guessing, this accuracy occurs primarily as a result of the majority of investors being classified into one of the two large clusters - "Buy-and-hold" and "Loss Averse". In the model that includes occupation, the accuracy is 50.3%; however, only 20 investors (0.66%) are classified into the three smaller clusters. As well, in 11 of these cases, membership in a smaller cluster is incorrectly predicted. Although the utility of the polytomous logistic regression models are not completely discounted, the several limitations described above greatly impede the ability of using any of the models as a decision tool. Consequently, further research and refinements are necessary before any conclusions can be drawn on the ability of a polytomous logistic regression model to predict in which cluster a client will belong. Possible areas for further investigation for the polytomous models will be discussed in the next chapter. © Nicole Marija Franjic 59 4.4 Seemingly Unrelated Regression (SUR) For the SUR model, the independent variables for all equations are identical to the predictor variables in the logistic regression analysis; however, the dependent variables differ. Several systems of equations are analyzed where the dependent variables include total transactions, total transactions less DCA transactions, transaction types, performance, and total number of funds in which a client invested during the first year. The performance dependent variable is continuous while the other dependent variables are discrete counts. The seemingly unrelated regression (SUR) model attempts to circumvent the process of creating clusters and predicting cluster membership to determine trading behaviour. Instead, the SUR model attempts to predict behaviour directly. To accomplish this, the outcome variables used to represent behaviour must be determined; however, the independent variables used to predict are the same as in the logistic regression models. Specifically, the predictor variables are the investment objective, investment knowledge, risk tolerance, occupation, income range, net worth range, year joined, age, gender, and initial market value of new clients. Once the dependent and independent variables are chosen, ordinary least squares (OLS) regression is performed on each of the equations to produce the covariance matrix of error terms between the three equations. This covariance matrix is subsequently used in the SUR model to determine whether the OLS parameter estimates are optimal with respect to the sum of squared errors or if there is significant correlation between equation error terms, which requires new model parameters to be estimated. Several dependent variables are analyzed prior to inclusion in the SUR model. The final SUR model contains three equations. One equation uses normalized portfolio performance as the outcome variable while a second equation uses the total number of funds in which a client invested during their first year with PH&N as the outcome variable. The third equation is somewhat more complicated. As a potential predictive model of trading behaviour, at least one equation in the SUR model is required to contain the client's number of transactions during their first year with PH&N. Nonetheless, transactions can be analyzed in several different ways. One method of analysis is to represent transactions in one equation containing the total number of transactions executed. Another method is to include separate equations for each of the different types of client-initiated transactions - buy, sell, switch, and transfer. An additional method is to once again aggregate into one equation the total transactions © Nicole Marija Franjic 60 executed; however, this total will exclude automatic DCA transactions. There are two reasons for excluding DCA transactions. First, this is an automatic transaction occurring at regular intervals so it is less necessary to predict. Second, and the more important of the two reasons, is due to the results from a survey of PH&N Investment Advisors. The only unanimous opinion among all Advisors was DCA transactions should not be included in any analysis to assess behaviour based on number of transactions executed. In particular, the belief is DCA transactions do not provide any insight into aggressive behaviour. A final method is to use transaction days rather than the number of transactions themselves. The reason for this is because a series of transactions might represent only one particular event and should be analyzed as a group. Table 4.12 presents the coefficients of determination as well as some of the OLS diagnostics for OLS models with each of these dependent variables. As can be seen, the total transactions excluding DCA transactions variable has a higher adjusted R2 than either the total transactions variable or the trade days variable. The root-MSE is also smaller than TABLE 4.12 ANALYSIS OF OLS EQUATION RESUL1 rs Dependent Variable Adj-R2 F-statistic p-value Root-MSE Normalized Returns 0.0328 3.79 < 0.0001 11.06 Total Funds 0.0769 7.84 < 0.0001 1.84 Total Transactions 0.041 4.51 < 0.0001 13.9 Total Transactions Less DCA 0.0414 4.54 < 0.0001 11.85 Buys 0.0598 6.22 < 0.0001 9.2 Sells 0.0615 6.38 < 0.0001 5.61 Switches 0.0188 2.57 < 0.0001 7.48 Transfers 0.0244 3.05 < 0.0001 0.856 Trade Days 0.0234 2.97 < 0.0001 4.11 the former, which suggests the data is less dispersed compared to the total transactions variable. Although the buy and sell transaction types have higher adjusted R2 values and lower root-MSEs, adjusted R2 values for switches and transfers are much lower. Nevertheless, based on the higher adjusted R2 and lower root-MSE as well as due to the results and opinions of PH&N Advisor surveys, total transactions excluding DCA transactions is chosen as the dependent variable to reflect client transaction behaviour in the model. After determination of the three SUR equations - normalized portfolio performance, total funds, and total transactions excluding DCA transactions - the ITSUR procedure in SAS is run. This procedure requires the user to input the three equations in OLS format. SAS then calculates the covariance matrix, £ . in addition to the ITSUR procedure, SAS has an © Nicole Marija Franjic 61 SUR procedure that allows the user to manually enter the E-hat. Since a customized covariance matrix is unnecessary, the USUR procedure is sufficient to compute the SUR parameter estimates. The SUR covariance matrix is shown in Table 4.13. TABLE 4.13 SEEMINGLY UNRELATED REGRESSION ERROR COVARIANCE MATRIX Total Funds Normalized Return Transactions Less DCA Total Funds 3.4 1.15 10.32 Normalized Return 1.15 122.29 2.96 Transactions Less DCA 10.32 2.96 140.41 After computation of SUR parameter estimates, comparison with OLS parameter estimates is performed; the parameter estimates and standard errors of both models are identical, indicating correlation between the error terms of the three equations does not provide any additional insight into predicting trading behaviour beyond a simple OLS model. The parameter estimates and standard errors are shown in Table 4.14. Although the parameter estimates for both SUR and OLS are identical, these coefficients still provide useful information regarding variability of transaction behaviour and correlation between transactions, funds, and performance. Total number of funds held has the highest adjusted-R2 and lowest root MSE values of the three equations used in the SUR model. As can be seen in Table 4.14, of the ten independent variables used, only income range, age, and gender are insignificant at the a = 0.1 level. Nevertheless, the parameter values of these variables provide interesting insights into how KYC and demographic information affect number of funds held. Year joined and initial deposit amount have positive relationships with total number of funds held. Consequently, the more recently a client has joined PH&N and the larger the initial deposit amount, the more funds the client is expected to hold. Although several occupation indicator variables are not significant in the model, the parameter estimates suggest there are differences among occupations and number of funds held. In particular, homemakers, real estate professionals, and retired clients are expected to hold fewer funds than are clients in other occupations. This is consistent with ANOVA and cross-tabulation analyses. Clients in the "Loss Averse" cluster have the lowest average number of funds held and this cluster also has the highest comparative percentage of clients classified in the homemaker, real estate, or retired occupations. In addition, clients with minimal and excellent investment knowledge would be expected to hold more funds compared to clients with good - or other - investment knowledge. Clients with minimal or excellent knowledge © Nicole Marija Franjic 62 TABLE 4.14 OLS AND SUR PARAMETER ESTIMATES Transactions Performance Funds Model Adjusted R 2 0.0414 0.0328 0.0769 Beta p-value Beta p-value Beta p-value Intercept -623.15 0.00 1363.09 < 0.0001 -81.02 0.01 Year Joined 0.32 0.00 -0.68 < 0.0001 0.04 0.00 Initial MV 0.00003 < 0.0001 0.000003 0.39 0.000006 < 0.0001 Age -0.07 0.01 -0.01 0.73 0.00 0.98 Gender (Female) 0.54 0.29 0.89 0.06 -0.07 0.41 Occupation Occl (Administrator) 0.96 0.40 1.63 0.13 -0.12 0.50 Occ2 (Business Analyst) 2.86 0.11 1.82 0.28 0.28 0.33 Occ3 (Broker) -0.35 0.95 5.57 0.32 0.09 0.92 Occ4 (Chartered Accountant) -0.60 0.63 0.97 0.41 0.20 0.31 Occ5 (Computer Professional) 3.25 0.01 1.78 0.13 -0.09 0.64 OcoS (Engineer) -0.55 0.62 2.54 0.01 -0.20 0.24 Occ7 (Executive) -0.76 0.58 0.32 0.81 0.13 0.54 Occ8 (Homemaker) -1.70 0.16 0.66 0.56 -0.57 0.00 Occ9 (Labourer) -1.83 0.31 0.91 0.59 -0.23 0.41 OcclO (Lawyer) 0.91 0.53 0.00 1.00 -0.22 0.33 Occll (Medical Professional) 0.06 0.95 1.63 0.11 -0.08 0.63 Occl2 (Real Estate Professional) -1.74 0.48 -0.94 0.68 -0.71 0.06 Occl3 (Retired) -0.40 0.68 1.09 0.23 -0.59 < 0.0001 Occl4 (Sales) 3.18 0.02 1.31 0.31 0.13 0.55 Occl5 (Self-Employed) -0.04 0.98 1.76 0.12 -0.04 0.83 Exduded: Occl6 (Teacher) 0.00 0.00 0.00 0.00 0.00 0.00 Knowledge KnowO (None) -0.53 0.73 0.67 0.64 -0.37 0.12 Knowl (Minimal) 1.92 0.00 0.34 0.49 0.28 0.00 Know2 (Limited) -0.32 0.82 -3.73 0.01 -0.20 0.37 Know3 (Fair) -0.92 0.30 -2.34 0.00 -0.04 0.79 Know5 (Excellent) 0.71 0.53 -1.09 0.29 0.30 0.08 Exduded: Know4 (Good) 0.00 0.00 0.00 0.00 0.00 0.00 Objective ObjO (Grow) 0.74 0.14 1.35 0.00 0.20 0.01 Objl (Income) 1.12 0.24 -1.46 0.10 -0.40 0.01 Exduded: Obj2 (Balanced) 0.00 0.00 0.00 0.00 0.00 0.00 Tolerance TolO (Low) -0.35 0.71 -1.42 0.12 -0.51 0.00 Toll (Medium) 0.72 0.27 -0.23 0.71 0.03 0.76 Exduded: Tol2 (High) 0.00 0.00 0.00 0.00 0.00 0.00 Income Range Incl ($0 - $24,999) 0.26 0.81 -0.65 0.51 0.08 0.62 Inc2 ($25,000 - $49,999) 1.14 0.19 -1.61 0.05 0.08 0.53 Inc3 ($50,000 - $74,999) 1.09 0.19 -0.72 0.35 0.17 0.18 Inc4 ($75,000 - $99,999) 1.42 0.12 -0.45 0.60 0.08 0.58 Exduded: Inc5 ($100,000+) 0.00 0.00 0.00 0.00 0.00 0.00 Net Worth Range Worth 1 ($0 - $49,999) 1.42 0.18 1.63 0.10 0.05 0.75 Worth2 ($50,000 - $99,999) -0.09 0.92 0.05 0.95 0.10 0.44 Worth3 ($100,000 - $199,999) -0.82 0.20 0.48 0.42 -0.09 0.36 Exduded: Worth4 ($200,000 - $499,999) 0.00 0.00 0.00 0.00 0.00 0.00 Worth5 ($500,000 - $999,999) -0.17 0.78 1.06 0.07 -0.10 0.28 Worth6 ($1,000,000 +) -1.46 0.08 -1.64 0.03 -0.61 < 0.0001 © Nicole Marija Franjic 63 may be expected to hold more funds because of beliefs regarding diversification of portfolios or their propensity to market time. Consequently, clients with minimal knowledge may hold many funds because they misinterpret investment literature and believe more diversification is better than less. Conversely, clients with excellent knowledge may be prone to holding many funds because they are trying to time the market. Since this analysis defines total funds held as the total number of funds held at any point during the first year of trading, market timers may not necessarily hold many funds at one time but rather, they have a high turnover of funds. Investment objective and risk tolerance also provide further insight into the number of funds a client is expected to hold. In particular, clients with a growth objective are expected to hold a larger number of funds, whereas clients with an income objective are expected to hold fewer funds compared to clients with a balanced objective. Consequently, growth clients would be more diversified - or prone to over-diversification - than would clients with other investment objectives. In addition, clients with low risk tolerance are expected to hold fewer funds than clients with a high risk tolerance. This is consistent with Markowitz theory. Clients with a low risk tolerance would be expected to hold the market, which can generally be accomplished by holding between one and three funds. Parameters for total transactions less DCA are generally insignificant. Nevertheless, the significant parameter estimates once again provide further information regarding trading behaviour. While many of the transactional relationships are similar to those for number of funds held, there are slight differences. First, the negative coefficient for age suggests older clients are expected to have fewer non-DCA transactions. Conversely, clients who have joined more recently and who have a larger initial deposit amount are expected to have more non-DCA transactions. In addition, those clients in computer or sales occupations and with lower net worth ranges are expected to have a larger number of non-DCA transactions. It is also interesting to note that higher initial deposit amounts tend to signify more trading while higher net worth suggests fewer expected trades. The adjusted-R2 for normalized returns is the lowest compared to total funds held and total transactions (less DCA), at 0.0328. The significant demographic variables indicate females are expected to have higher returns than males and Engineers are expected to have better performance than other occupations. Conversely, more recent clients are expected to have lower returns. In addition, investors with limited and fair investment © Nicole Marija Franjic 64 knowledge are expected to have lower returns compared to investors with good investment knowledge. Furthermore, investors who classify themselves as having low to moderate net worth are expected to have higher returns compared to investors who classify themselves as having high net worth. Nevertheless, risk tolerance is not significant in the performance equation. This is somewhat inconsistent with Markowitz portfolio theory, which states investors with lower risk tolerance should be expected to have lower returns. Despite the evidence provided regarding certain relationships between the dependent and independent variables, the SUR and OLS models have inherent limitations. Due to the relatively low adjusted-R2 values, the variability in the dependent trading and performance variables are not very well explained by demographics, initial market value, and the KYC independent variables. One of the key problems is the large number of insignificant variables, especially when there are some significant and many insignificant indicators within a categorical variable. In addition, total number of funds held and total non-DCA transactions must be greater than or equal to zero, but the models in this research occasionally predict a negative number of funds or transactions. Obviously, it is impossible to hold less than zero funds or perform less than zero transactions. Based on the analysis of SUR and OLS parameter estimates, further evidence is presented to support the hypothesis that investment personality and demographic information have a predictive relationship with investor trading behaviour and performance. In addition, the SUR and OLS model provides many results that are consistent with conclusions from the cross-tabulation and ANOVA of predictor variables on clusters as well as the logistic regression. For example, Engineers are categorized as being comparatively higher in the "Buy-and-hold" cluster - the cluster with the highest returns - and in the SUR/OLS model, the parameter estimate for Engineers is positive, indicating Engineers are expected to have higher returns compared to other occupations. In addition, clients who have an income investment objective are expected to have lower comparative returns than clients with other objectives and the "Loss Averse" cluster - which had the lowest returns -also has the highest comparative proportion of clients with an income investment objective. Consequently, the results from the SUR/OLS model appear to be consistent with previous conclusions and further support the premise that trading behaviour and performance have a predictive relationship with investor personality and demographics. © Nicole Marija Franjic 65 5.0 APPLICATION AND AREAS FOR FURTHER INVESTIGATION Although the results from the previous analyses provide useful information regarding the trading behaviour of clients at PH&N, none of these analyses are static. All the models will change as clients join and leave PH&N. Consequently, the assumptions and proportion of clients in each cluster will continuously change. In addition, the types of clusters themselves might change when new behaviours emerge. The logistic regression models developed can be practically applied at PH&N. These models include parameter estimates, which enables computation of the probability of membership in a cluster for new clients. Nevertheless, probabilities would be difficult to compute by directly applying the logistic regression equations. Software programs - such as SAS's Enterprise Miner - can automatically compute these probabilities. Although validation of the logistic regression models could not be performed, trading behaviour in 2001 for clients who joined PH&N in 2000 could be used to validate the models. Re-running the cluster analysis and categorizing the clients who joined in 2000 to one of the five clusters would be the first step. Next, cluster membership could be predicted for the additional new clients by applying the logistic regression parameter estimates from this study and updated optimal cutoff values based on the new proportion of clients in the cluster. The predicted cluster memberships and actual cluster memberships could be compared to determine accuracy, thus validating the model. Despite the ability to apply the models developed, there are refinements that can be made to these models to improve them. In addition, there are further models that can be developed to extend application of theories and models undertaken here. 5.1 Model Refinement and Improvement Although six clusters are chosen from the K-means clustering method, this is later reduced to 5 clusters due to the presence of a small cluster, accounting for only 0.40% of the total sample. Nevertheless, reduction and combination of clusters is very ad hoc and consists of comparison by observation across key variables, not statistical tests. Despite use of two validation techniques - analysis of clusters based on initial assumptions and whether the clusters make intuitive sense in relation to the business goals - more robust statistical tests should be researched and applied when attempting to combine clusters. © Nicole Marija Franjic 66 In addition, the polytomous logistic regression model is restrictive, inaccurate, and violates several diagnostic tests. Nevertheless, a polytomous model would be very useful if it could be refined and the violations corrected. Menard (1995) suggests "calculating a multinomial logit model, then translating that model...in the logistic regression format'"2 could be done to develop a polytomous logistic regression model. The polytomous model developed here uses SPSS's multinomial logistic regression function; however, using log-linear and logit modeling could potentially produce probability estimates - which could not be obtained from SPSS's multinomial logistic regression function - and better diagnostics. Dividing the polytomous logistic regression into its parts - through use of multinomial logit modeling - would enable analysis of each step in the process to determine where the multinomial logistic regression function in SPSS erred. Nevertheless, log-linear and logit modeling may not correct the problems of the polytomous model. This could be due to the lack of continuous independent variables and subjective client responses within the nominal independent variables. Consequently, the logistic regression and SUR models developed here may be improved with inclusion of different independent variables. Rather than inclusion of all predictor variables that may affect the outcome, a principal components and factor analysis could also be performed. By executing this analysis prior to model development, only relevant variables would be included in the model. In addition, the factor analysis could be performed on a smaller sample of the data; therefore, data collection and the associated costs can be minimized. In addition to refinement of the models already discussed, further models could be developed, which may improve upon the limitations of the logistic regression and SUR/OLS models. In particular, artificial neural networks shall be discussed. Artificial neural networks (ANN) combine a series of mathematical models in an attempt to create a model that "learns" as new information is added. ANN create initial predictions and then modify these predictions when new information is available. ANN have been used to predict critical care patients in hospital emergency rooms as well as bankruptcy prediction. ANN have been very successful in categorization of objects and pattern recognition. This type of model can be extremely useful to PH&N by furthering research undertaken here and to improve the accuracy of categorization and prediction. Due to the complexity, an © Nicole Marija Franjic 67 ANN model was beyond the scope of this project; however, this can be pursued in the future to improve predictive efficiency of the models developed here. 5.2 Extension of Research and Areas for Further Investigation This project primarily focuses on categorization and prediction of new clients as they join PH&N. There are three areas of research that would be natural extensions of the analyses undertaken here. First, performing similar classification and prediction analyses on existing - rather than new - clients. Second, examining how clients move, or migrate, from one cluster to another. Third, the monetary costs and benefits of incorrectly or correctly classifying or predicting behaviour should be explored. Analysis of new clients was undertaken because Advisors would more readily accept and apply results from analysis of new clients. Nevertheless, analyzing behaviour of existing clients should not be discounted merely because undertaking such an analysis may not be well received initially. Categorization of existing clients could be performed on myriad levels other than simple transaction behaviour and market value. These clients have a relationship with PH&N and information such as whether they have sought advice, type of advice sought, and duration of relationship with PH&N could be included in the analysis. Comparison of the results from the analyses of new and existing clients to see where - and when - behaviour is different could also be undertaken. Additionally, change in behaviour over a period of time can be studied. Migration of clients - or movement of clients from one cluster to another - during their time with PH&N would undoubtedly provide further insights into how client life cycles impact their trading behaviour. Clients are seen to belong to a particular cluster during one time period and migrate to another cluster at some point in the future, with a particular probability. This can be formulated as a Markov chain where the clusters are the state space and membership in a cluster determines transition probabilities to future clusters. Finally, analysis of the monetary costs and benefits associated with categorization and prediction of client trading behaviour would be beneficial to PH&N. Should the monetary costs and benefits be substantial, refinement and development of improved models should be undertaken. © Nicole Marija Franjic 68 6.0 CONCLUSION Investor behaviour is an area of finance that has not received much academic attention, until recently. Although traditional financial theories explain the theoretical operation of financial markets, they do little to explain actual market events - especially stock market anomalies. Nonetheless, theories of investor behaviour have direct application to categorization of investors and prediction of future behaviour. Specifically, these theories are applied to segmentation and predictive modeling of assigned and unassigned Retail investors at PH&N. As competition in financial services increases, financial service providers such as PH&N must better understand their clients. Through this understanding, PH&N can develop better service offers and more effectively allocate Advisors to clients. Although this research focuses on new Retail clients, these techniques can also be applied to new discretionary clients and existing Retail or discretionary clients. In this research, four models are developed to segment clients and predict future behaviour. The first model uses cluster analysis to segment clients based on transaction behaviour and market value. Using the results of this analysis, 5 clusters are identified and assigned descriptive labels. The five clusters are "Buy-and-hold", "Loss Averse", "Market Timer", "Overconfident/DCA", and "Novice". Through ANOVA and Cross-tab analysis of each cluster, it is evident the behaviour of clusters can be distinguished based on investment beliefs and investor personality through KYC information and demographics. Nevertheless, cross-tabulation of gender on clusters provides little information regarding segment membership - a proxy for future trading behaviour. Subsequent to segmentation of clients, a series of logistic regression models are used in an attempt to predict segment membership. These models include 5 dichotomous logistic regression models - one for each of the five clusters identified. Analysis of parameter estimates from these models provide further evidence to support the hypothesis that investment personality - through KYC information - and demographics have a predictive relationship with future trading behaviour. Nevertheless, accuracy of these models is also important to ensure the models can be practically applied at PH&N. Although the dichotomous models predict more accurately than a simple coin toss - where the probability of either outcome is 50% - one of the inherent limitations is the five models, when combined, result in clients being classified into more than one cluster. Consequently, © Nicole Marija Franjic 69 analysis of respective probabilities would need to be undertaken; however, this would be infeasible for large analyses and only probable on a client-by-client basis. Due to the limitations in the dichotomous models, three polytomous models are also examined. All three models are statistically significant with overall predictive accuracy between 49.2% and 50.3%. Nevertheless, these models fail several diagnostic tests, such as quasicomplete separation and a large number of zero count cells. In addition, computational limitations restrict probability estimates from being calculated for client membership in a cluster. The final predictive model is a seemingly unrelated regression model. The intention of this model is to predict transaction and performance behaviour directly rather than through cluster membership. The SUR model combines the output of several ordinary least squares (OLS) regression equations with the covariance matrix of these equations. Despite the identical parameter estimates for both the SUR and OLS models, which indicates the SUR model provides no additional information to optimize the OLS parameter estimates, analysis of the model parameters provides further evidence that investment personality and demographics exhibit an explanatory relationship with trading behaviour and performance. In addition, the results from the SUR/OLS model are consistent with conclusions from the cross-tabulation and ANOVA analysis of predictor variables on clusters. Of the models developed in this project, the cluster analysis and resulting ANOVA and cross-tabulation analyses provide the most useful information regarding who PH&N's clients are. Despite the limitations of the SUR/OLS and logistic regression models, the results verify previous conclusions from the ANOVA and cross-tabulation analyses and they also provide further information to support the explanatory relationship between investor behaviour, personality, and demographics. Nonetheless, results from all models should still be used in conjunction with advisor intuition and additional analyses. Although the results of this research are both beneficial and contain several limitations, areas for further investigation appear promising. In particular, this research provides consistent evidence that different trading behaviours exist at PH&N and investor personality and demographics provide an explanatory and predictive relationship with future investor behaviour. © Nicole Marija Franjic 70 1 Sean Silicoff, (Title Unknown), National Post - Financial Post [Toronto] 13 January 2001. 2 The Canadian Securities Course, Volume 2, April 1998: 7-2. 3 Investment Funds Institute of Canada Main Menu, Sept. 2001 <http://www.ific.ca/eng/home/index.asp> 4 Investment Company Institute Home Page, Sept. 2001 <http://www.ici.org> 5 Compiled and summarized from: Zvi Bodie, Alex Kane, Alan J. Marcus, Stylianos Perrakis, and Peter J. Ryan, Investments - First Canadian Edition, (Richard D. Irwin Inc., 1993). William F. Sharpe, Gordon J. Alexander, Jeffery V. Bailey, and David J. Fowler, Investments - Second Canadian Edition, (Prentice Hall, 1997). Peter Lusztig, Randall Morck, and Bernard Schwab, Managerial Finance in a Canadian Setting - Fifth Edition. (John Wiley & Sons, 1994). 6 William F. Sharpe, Gordon J. Alexander, Jeffery V. Bailey, and David J. Fowler, Investments - Second Canadian Edition, (Prentice Hall, 1997) 93. 7 Risk is represented by the statistical measure of standard deviation, derived from a probability distribution. 8 William F. Sharpe, Gordon J. Alexander, Jeffery V. Bailey, and David J. Fowler, Investments - Second Canadian Edition, (Prentice Hall, 1997) 150. 9 Cloda Lane and Junior Sophister, "The Rationality of Rational Expectations", 20 August 2001 <http://www.maths.tcd.ie/pub/econrev/ser/html/rationality.htm>! 1 0 Amos Tversky and Daniel Kahneman, "Judgment under uncertainty: Heuristics and biases" in Daniel Kahneman, Paul Slovic, and Amos Tversky eds., Judgment under uncertainty: Heuristics and biases. (Cambridge University Press, 1982 (1974)) 3. 1 1 Russell J. Fuller, "Behavioural Finance and Sources of Alpha", 6 Feb. 2000, Aug. 2001: 3. <http://www.behaviouralfinance.com> 1 2 Stuart Oskamp, "Overconfidence in case-study judgments" in Daniel Kahneman, Paul Slovic, and Amos Tversky eds, Judgment under uncertainty: Heuristics and biases, Cambridge University Press, 1982 (1965). 1 3 Terrance Odean, "Do Investors Trade Too Much?", 24 Feb. 2000, May 2001: 14. <http://www.gsm.ucdavis.edu/~odean> 1 4 Terrance Odean, "Do Investors Trade Too Much?", 24 Feb. 2000, May 2001: 3. <http://www.gsm.ucdavis.edu/~odean> 1 5 Terrance Odean and Brad M. Barber, "Trading is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors", Journal of Finance LV.2 (Apr 2000): 800. 1 6 Whitney Tilson, "The Perils of Overconfidence", 20 Sept. 1999, Apr. 2001 <http:// www.fool.com/boringport/1999/boringport990920.htm>. 1 7 Kenneth L. Fisher and Meir Statman, "Cognitive biases in market forecasts", Journal of Portfolio Management, (Fall 2000): 4. 1 8 Candice Prendergast and Lars Stole, "Impetuous Youngsters and Jaded Old-Timers: Acquiring a Reputation for Learning". The Journal of Political Economy. 104. (1996): 1106. © Nicole Marija Franjic 71 1 9 Candice Prendergast and Lars Stole, "Impetuous Youngsters and Jaded Old-Timers: Acquiring a Reputation for Learning" The Journal of Political Economy, 104. (1996): 1125. 2 0 William N. Goetzmann and Nadav Peles, "Cognitive dissonance and mutual fund investors", The Journal of Financial Research. (Summer 1997): 1. 2 1 Russell J. Fuller, "Behavioural Finance and Sources of Alpha", 6 Feb. 2000, Aug. 2001: 13. <http://www.behaviouralfinance.com> 2 2 Candice Prendergast and Lars Stole, "Impetuous Youngsters and Jaded Old-Timers: Acquiring a Reputation for Learning", The Journal of Political Economy. 104. (1996): 1106. 2 3 Sendhil Mullainathan and Richard H Thaler, "Behavioural Economics" - Abstract, NBER Working Paper No. W7948: October 2000. 2 4 Terrance Odean and Brad M. Barber, "Trading is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors", Journal of Finance LV.2 (Apr 2000): 794. 2 5 Shlomo Benartzi and Richard H. Thaler, "Myopic Loss Aversion and the Equity Premium Puzzle", Quarterly Journal of Economics, (February 1995): 73. 2 6 Daniel Kahneman and Amos Tversky, "Prospect Theory: An Analysis of Decision Under Risk", Econometrica, 47.2 (March 1979): 268. 2 7 Ibid. 2 8 John H. Cochrane, "Portfolio advice for a multifactor world", Economic Perspectives, (1999): 62-63. 2 9 John H. Cochrane, "Portfolio advice for a multifactor world", Economic Perspectives, (1999): 70. 3 0 An in-house application - referred to as the Index of Performance (IOP) - was built to perform these calculations. The IOP creates an index measurement for each month, where the first month of the calculation is assigned an index value of 100 and each subsequent month is compared against the first month. In addition, annualized returns can be calculated from these indices using three methods, of which the time-weighted method was chosen for this analysis. The time weighted method divides the period being analyzed into several sub-periods, where each sub-period starts immediately after a cash flow and ends immediately prior to a subsequent cash flow. Each of these sub-periods is then geometrically aggregated to calculate the annualized return for the period of interest. 3 1 In Canada, the federal government restricts the percentage of investments (without using derivatives) in RRSP portfolios that can come from mutual funds investing in foreign (non-Canadian) markets. Prior to 2000, foreign funds were limited to being 20% of the value of an RRSP portfolio. In 2000 this increased to 25% and after 2000 the limit is 30%. 3 2 William F. Sharpe, Gordon J. Alexander, Jeffery V. Bailey, and David J. Fowler, Investments - Second Canadian Edition, (Prentice Hall, 1997): 155. 3 3 SPSS Inc., Market Segmentation Using SPSS, (SPSS, Inc., 1999): Practice 3-47. 3 4 Scott Menard, Applied Logistic Regression Analysis. (Thousand Oaks: Sage Publications, 1995) 13. 3 5 Ibid. 3 6 David Kleinbaum, Lawrence Kupper, Keith Muller, Azhar Nizam, Applied Regression Analysis and Other Multivariable Methods 3rd Edition, (Duxbury Press, 1998): 642. 3 7 Ibid. © Nicole Marija Franjic 72 Scott Menard, Applied Logistic Regression Analysis, (Thousand Oaks: Sage Publications, 1995) 38. J y Carnegie Mellon. 21 Oct. 2001 <http://wvw.ece.cmu.edu/afs/ece/usr/moura/public_html/hyperspertral/IT_Workshop/ 4 0 Web sites used in the discussion of SUR in this analysis were: Resa Corporation - SUR page. 21 Ort. 2001 < http: //www, resacorp.com/sur. htm > Economics - Seemingly Unrelated Regression. Department of Economics, Temple University, 21 Oct. 2001 <http://oll.temple.edu/economics/notes/seeminly/seeminly.HTM> 4 1 This information was compiled from the following website: College of Humanities and Social Sciences - Latent Class Analysis. NC State University, 26 Ort 2001. < http: //www2 .chass. ncsu.edu/qa rson/pa765/logistic. htm: > 4 2 Scott Menard, Applied Logistic Regression Analysis. (Thousand Oaks: Sage Publications, 1995) 81. © Nicole Marija Franjic 73 REFERENCES Benartzi, Shlomo and Richard H. Thaler. "Myopic Loss Aversion and the Equity Premium Puzzle", Quarterly Journal of Economics, (February 1995): 73. Bodie, Zvi, Alex Kane, Alan J. Marcus, Stylianos Perrakis, and Peter J. Ryan. Investments - First Canadian Edition, Richard D. Irwin Inc., 1993. The Canadian Securities Course, Volume 2, April 1998: 7-2. Carnegie Mellon. Carnegie Mellon University. <http://www.ece.cmu.edu/afs/ece/usr/moura/public_html/hyperspectral/IT_Workshop/sld010.htm> Cochrane, John H. "Portfolio advice for a multifactor world", Economic Perspectives, (1999). College of Humanities and Social Sciences - Latent Class Analysis. NC State University. <http://www2.chass.ncsu.edu/garson/pa765/logistic.htm:> Economics - Seemingly Unrelated Regression. Department of Economics, Temple University. <http://oll.temple.edu/economics/notes/seeminly/seeminly.HTM> Fisher, Kenneth L. and Meir Statman. "Cognitive biases in market forecasts", Journal of Portfolio Management. (Fall 2000): 4. Fuller, Russell J.. "Behavioral Finance and Sources of Alpha", 6 Feb. 2000. <http://www.behavioralfinance.com> Goetzmann, William N. and Nadav Peles. "Cognitive dissonance and mutual fund investors", The Journal of Financial Research, Summer 1997. Investment Company Institute Home Page. <http://www.ici.org> Investment Funds Institute of Canada Main Menu <http://www.ific.ca/eng/home/index.asp> Johnson, Richard A. and Dean W. Wichern. Applied Multivariate Statistical Analysis - Fourth Edition. New Jersey: Prentice Hall, 1998. Kahneman, Daniel and Amos Tversky. "Prospect Theory: An Analysis of Decision Under Risk", Econometrica. 47.2 (March 1979): 268. Kleinbaum, David, Lawrence Kupper, Keith Muller, Azhar Nizam. Applied Regression Analysis and Other Multivariable Methods 3 r d Edition. Duxbury Press, 1998. Lane, Cloda and Junior Sophister. "The Rationality of Rational Expectations" <http://www.maths.tcd.ie/pub/econrev/ser/html/rationality.htm>! © Nicole Marija Franjic 74 Lusztig, Peter, Randall Morck, and Bernard Schwab. Managerial Finance in a Canadian Setting -Fifth Edition. John Wiley & Sons, 1994. Menard, Scott. Applied Logistic Regression Analysis. Thousand Oaks: Sage Publications, 1995. Mullainathan, Sendhil and Richard H Thaler. "Behavioral Economics" - Abstract, NBER Working Paper No. W7948: October 2000. Odean, Terrance. "Do Investors Trade Too Much?", 24 Feb. 2000, May 2001: 14. <http://www.gsm.ucdavis.edu/~odean> Odean, Terrance and Brad M. Barber. "Trading is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors", Journal of Finance LV.2 (Apr 2000): 800. Oskamp, Stuart. "Overconfidence in case-study judgments" in Daniel Kahneman, Paul Slovic, and Amos Tversky eds, Judgment under uncertainty: Heuristics and biases, Cambridge University Press, 1982. Prendergast, Candice and Lars Stole. "Impetuous Youngsters and Jaded Old-Timers: Acquiring a Reputation for Learning", The Journal of Political Economy. 104. (1996): 1106-1125. Resa Corporation - SUR page. <http://www.resacorp.com/sur.htm> Romesburg, Charles H. Cluster Analysis for Researchers. Malabar: Robert E. Krieger Publishing Company, 1990. SAS Institute. SAS On-line Help Files. Sharpe, William F., Gordon J. Alexander, Jeffery V. Bailey, and David J. Fowler. Investments -Second Canadian Edition. Prentice Hall, 1997. Silicoff, Sean. (Title Unknown), National Post - Financial Post [Toronto] 13 January 2001. SPSS Inc. Market Segmentation Using SPSS. Chicago: SPSS Inc., 1999. Tilson, Whitney. "The Perils of Overconfidence", 20 Sept. 1999. <http:// www.fool.com/boringport/1999/boringport990920.htm>. Tversky, Amos and Daniel Kahneman. "Judgment under uncertainty: Heuristics and biases" in Daniel Kahneman, Paul Slovic, and Amos Tversky eds., Judgment under uncertainty: Heuristics and biases. Cambridge University Press, 1982. Urbanovich, Ernest. Identifying High-Risk Claims Within the Workers' Compensation Board of British Columbia's Claim Inventory by Using Logistic Regression Modeling. Vancouver: University of British Columbia. 1999. © Nicole Marija Franjic 75 APPENDIX I Bond Fund Canadian Money Market Fund Canadian Equity Fund Canadian Growth Fund Dividend Income Fund U.S. Equity Fund European-Pacific Fund Short-term Bond and Mortgage Fund U.S. Growth Fund High Yield Bond Fund Balanced Pension Trust Global Equity RSP Fund Total Return Bond Fund Balanced Fund U.S. Money Market Fund . . . . . . — . . . . . . . TABLE 1.2 INDICES USED IN CALCULATION OF NORMALIZED CLIENT RETURNS Year S&P Total Return Index TSE Total Return Index Weighting1 Scotia Universal Bond Index 2 Total Weighted (40%/60%) 3 1985 31.73 1986 18.66 8.95 10.90 14.70 12.42 1987 5.25 5.88 5.75 4.04 5.07 1988 16.61 11.08 12.19 9.79 11.23 1989 31.69 21.37 23.44 12.81 19.19 1990 -3.10 -14.80 -12.46 7.54 -4.46 1991 30.47 12.02 15.71 22.14 18.28 1992 7.62 -1.43 0.38 9.84 4.16 1993 10.08 32.80 28.26 18.14 24.21 1994 1.32 -0.63 -0.24 -4.31 -1.87 1995 37.58 14.83 19.38 20.67 19.90 1996 22.96 28.35 27.27 12.26 21.27 1997 33.36 14.98 18.65 9.63 15.04 1998 28.58 -1.58 4.45 9.18 6.34 1999 21.04 31.71 29.58 -1.14 17.29 2000 -9.10 7.41 3.28 10.25 6.07 1 Equities are weighted at 60% S&P = 20% prior to 2000, 25% in 2000 TSE = 80% prior to 2000, 75% in 2000 (based on Canadian RRSP Foreign Content Rules) 2 Bonds are weighted at 40% 3 This amount is subtracted from the estimated annualized return for each client based the year after the client joined PH&N © Nicole Marija Franjic 76 TABLE 1.3 OCCUPATION CATEGORIES lAdministrator Broker Business Analyst Chartered Accountant Computer Professional Engineer Executive Homemaker Labourer Lawyer Medical Professional I Real Estate Retired Sales Self-Employed iTeacher TABLE 1.4 NOMINAL VARIABLES Nominal Variable Nominal Variable Value Name 1) Investment Objective Grow 0 ObjO Income 1 Objl Balanced 2 omitted 2) Investment Knowledge None 0 KnowO Minimal 1 Knowl Limited 2 Know2 Fair 3 Know3 Good 4 omitted Excellent 5 Know5 3) Risk Tolerance Low 0 TolO Medium 1 Toll High 2 omitted 4) Occupation ADMIN 1 Occl BA 2 Occ2 BKR 3 Occ3 CA 4 Occ4 COMPR 5 Occ5 EGNR 6 Occ6 EXEC 7 Occ7 HMKR 8 Occ8 LAB 9 Occ9 LWYR 10 OcclO MP 11 Occll REA 12 Occl 2 RETIR 13 Occl3 SALES 14 Occl4 SEMP 15 Occl5 TCHR 16 omitted 5) Income Range $0 - $24,999 1 Incl $25,000 - $49,999 2 Inc2 $50,000 - $74,999 3 Inc3 $75,000 - $99,999 4 Inc4 $100,000+ 5 omitted 6) Net Worth Range $0 - $49,999 1 Worth 1 $50,000 - $99,999 2 Worth2 $1000,000 - $199,999 3 Worth3 $200,000 - $499,999 4 omitted $500,000 - $999,999 5 Worth5 $1,000,000+ 6 Worth6 > $1,000,000+ 7 Worth6 7) Sex Male 0 Female 1 © Nicole Marija Franjic 77 APPENDIX II RE II.l PH&N INVESTMENT PROFILE FORM PIIILLI PS, HAGER & NORTH Investment M a n a g e m e n t Ltd. Account Administration Investment Profile Account holder Account number Investment Profile Your investment experience I ! Stocks ! Bonds 0 Mutual Funds 0 None Securities regulators require us to obtain this information, ll will remain confidential. Your investment knowledge • txcellenr IGood • Fair L~ Limited Please indicate only one choice: Your PHN investment objective • Income • Balanced i .1 Growth Please indicate only one choice: Your risk tolerance J High I! Medium 11 Low Your occupation 2 Comments Your approximate annual income Q SO - $24,999 !' 125,000-$49,999 r $50,000 - $74,999 (" $75,000 - $99,999 ! SI 00.000-Your approximate net worth T $0-549,999 I $50.000-$99,999 r $100.000-$199,999 § $200,000 - $499,999 0 $500,000 - $999,999 1 $1,000,(100+ Please indicate only one choice: Your overall investment objective • Income • Balanced :.! Growth Signature L Oate (yyyy/mrn/dd) Contact us Client Contact Centre: 1-800-661-oUI Fund Prices: 1-800-997-2799 Facsimile: I-80U-666-9S99 E-mail • niliyaphii.com Website: www.phn.aim Imcsimcni Profile 9.41 (Sen 30011 © Nicole Marija Franjic APPENDIX III a = 0.10 E^ B ^ l ^ l ^ j B U Y-'AN ffiojjgj i iRA 'R 'A 'MEiTiERlESJTl IM^aiEsi l^P Parameter Wald Variable Estimate Statistic p-value Age -0.003 0.306 0.580 Initial Market Value 0.000 0.039 0.844 Year Joined -0 068 ~ 177101 0.000 Income 7.513' 0.111 Incl ($0 - $24,999) -0.257 1.907 0.167 Inc2 ($25,000 - $49,999) -0 312 4 144 0.042 Inc3 ($50,000 - $74,999) -0".055" ~ "~0"7l49~ 0.699 Inc4 ($75,000 - $99,999) -0.184 1.350 0.245 Omitted ($100,000+) 0.000 0.000 0.000 Knowledge KnowO (None) 0.223 5.448 0.696 0.364 0.404 Knowl (Minimal) 0.000 0.000 0.996 Know2 (Limited) -0.191 0.526 0.468 Know3 (Fair) 0.064 0.173 0.678 Omitted (Good) 0.000 0.000 0.000 Know5 (Excellent) "-0.397 3.838 " 0.050 Objective 15.264 0.001 ObjO (Grow) 0.271 :• 9.532 0.002 Objl (Income) -0.329 ''' 3::223^ %: 0.073 Omitted (Balanced) 0.000 0.000 0.000 Occupation 8.952 0.880" Occl (Administrator) 0.120 0.361 0.548 Occ2 (Business Analyst) 0.051 0.027 0.870 Occ3 (Broker) 0.652 0.399 0.528 Occ4 (Chartered Accountant) 0.083 0.146 0.702 Occ5 (Computer Professional) Occ6 (Engineer) -0.162 0.067 0.530 0.125 0.467 0.724 Occ7 (Executive) 0.083 0.123 0.726 Occ8 (Homemaker) -0.119 0.303 0.582 Occ9 (Labourer) 0.250 0.657 0.418 OcclO (Lawyer) -0.216 0.737 0.391 Occll (Medical Professional) Occl2 (Real Estate Professional) -0.014 -0 862 0.006 3 064 0.940 0.080 6ccl3 (Retired) -0.028 0.027" " 0.869 Occl4 (Sales) -0.021 0.008 0.930 Occl5 (Self-Employed) -0.138 0.427 0.513 Omitted (Teacher) 0.000 0.000 0.000 Gender (Male) -0.011 0.015 0.904 Tolerance 3.376 0.185 TolO (Low) -0.317 3.372 0.066 Toll (Medium) -0.120 1.133 " 6.2Q7 Omitted (High) 0.000 0.000 0.000 "Worth , L ,'<' '" 14.618 0.012 Worthl ($0 - $49,999) -0.248 1.797 0.180 Worth2 ($50,000 - $99,999) -0.183 1.538 0.215 Worth3 ($100,000 - $199,999) 0.002 0.000 0.987 Omitted ($200,000 - $499,999) 0.000 0.000 0.000 Worth5 ($500,000 - $999,999) -0.386 " 6.493 . . . . 0.011 Worth6 ($1,000,000 + ~) 0.121 0.263 Intercept 135.153 177084 0.000 © Nicole Marija Franjic a = 0.10 Parameter Wald Variable Estimate Statistic p-value Age . 0.008 3.096 0.079 Initial Market Value -0.0000031 15.000 o.ooo • Year Joined 0.031 3.568 0.059 Income 4.261 ""6.372 Incl ($0 - $24,999) 0.064 0.123 0.726 Inc2 ($25,000 - $49,999) 0.019 0.015 0.902 Inc3 ($50,000 - $74,999) -0.153 1.157 0.282 Inc4 ($75,000 - $99,999) -0.123 0.615 0.433 Omitted1 ($100,000+) _ 0.000 0.000 0.000 knowledge 9.315 0.097 KnowO (None) -0.287 ~ "~L155 ~ " "6.283 know! (Minimal) -0.191 4.281 0.039 Know2 (Limited) ""'6.256 " 1.006 6.316 Know3 (Fair) 0.093 0.367 0.545 Omitted (Good) 0.000 0.000 0.000 Know5 (Excellent) 0.223 1.341 0.247 Objective ""21.660 0.000 ObjO (Grow) -0.319 13.803 0.000 Objl (Income) 0.354 4.289 0.038 Omitted (Balanced) 0.000 0.000 "" n 000 " Occupation 14.816 0.465 Occl (Administrator) -0.205 1.053 0.305 Occ2 (Business Analyst) -0.324 1.051 0.305 Occ3 (Broker) -0.156 0.023 0.881 Occ4 (Chartered Accountant) -0.131 0.360 0.548 Occ5 (Computer Professional) -0.072 0.108 0.743 Occ6 (Engineer) 0.000 0.000 1.000 Occ7 (Executive) -0.034 0.020 0.887 Occ8 (Homemaker) 0.331 2.483 0.115 Occ9 (Labourer) 0.032 0.011 0.918 OcclO (Lawyer) 0.062 0.063 0.802 Occll (Medical Professional) 0.027 0.020 0.887 Occl2 (Real Estate Professional) 1.035 5.230 0.022 Occl3 (Retired) 0.117 0.495 "~ 6.482 Occl4 (Sales) -0.189 0.629 0.428 Occl5 (Self-Employed) 0.049 0.055 0.815 Omitted (Teacher) 0.000 0.000 0.000 Gender (Male) 0.099 1.270 0.260 Tolerance 10.447 0.005 TolO (Low) . 0.428 6.487 0.011 Toll (Medium) 0.005 0.022 "0.963 "*'" Omitted (High) 0.000 0.000 0.000 Worth 12.202 0.032 " Worth1 ($0 - $49,999) "o.bi6 ""67668 0:931 "~ Worth2 ($50,000 - $99,999) 0.151 1.094 0.296 Worth3 ($100,000 - $199,999) 0.132 1.409 0.235 Omitted ($200,000 - $499,999) 0.000 0.000 0.000 Worth5 ($500,000 - $999,999) " 0.369 6.548 0.011 " Worth6 ($1,000,000 +) "" "-0. 089 0.702 "0.402 Intercept " :62.544 3.614 07057 © Nicole Marija Franjic 80 a = 0.10 Parameter Wald Variable Estimate Statistic p-value Age 0.010 0.865 0.352 Initial Market Value 0.00000516 "'23.136 ,0.000 Year Joined 0.057 1.684 0.194 Income 14.663 0.006 Incl ($0 - $24,999) 1.700 9.507 r 0.002 Inc2 ($25,000 - $49,999) 1.760 12.563 0.000 Inc3 ($50,000 - $74,999) 1.484 9.297 0.002 Inc4 ($75,000 - $99,999) 1.794 13.085 0.000 Omitted ($1007000+) 0.000 0.000 o.oob Knowledge 6.308 0.277 KnowO (None) 0.014 0.001 0.983 Knowl (Minimal) 0.065 0.100 0.751 Know2 (Limited) -1.232 1.451 0.228 Know3 (Fair) -0.104 0.081 0.776 Omitted (Good) 0.000 0.000 0.000 Know5 (Excellent) 0.756 4.491 O.034 Objective " 1.547 "0.461 ObjO (Grow) -0.039 0.042 0.837 Objl (Income) -0.564 1.547 0.214 Omitted (Balanced) 0.000 0.000 0.000 Occupation 17.552 0.287 Occl (Administrator) -0.487 1.506 0.220 Occ2 (Business Analyst) 0.395 0.524 0.469 Occ3 (Broker) -4.383 , 0.062 0.804 Occ4 (Chartered Accountant) -0.145 0.120 0.729 Occ5 (Computer Professional) -1.093 "3.697 "07O55 Occ6_(Engineer) -0.676 2.735 0.098 6cc7 (Executive) -07509 """ 0.924" 67337 Occ8 (Homemaker) -1.451 6.215 "67613 Occ9 (Labourer) -1.007 ' 1.726 " 6.189 OcclO (Lawyer) "" -1.873 3.213 0.073 Occii (Medical Professional) " -67479" ' "1.482 " 0.224" Occl2 (Real Estate Professional) -0.796 0.552 0.457 Occl3 (Retired) -0.799 5 781 0.016 6ccl4 (Sales) -0.515 0.973 " ~i0".324 Occl5 (Self-Employed) -0.493 1.339 0.247 Omitted (Teacher) 0.000 0.000 0.000 Gender (Male) 0.143 0.551 0.458 Tolerance 4.139 0.126 TolO (Low) -0.443 1.016 0.313 Toll (Medium) 0.232 0.785 0.376 Omitted (High) 0.000 0.000 0.000 Worth 9.422 " "0.093 Worthl ($0 - $49,999) 0.354 0.920 "6.338 Worth2 ($50,000 - $99,999) 0.225 0.539 0.463 Worth¥($100';006 - $1997999) -07769 5.875" "o7bi"5""" Omitted ($200~000 ~ $499,999)" 0.000 " "6.000" " o76oo Worth5 ($500,000 - $999,999) 0.036 0.013 0.910 Worth6 ($1,000,000 +) -0.119 0.257 0.612 Intercept -117.862 1.826 0.177 © Nicole Marija Franjic 81 a = 0.10 T A B % E f m ^ V / ' O V ^ Parameter Wald Variable Estimate Statistic p-value Age -0.002 0.032 0.858 Initial Market Value 0.00000497 16.854 0.000 Year Joined 2.839 0.092 Income 2.438"" ~o!656'~'" Incl ($0 - $24,999) -0.179 0.127 0.722 Inc2 ($25,000 - $49,999) -0.027 0.005 0.946 Inc3 ($50,000 - $74,999) 0.305 0.680 0.410 Inc4 ($75,000 - $99,999) 0.228 0.342 0.559 Omitted ($100,000+) 0.000 0.000 0.000 Knowledge 8.576 0.127 KnowO (None) 0.646 1.036 0.309 Knowl (Minimal) 0.505 4.778 0~029 Knowi (Limited) -07611"""" 0.355 " 0.551'" Know3 (Fair) -0.670 1.232 0.267 Omitted (Good) 0.000 0.000 0.000 Know5 (Excellent) -0.358 0.338 0.561 Objective 0.605 0.739 ObjO (Grow) 0.133 0.311 0.577 Objl (Income) 0.305 0.410 0.522 Omitted (Balanced) 0.000 0.000 0.000 Occupation 15.049 0.448 Occl (Administrator) 0.809 1.493 0.222 Occ2 (Business Analyst) 0.348 0.094 0.759 Occ3 (Broker) -3.616 0.015 0.904 Occ4 (Chartered Accountant) 1.436 5.066 0.024 Occ5 (Computer Professional) -6.686 0.367 "6.545 Occ6 (Engineer) 0.904 2.050 0.152 Occ7 (Executive) ""'1.492 """ 5.126 0.024 Occ8 (Homemaker) 0.934 1.835 """07176 Occ9 (Labourer) 0.327 0.082 0.775 OcclO (Lawyer) 1.774 7.288 0.007 Occl l (Medical Professional) " "0.973 " 2.482 0.115 Occl2 (Real Estate Professional) -3.901 0.113 0.737 Occl3 (Retired) 0.807 1.898 0.168 Occi4 "(Sales) - - - 1.463 4.797 0.029 Occl5 (Sejf-Emplqyed) 1.167 ' 3.241 0.072 Omitted (teacher) """ b.ooo " o^obo b.ooo Gender (Male) -0.323 1.875 0.171 Tolerance 4.276 0.118 TolO (Low) -0.973 3.399 0.065 Toll (Medium) " -07055 " 0.034 ~ 0^855 Omitted (High) 0.000 0.000 0.000 Worth 2.491 0.778 Worthl ($0 - $49,999) -0.388 0.558 0.456 Worth2 ($50,000 - $99,999) -0.692 2.213 0.137 Worth3 ($100,000 - $199,999) -0.101 0.114 0.736 Omitted ($200,000 - $499,999) 0.000 0.000 0.000 Worth5 ($500,000 - $999,999) -0.091 0.056 0.813 Worth6 ($1,000,000 +) -0.126 0.189 0.664 Intercept -216.908 2.953 0.086 © Nicole Marija Franjic a = 0.10 T A B L E III.5 " N O V I C E " P A R A M E T E R E S T I M A T E S Parameter Wald Variable Estimate Statistic p-value Age -0.029 8.071 0.005 Initial Market Value 0.000 "" 6.242" 0.623 Year Joined 0.114 5.722 0.017 Income 1.582 0.812 Incl ($0 - $24,999) 0.062 0.022 0.882 Inc2 ($25,000 - $49,999) 0.239 0.511 0.475 Inc3 ($50,000 - $74,999) -0.004 0.000 0.991 Inc4 ($75,000 - $99,999) 0.176 0.257 0.612 Omitted ($100,000+) 0.000 0.000 0.000 Knowledge 9.366 0.095 KnowO (None) -0.169 0.073 0.787 Knowl (Minimal) 0.436 5.645" 0.018 Know2 (Limited) 07409 "~ 0.675" OAil" Know3 (Fair) -0.646 1.851 0.174 Omitted (Good) 0.000 0.000 0.000 Know5 (Excellent) 0.076 0.028 0.867 Objective 1.522 0.467 ObjO (Grow) 0.207 1.211 0.271 Objl (Income) -0.172 0.120 0.729 Omitted (Balanced) 0.000 0.000 0.000 Occupation 30.681 0.010 Occl (Administrator) 0.452 1.516 " 6.218 Occ2 (Business Analyst) 0.579 1.082 0.298 Occ3 (Broker) -3.282 0.096 0.757 Occ4 (Chartered Accountant) -0.427 0.708 0.400 Occ5 (Computer Professional)'"_ _ 1.202 10.722 0.001 Occ6 (Engineer) 0.015"" " oTooi 0.970 "' Occ7 (Executive) -0.741 1.272 0.259 Occ8 (Homemaker) -0.310 0.409 0.522 Occ9 (Labourer) -0.541 0.478 0.489 OcclO (Lawyer) 0.441 0.867 0.352 Occll (Medical Professional) 0.029 0.006 0.939 Occl2 (Real Estate Professional) -0.262 0.060 0.807 Occl3 (Retired) -0.168 0.185 0.667 Occl4 (Sales) 0.514 1.439 0.230 Occl5 (Self-Employed) 0.301 0.523 0.470 Omitted (Teacher) 0.000 0.000 0.000 Gender (Male) -0.297 2.383 0.123 Tolerance 2.244 0.326 TolO (Low) 0.058 0.022 0.884 Toll (Medium) 0.311 1.764 0.184 Omitted (High) 0.000 0.000 0.000 Worth 1.717 0.887 Worth 1 ($0 - $49,999) 0.281 0.835 0.361 Worth2 ($50,000 - $99,999) 0.093 0.115 0.734 WortfO ($100,000 - $199,999) -0.114 0.224 0.636 Omitted ($200,000 - $499,999) 0.000 0.000 0.000 Worth5 ($500,000 - $999,999) -0.058 0.021 0.884 Worth6 ($1,000,000 +) 0.044 0.028 0.866 Intercept -229.206 5". 824 "67016 © Nicole Marija Franjic 83 TABLE III.6 ANALYSIS OF CUTOFF VALUES FOR "LOSS AVERSE" CLUSTER Cutoff Value Non-membership correct (Y=0) Membership correct (Y=l) Total Correct 0.3000 3.06% 98.68% 48.34% 0.4000 34.08% 80.46% 56.04% 0.4500 54.41% 62.80% 58.38% 0.4700 62.41% 54.94% 58.87% 0.4734 63.48% 53.89% 58.94% 0.4800 65.35% 51.39% 58.74% 0.4900 68.17% 48.89% 59.04% 0.5000 71.48% 45.69% 59.26% 0.5100 74.17% 42.98% 59.40% 0.6000 91.56% 18.50% 56.96% 0.7000 98.81% 4.59% 54.20% TABLEIIIL7 ANALYSIS OF CUTOFI^LU^ Cutoff Value Non-membership correct (Y=0) Membership correct (Y=l) Total Correct 0.0400 45.71% 83.33% 47.65% 0.0500 57.10% 73.08% 57.95% 0.0514 58.90% 73.08% 59.60% 0.0575 65.36% 66.03% 65.39% 0.0600 67.93% 61.54% 67.60% 0.1000 92.50% 24.36% 89.00% 0.2000 99.27% 3.21% 94.34% 0.3000 99.83% 1.28% 94.76% 0.4000 99.93% 0.64% 94.83% 0.5000 99.97% 0.00% 94.83% TABlEtfi.8 A N A l ^ r S l ! ^ Cutoff Value Non-membership correct (Y=0) Membership correct fY=l) Total Correct 0.0300 56.51% 73.79% 57.10% 0.0339 64.49% 63.11% 64.44% 0.0400 72.67% 54.37% 72.04% 0.0500 81.83% 37.86% 80.34% 0.1000 97.92% 13.59% 95.06% 0.2000 99.63% 2.91% 96.35% 0.3000 99.93% 0.97% 96.58% 0.4000 99.97% 0.00% 96.58% © Nicole Marija Franjic IHIE III.9 ANALYSISKiPli lPFF VALUES FOR "NOVICE" CLUSTER ' , .J Cutoff Value Non-membership correct (Y=0) Membership correct (Y=l) Total Correct 0.0400 51.60% 77.78% 53.08% 0.0500 62.14% 71.35% 62.66% 0.0563 67.52% 67.25% 67.50% 0.0600 69.92% 63.16% 69.54% 0.1000 87.33% 42.11% 84.79% 0.2000 98.15% 12.87% 93.35% 0.3000 99.83% 5.85% 94.53% 0.4000 99.93% 1.75% 94.40% © Nicole Marija Franjic 


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