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Empirical tests for the impact of trusteed pension plans in the Canadian equity market Hilton, Donald Bruce 1973

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C ) EMPIRICAL TESTS FOR THE IMPACT OF TRUSTEED PENSION PLANS IN THE CANADIAN EQUITY MARKET by DONALD BRUCE HILTON B. Comm., University of B r i t i s h Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN BUSINESS ADMINISTRATION in the Department of Commerce We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1973 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Commerce  The University of British Columbia Vancouver 8, Canada Date i ABSTRACT The purpose of th i s study is to empirically test the hypothesis that the aggregate a c t i v i t y of pension funds in the Canadian equity market has created a segmenta-tio n of that market. I t i s possible that t h i s aggregate a c t i v i t y has a measurable impact on the market price of the stocks purchased. I f i t can be shown that pension funds do command a r e l a t i v e l y strong p o s i t i o n in the market for Canadian equities then a study of t h i s nature would be j u s t i f i e d . The importance of pension funds in recent years w i l l be discussed and any trends of significance to the development of the Canadian equity market i d e n t i -f i e d . The empirical study w i l l cover the period 1964-72 and w i l l determine whether the concentration of pension fund investments in a small number of Canadian common stocks has in fact had a measurable impact on the market prices of these stocks. I f pension fund a c t i v i t y was bidding up the market price of these stocks one would expect this to be indicated in a s i g n i f i c a n t l y d i f f e r e n t rate of return for these stocks in comparison with other non-pension stocks. i i TABLE OF CONTENTS Page Abstract i Chapter I The Canadian Pension Fund Industry 1 II Pension Funds and the Canadian Equity Market 5 III Summary and Implications 12 IV Empirical Study 14 Introduction 14 Data and Method 14 Empirical Tests 17 Empirical Results 21 Conclusion 26 Bibliography 27 Appendix A 28 i i i LIST OF TABLES Table Page 1 Selected Data for L i f e Insurance Companies group annuities, Federal Government group annuities and Trusteed Pension Funds, 1964-71 2 2 Selected Financial Assets - Trusteed Pension Funds, 1964-71 6 3 Net Increase in Fin a n c i a l Assets - Trusteed Pension Funds, 1964-71 8 4 Income and Expenditures - Trusteed Pension Funds, 1964-71 9 5 Sample of Stocks Selected for the Study as of December 19, 1964 16 6 Returns of Randomly Selected P o r t f o l i o s Over Various Holding Periods 18 7 Changes i n Price Earnings Ratios Over Selected Holding Periods 23 8 Means of the D i s t r i b u t i o n of Weighted Means 25 1 Chapter I The Canadian Pension Fund Industry The significance of pension funds in the Canadian economy i s extensively documented. In 1964 the Royal Commission on Banking and Finance reported that pension plans absorbed more than 30 percent of a l l private savings in Canada. At the end of 1964 the assets of the trusteed plans alone amounted to $5,766 m i l l i o n (Table 1). If we were to include assets of plans funded either through Canadian government or l i f e insurance group annuities t h i s figure for 1964 would increase by a further $2,722 m i l l i o n . By 1971 the book value of assets held by the trusteed pension plans amounted to $12,461 m i l l i o n , while those of the l i f e insurance companies reached $4,369 m i l l i o n , including $827 m i l l i o n c l a s s i f i e d as segregated funds. In t o t a l assets held, the trusteed pension funds are the t h i r d largest f i n a n c i a l i n s t i t u t i o n , exceeded only by the l i f e insurance companies and the chartered banks. Judged by number of plans, the l i f e insurance companies do the largest business, with close to 14,000 plans in 1971 (Table 1); by volume of assets and also by number of employees covered the trusteed plans take the Table 1 Selected Data for L i f e Insurance Company Group Annuities, Federal Government Group Annuities and Trusteed Pension Funds 1964 - 1971 Number of Plans 1964 1965 1966 1967 1968 1969 1970 1971 Trusteed L i f e Insurance -group annuities -segregated Federal Government group annuities Trusteed L i f e Insurance -group annuities -segregated Federal Government group annuties 2118 2997 3467 3789 4065 4072 3859 3946 10048 10866 11459 11718 12891 13209 13530 13900 92 160 246 413 571 822 978 1216 1312 1267 1416 1398 1365 1110 1076 1041 Total Assets (Book Value) M i l l i o n s of Dollars 5766 6541 7250 8068 8972 10003 11059 12461 2049 2333 2491 2668 2891 2969 3138 3542 58 94 139 194 259 401 545 827 615 634 644 636 635 634 631 624 Source: S t a t i s t i c s Canada, Trusteed Pension Plans Financial S t a t i s t i c s 1971, Catalogue 74-201 published by authority of the Minister of Industry, Trade and Commerce. to 3 lead. Table 1 indicates that in 1971 the trusteed plans, while being less than 20 percent of a l l plans in number, controlled over 70 percent of a l l pension fund assets. The larger employers appear to favor the trusteed plan and the smaller employer, the insured plan.^" In recent years however, the t r u s t companies have made e f f o r t s to extend the trusteed plan to the smaller employer by the use of pooled funds, thus giving greater opportunities for investment d i v e r s i f i c a t i o n . The t r u s t companies have further increased competition for pension funds by emphasizing the advantages of investment in common stocks with growth p o t e n t i a l . This greatly r e s t r i c t e d the l i f e insurance companies as they are limited to a maximum investment of 25 percent of t o t a l assets in common stock. As t r u s t companies are not r e s t r i c t e d as to the proportion of pension fund assets which may be invested in common stock they w i l l continue to be a powerful factor in the future demand for Canadian egu i t y . The Report of the Royal Commission on Banking and Finance found the t r u s t industry in Canada to be highly concentrated with 10 companies accounting for the majority of the industry's a c t i v i t y . Due to t h i s high concentration •••Arthur Pedoe, L i f e Insurance, Annuities and Pensions, (University of Toronto Press, Toronto, Canada, 1970), p. 357. 4 and the fact that these t rus t companies are exposed to the research of the same major investment houses we could expect that much of t h e i r funds would be invested i n a s imi l a r manner. As the l i f e insurance and Government annuity plans are r e s t r i c t e d in the i r investment p o l i c i e s toward common stock, for purposes of th i s study we w i l l re fer mainly to trusteed pension funds; 75 percent of which are under the management of t rus t companies, the balance being managed by i n d i v i d u a l t rus tees . Having determined the s ize of the pension fund industry and i n p a r t i c u l a r the trusteed pension plans , the next chapter w i l l look at the a c t i v i t y of these trusteed funds in the Canadian equity market. 5 Chapter II Pension Funds and the Canadian Equity Market As pension funds achieved growing importance in the post-war years they have undergone extensive changes. As costs rose r a p i d l y management was forced to revise objectives from those of reasonable safety of funds to more aggressive investment goals with emphasis on perfor-mance. I t was not u n t i l the 1960's that the trusteed pension funds chose common stocks as a solution to r i s i n g pension costs. By 1964 pension fund investment in common stock accounted for 17 percent of t o t a l assets. While up considerably from less than 10 percent of t o t a l assets in 1960 t h i s i s s t i l l r e l a t i v e l y small in comparison with the investment of over 60 percent of t o t a l assets i n fix e d income s e c u r i t i e s . Table 2 indicates that by 1971 this trend toward greater equity investment was continuing as trusteed pension funds held $3,547 m i l l i o n of common stock, 80 percent of which was Canadian equity. By 1971 this increased equity investment had accounted for approximately 28 percent of t o t a l assets while investment in f i x e d income s e c u r i t i e s had f a l l e n to 48 percent of t o t a l assets on a market value basis. Evidence that this trend could continue for some time i s found in the United States experience. Canadian Table 2 Selected Financial Assets-Trusteed Pension Funds 1964 - 1971 1964 ($ millions) Market Value and % of Total Assets 1965 1966 1967 1968 1969 1970 1971 Bonds Stocks: Canad ian Common Non-Canad ian Common Preferred 5 % 3812 63.1 ? % 4024 59.9 $ % 4134 58.6 $ % 4225 53.8 y % 4359 48.7 $ % 4270 45.7 5 % 5154 48.9 ? % 6038 48.0 868 14.3 170 2.8 22 0.4 1042 15.5 223 3.3 30 0.5 1056 15.0 265 3.7 49 0.7 1352 17.2 413 5.3 61 0.7 1854 20.7 600 6.7 81 0.9 2062 22.1 655 7.0 81 0.8 2223 21.0 541 5.1 76 0.7 2902 23.1 645 5.1 85 0.7 1060 17.5 1295 19.3 1370 19.4 1826 23.2 2535 28.3 2798 29.9 2840 26.8 3632 28.9 Source: S t a t i s t i c s Canada, Trusteed Pension Plans Financial S t a t i s t i c s 1971, Catalogue 74-201. 7 f i n a n c i a l development has h i s t o r i c a l l y lagged the American development and therefore i t i s conceivable that Canadian trusteed pension funds w i l l approach the s i t u a t i o n experienced by United States funds in recent years where over 50 percent of t o t a l assets have been held in investments of common stock. With the aid of Table 3 we get some idea of the impact of pension fund investing in the equity market. While trusteed pension funds, in recent years, have added over $1,000 m i l l i o n annually to t h e i r p o r t f o l i o s of f i n a n c i a l assets, in 1971 $396 m i l l i o n of this was due to common stock investment alone. The magnitude of investments i s further i l l u s t r a t e d in Table 4 where we see that in 1971 the trusteed pension plans could have covered pension payments and cash with-drawals e n t i r e l y from investment income, thereby leaving the entire volume of $1,260 m i l l i o n in contributions for investment purposes. The supply of net new issues of Canadian common stock averaged $388 m i l l i o n per annum over the period of study while the trusteed pension funds alone increased t h e i r common stock holdings (at book value) at an average annual rate of $235 m i l l i o n . When we consider that t h i s average annual increase of $388 m i l l i o n includes stocks which are generally not of suitable quality for pension funds, and when the demands of the other i n s t i t u t i o n s for Table 3 Net Increase in Financial Assets Trusteed Pension Funds 1964 - 1971 (millions of dollars) 1964 1965 1966 1967 1968 1969 1970 1971 Net Increase in Financial Assets due to common stock investment 148 174 187 223 293 177 280 396 ro Total Increase 506 468 514 580 668 725 1059 1048 Source: S t a t i s t i c s Canada, Trusteed Pension Plans Financial S t a t i s t i c s , 1971. Table 4 Income and Expenditures, Trusteed Pension Funds 1964 - 1971 (millions of Dollars) 1964 1965 1966 1967 1968 1969 1970 1971 Income Employer contributions 345 403 431 474 557 591 658 798 Employee contributions 248 271 261 274 306 370 396 462 Total 593 674 692 748 863 961 1054 1260 Investment income 270 306 348 386 429 475 546 631 Net p r o f i t on sale of se c u r i t i e s 9 11 7 19 32 48 15 34 Miscellaneous 3 7 19 9 7 10 10 21 Total 282 324 374 414 468 533 571 686 Total Income 875 998 1066 1162 1331 1494 1625 1946 Expenditures Pension payments out of funds 169 197 227 25 7 295 333 377 482 Cost of pensions purchased 8 8 11 11 9 11 16 21 Cash withdrawals 54 84 106 82 82 95 110 115 Administration costs 4 5 6 7 8 9 12 15 Net loss on sale of se c u r i t i e s 4 2 7 6 1 10 99 60 Other expenditures 8 7 16 6 20 18 15 57 Total Expenditures 247 303 373 369 425 476 629 750 Source: S t a t i s t i c s Canada, Trusteed Pension Plans Fi n a n c i a l S t a t i s t i c s , 1971. 10 equities is added to that of the pension funds, i t i s apparent that not only is the supply of investment q u a l i t y stocks in Canada limited but i t is not growing as r a p i d l y as the demand.2 I t could be argued that t h i s large pool of resources of the pension funds would be a p o s i t i v e influence on the economy by providing necessary r i s k c a p i t a l to finance Canadian industry. Studies have shown that t h i s is not the case, in fact the Canadian pension funds have invariably concentrated their a c t i v i t y i n the stocks of large, "blue chip" companies. A study of the Canadian equity markets by Professor G.R. Conway of York University under the j o i n t sponsorship of the Federal government and the Toronto 3 Stock Exchange demonstrates t h i s concentration. Conway's sample of trusteed plans accounted for 51 percent of the t o t a l market value of stocks in a l l trusteed plans and 93 percent of these equity investments were in the stocks of the 101 largest Canadian l i s t e d companies. One reason for the concentration of funds i n t h i s group of stocks by the pension funds, as well as the l i f e insurance companies and the mutual funds, i s the growing need for l i q u i d i t y which issues of small, t h i n l y c a p i t a l i z e d companies can-not o f f e r . 2M.A. Hasley, The Importance of Pension Planning  in the Economy, in Pension Planning i n Canada, The Canadian In s t i t u t e of Chartered Accountants, Toronto, 1970, p. 4. 3 I b i d . , p. 3. 11 The evidence presented thus far seems to support the contention that pension funds, because of t h e i r s i z e , could have some impact on the Canadian equity market. Chapter I I I w i l l summarize the evidence presented in Chapters I and II and examine the implications of t h i s evidence. 12 Chapter III Summary and Implications The purpose of t h i s chapter i s to summarize the evidence presented in previous chapters and to examine what implications t h i s evidence may have for the Canadian equity market. Chapter I discussed the rapid growth of trusteed pension plan assets, enabling pension plans to become the t h i r d largest Canadian f i n a n c i a l i n s t i t u t i o n in terms of t o t a l assets. Increased competition, by stressing invest-ment performance, could see the trusteed plans improve th e i r r e l a t i v e p o s i t i o n i n the f i n a n c i a l system in years to come by a t t r a c t i n g plans from other types of funding arrangement. Chapter II revealed the fact that the trusteed pension plans alone could have absorbed more than h a l f of net hew issues of Canadian equity, had these funds been active in this segment of the market. I t was discovered that the trusteed pension funds were not active in t h i s market for new issues and in f a c t were concentrating t h e i r investments in the stock of the largest 101 Canadian companies. For segmentation of this market to occur i t would be necessary for the majority of the funds to be 13 moving in a si m i l a r pattern. I t i s reasonable to assume some common movement as the bulk of the trusteed pension funds are managed by a r e l a t i v e l y small number of t r u s t companies most of which are exposed to the same invest-ment research. In a si t u a t i o n where a small number of t r u s t companies are managing a large volume of investment funds, concentrated in a small group of Canadian common stocks, we could expect to be able to i d e n t i f y a difference in the price behaviour of these pension fund stocks i n comparison with other stocks. I f t h i s market p r i c e behavior i s evident i t would be revealed by a s i g n i f i c a n t l y d i f f e r e n t rate of return for the two groups of stocks. The s u p e r f i c i a l evidence seems to indicate the strong p o s s i b i l i t y of a market impact by the invest-ment of trusteed pension funds. Chapter IV w i l l present a study that empirically tests for any inpact. 14 Chapter IV Empirical Study 1. Introduction The purpose of t h i s chapter is to empirically t e s t the hypothesis that the aggregate a c t i v i t y of pension funds i n the Canadian equity market has created a seg-mentation of that market. Previous chapters have shown that pension funds do command a powerful p o s i t i o n in the Canadian equity market and i f t h i s has an impact on the price of stocks purchased by pension funds i t should be revealed by a s i g n i f i c a n t difference in the rate of return earned on these stocks versus other non-pension stocks. The following sections of this chapter w i l l present the te s t of t h i s hypothesis and any r e s u l t s . 2. Data and Method The sample of stocks used in this study was obtained from the Canadian Compustat Data f i l e s and from The F i n a n c i a l Post's l i s t i n g of the Toronto Stock Exchange i n d u s t r i a l stocks. The sample consisted of 359 Canadian i n d u s t r i a l stocks, 113 of which were i d e n t i f i e d as pension fund stocks 15 and 246 as non-pension fund stocks. To be included in the sample a stock must have been available for trading during December of 1964. Once i d e n t i f i e d as either a pension or a non-pension stock the two groups were arranged by price range and price-earnings r a t i o as indicated in Table 5. As the pension funds concentrate t h e i r a c t i v i t y i n the higher priced, higher p r i c e -earnings ranges i t would be of interest to i d e n t i f y in what price-earnings range a difference of rate of return a c t u a l l y occurred. For each group, pension and non-pension, and for each price-earnings range, a table of random d i g i t s was used to s e l e c t 30 stocks for each p o r t f o l i o , as of December 19, 1964.^ A t o t a l of ten p o r t f o l i o s were selected. As indicated in Table 5 only the twenty-plus price earnings range for the pension stocks had a complete p o r t f o l i o of 30 stocks. The small number of stocks (three) in the 0 - 8 price-earnings range would cast doubt on the r e l i a b i l i t y of any r e s u l t s from th i s grouping. Of the f i v e non-pension p o r t f o l i o s only the 17 - 19 price-earnings range had less than the t h i r t y stocks in the random p o r t f o l i o . The p o r t f o l i o s were then weighted on a value basis with one share of each stock being purchased. The table was found i n : Donald L. Harnett, Introduction to S t a t i s t i c a l Methods, (Addison-Wesley Publishing Company, Inc., 1970), p. 516. 16 Table 5 Sample Of Stocks Selected For The Study As Of December 19, 1964. Pension Fund Stocks Price Ranges P/E Ranqes 0-5 6-12 13-19 20+ 0-8 - 1 1 1 3 9-12 4 - 2 8 14 13-16 - 5 7 16 28 17-19 - 3 1 16 20 20+ 1 3 11 33 48 Total 5 12 22 74 113 Non--Pension Fund Stocks P/E Ranges 0-5 6-12 Price Ranges 13-19 20+ 0-8 11 14 6 6 37 9-12 22 17 19 12 70 13-16 7 20 8 11 46 17-19 4 5 6 5 20 20+ 36 15 9 13 73 Total 80 71 48 47 246 17 The average annual rate of return of each random p o r t f o l i o was calculated over eight holding periods, one through eight years, and the r e s u l t s recorded in Table 6. The annual returns included both dividends and c a p i t a l gains or losses. In the non-pension group several firms were taken over or went into bankruptcy in which case a cash settlement was determined, which in turn was invested in treasury b i l l s . 3. Empirical Tests i) Differences in P o r t f o l i o Mean Returns Application of the " t " s t a t i s t i c w i l l indicate whether any s i g n i f i c a n t difference e x i s t s between the 5 mean returns of the two groups of stocks. This is an appropriate t e s t since the population variances i s unknown. The " t " t e s t requires the assumptions of normality of the population d i s t r i b u t i o n s , independence of the two samples as well as independence within each sample, and equality of the population variances. In this case i t is assumed the returns of the in d i v i d u a l s e c u r i t i e s are normally d i s t r i b u t e d . The second assumption of independence is ^The formula used to test for the difference in means was found i n : John E. Freund, Elementary Business  S t a t i s t i c s : The Modern Approach, (Prentice-Hall, Inc., Englewood C l i f f s , N.J., 1964), p. 294. x l ~ X2  t = IZiXi - Xj)* + Z ( x 2 - x2)z, / i + 1 \ J n i + n 2 - 2 U l N2J Table 6 Returns of Randomly Selected Po r t f o l i o s Over Various Holding Periods Holding Period P/E Ranqe One Year Two Years Three Years Four Years P/E 0-8 Non- Non- Non- Non-Pension Pension Pension Pension Pens ion Pens ion Pension Pension x return 0.2216 0.3170 0.0546 0.0971 0.0418 0.0913 0.0602 0.1550 0.9129 0.4438 0.0015 0.0579 0.0037 0.0340 0.0056 0.0363 " t " test 0.2444 0.6780 0.4575 0.8457 "F" test 34,4031 38.6000 0.1891 6.4821 P/E 9-12 x return 0.3128 0.0562 0.0663 -0.0145 0.1384 0.0266 0.2018 0.1120 0.0800 0.1151 0.0405 0.0749 0.0809 0.0691 0.0520 0.0619 " t " t e s t 2.4602* 0.9854 1.2806 1.1454 "F" t e s t 1.4388(A) 1.8494(A) 1.1708(A) 1.1904(A) P/E 13-16 x return 0.1170 0.0668 0.0278 0.0013 0.0663 0.0882 0.0846 0.1159 •cr7- 0.0743 0.0809 0.0520 0.0669 0.0562 0.0460 0.0316 0.0408 " t " t e s t 0.6858 0.4134 0.3693 0.6260 "F" te s t 1.0888(A) 1.2865(A) 1.2217(A) 1.2911(A) P/E 17-19 x return 0.0449 0.0642 -0 .0486 -0.0137 -0 .0123 0.0516 0. 0239 0.1239 0.0347 0.1999 0 .0107 0.0483 0 .0142 0.0570 0. 0083 0.0228 " t " t e s t 0.1776 0.6415 1.0668 2.5157* "F" t e s t 5.7608(R) 4.5140(R) 4.0141(R) 2.7469(R) P/E 20+ • 5c" return 0.0706 0.2178 -0 .0031 0.0144 0 .0497 0.0596 0. 0816 0.1910 0.0399 0.5286 0 .0295 0.1055 0 .0274 0.0940 0. 0141 0.1195 " t " test 1.0697 0.2612 0.1557 1.6402 "F" te s t 13.2481(R) 3.5762(R) 3.4306(R) 8.4751(R) <r - Sample variance (A) - Accept hypothesis of equal (R) - Reject hypothesis of equal population population variance variance * _ s i g n i f i c a n t at the .05 l e v e l Table 6 Continued Returns of Randomly Selected P o r t f o l i o s Over Various Holding Periods Hold ing Period P/E Range Five Years Six Years Seven Years Eight Years Non- Non- Non- Non-P/E 0-8 Pension Pension Pens ion Pens ion Pens ion Pens i on Pension Pension x return 0 .0516 0.1054 0. 0307 0.0515 0.0596 0.0498 0.1015 0.0622 0 .0049 0.0167 0. 0057 0.0147 0.0042 0.0132 0.0064 0.0186 " t " test 0.7051 0.2897 0.1443 0.4870 "F" te s t 3.4082 2.5789 3.1429 2.9063 P/E 9-12 x return 0 .1415 0.0871 0. 0607 0.0307 0.0739 0.0375 0.1127 0.0457 0 .0399 0.0406 0. 0223 0.0218 0.0157 0.0188 0.0121 0.0129 " t " t e s t 0.8369 0.6263 0.8445 1.8457 "F" te s t 1.0175(A) 1.0229(A) 1.1975(A) 1.0661(A) P/E 13-16 x return 0 .0522 0.0483 0. 0344 0.0171 0.0273 0.0157 0.0456 0.0406 0 .0117 0.0148 0. 0089 0.0147 0.0074 0.0131 0.0058 0.0108 " t " test 0.1291 0.6049 0.4328 0.2083 "F" t e s t 1.2649(A) 1.6517(A) 1.7703(A) 1.8621(R) P/E 17-19 x return 0 .0239 0.0513 -0. 0007 0.0415 0.0076 0.0409 0.0273 0.0603 0 .0089 0.0123 0. 0061 0.0056 0.0072 0.0029 0.0115 0.0078 " t " t e s t 0.8303 1.7154 1.4669 1.0043 "F" t e s t 1.3820(A) 1.0893(A) 2.4828(R) 1.4744(A) P/E 20+ x return 0 .0518 0.1182 0. 0148 0.0606 0.0495 0.0576 0.0658 0.0761 0 .0092 0.0612 0. 0102 0.0308 0.0075 0.0235 0.0083 0.0171 " t " test 1.3719 0.5081 0.2523 0.3539 "F" t e s t 6.6522(R) 3.0196(R) 3.1333(R) 2.0602(R) 20 reasonable as the samples were drawn randomly. The t h i r d assumption of equality of population variance w i l l be tested by use of the "F" s t a t i s t i c . The ",.t" s t a t i s t i c as calculated for each pair of returns over a l l price-earnings ranges and for a l l eight holding periods, is recorded in Table 6. i i ) Equality of Population Variance To t e s t the t h i r d assumption of the " t " s t a t i s t i c we w i l l use the "F" d i s t r i b u t i o n , which is the r a t i o of g the variances of two independent random samples. To use t h i s t e s t to determine the p r o b a b i l i t y that the two samples were drawn from populations having the same variance the assumption of a normal parent population must hold. The "F" values for each pair of returns is recorded below the " t " values in Table 6. i i i ) Differences i n the Means of Pooled Samples If the " t " t e s t f a i l s to indicate any s i g n i f i c a n t difference between the mean returns of the two groups then ^The r a t i o F = S^/s^ follows an F d i s t r i b u t i o n with V]_ = n]_ - 1 and V 2 * n 2 - 1 degrees of freedom where 2 S1 = the variance of p o r t f o l i o 1 2 S~ => the variance of p o r t f o l i o 2 21 there is an advantage in pooling the sample values to get an unbiased estimated. I t i s then possible to test for a difference in the weighted means of the pooled samples. As the sample size is now reasonably large (>30) a normal "Z" t e s t can be applied to determine any •7 difference in means.' These pooled estimates are a c t u a l l y weighted averages of the estimates from the two samples. The advantage of pooling l i e s in the fact that the sampl-ing error w i l l tend to be smaller for the pooled estimate Q than that for any single sample's value taken alone. The r e s u l t s of this pooling are reported i n Table 8. 4. Empirical Results i) Changes i n Price-Earnings Ratios I f a s i g n i f i c a n t l y higher return i s found for the pension fund group, thereby indicating upward market p r i c e behavior, i t becomes important to determine the cause of t h i s p r i c e behavior. I f the price of a pension stock was to r i s e sub-s t a n t i a l l y with no apparent increase in earnings then this could be evidence of the pension funds having an impact on 'For the formula used to calculate the weighted means see Appendix A. Q William L. Hays and Robert L. Winkler, S t a t i s t i c s ;  P r o b a b i l i t y , Inference, and Decision (Holt, Rinehart and Win ton, Inc., N.Y., 1971), p. 324. 22 stock p r i c e s . For the pension funds to have a s i g n i f i -cant impact on the price of a stock we must observe an upward trend in the price-earnings r a t i o s of the pension fund stocks over the period of study. Any s i g n i f i c a n t results should be evident in Table 7, which shows the proportion of each group of stocks that moved either up or down one price-earnings range over three selected holding periods. No s i g n i f i c a n t patterns can be found in Table 7. I t is i n t e r e s t i n g to note that over the eight year period as many stocks moved up as moved down in the 13-16 and the 17-19 price-earnings ranges. Over this period the average price-earnings r a t i o of the Toronto Stock Exchange I n d u s t r i a l Index remained within the 17-19 price-earnings range. i i ) Sample Means The f i r s t empirical t e s t performed i n the previous section was the " t " t e s t to determine i f there was a s i g n i f i c a n t difference between the mean returns of the pension stocks and the non-pension stocks. The results as shown in Table 6 indicate no s i g n i f i c a n t difference between means at the .01 l e v e l of s i g n i f i c a n c e . However in two cases there was a s l i g h t l y s i g n i f i c a n t difference at the .05 l e v e l . The p o r t f o l i o of pension fund stock in the 9-12 price-earnings range earned a s i g n i f i c a n t l y higher mean return than the non-pension 23 Table 7 Changes in Price Earnings Ratios Over Selected Holding Periods Pens ion Stocks Non-Pension Stocks % Up % Down % Up % Down One-Year Holding Period P/E 0-8 100.00 9-12 21.43 13-16 32.16 17-19 15.00 20+ 25.00 45.00 33.33 43.24 32.86 28.26 5.00 18.57 30.43 70.00 20.55 Four-Year Holding Period P/E 0-8 66.67 - 61.11 9-12 92.85 - 65.08 8.00 13-16 39.30 25.00 52.50 30.00 17-19 35.00 50.00 61.10 38.89 20+ - 29.16 - 26.08 Eight-Year Holding Period P/E 0-8 33.33 - 76.67 9-12 57.14 7.14 56.85 15.70 13-16 35.71 32.14 40.00 47.20 17-19 35.00 45.00 60.00 35.30 20+ - 64.58 - 47.70 24 p o r t f o l i o over a one year holding period. In the second case the non-pension fund p o r t f o l i o earned a s i g n i f i c a n t l y higher mean return than the pension p o r t f o l i o over the price-earnings range 17-19 for a holding period of four years. I f a s i g n i f i c a n t " t " value is reported i t can be substantiated to some extent by the "F" s t a t i s t i c . i i i ) Sample Variance I f the " t " t e s t is to be accepted i t must f u l f i l l the requirement that the populations from which the samples were drawn have the same variance. The "F" s t a t i s t i c was calculated for each p a i r of sample variances and reported i n Table 6. As the pension fund sample in the 0-8 price-earnings range contained only 3 stocks, no inferences w i l l be made regarding the results of tests in t h i s grouping. For the other four price-earnings groups, however, 18 of 32 "F" s t a t i s t i c s were accepted indicating that these p a r t i c u l a r samples were drawn from populations of equal variance. iv) Pooled Sample Means If either group of stocks was to earn a higher return i t should become evident in a pooled sample where the means of the d i s t r i b u t i o n were weighted. This i s not the case as Table 8 indicates there was no s i g n i f i c a n t difference between these two groups. 25 Table 8 Means of the D i s t r i b u t i o n of Weighted Means Holding Period Pens ion Stocks One year Z Two years Z Three years Z Four years Z Five years Z Six years Z Seven years Z Eight years Z 0.1194 0.0085 0.0543 0.0874 0.0593 0.0331 0.0380 0.0598 " Z " S t a t i s t i c 0.1143 0.0705 0.0675 0.3963 0.2553 0.0880 0.0302 0.0434 Non-Pension Stocks 0.1507 0.0194 0.0644 0.1407 0.0845 0.0402 0.0402 0.0567 26 5. Conclus ion Although the pension fund stocks in the 9-12 pric e earnings range earned a s i g n i f i c a n t l y higher return than the non-pension stocks, very l i t t l e importance can be placed on t h i s r e s u l t . The " t " s t a t i s t i c was so close to the c r i t i c a l value at the .05 l e v e l that any strong conclusions would be highly suspect. While i n i t i a l evidence seems to indicate that the pension funds command a strong p o s i t i o n in the market for Canadian equities, the empirical results of this study indicate t h i s large concentration of funds has l i t t l e impact on the market pr i c e of the stocks in which the pension funds invest. The pension funds concentrate t h e i r investments in the higher priced, higher price-earnings common stocks mainly because the stocks of smaller t h i n l y c a p i t a l i z e d campanies lack the l i q u i d i t y necessary to allow a large investment by an i n s t i t i t u t i o n of this s i z e . Legal r e s t r i c t i o n s l i m i t i n g a pension fund to a maximum of 10 percent of the outstanding stock of any one company could also account for the concentration i n the higher priced stocks. 27 Bibliography Freund, John E., Elementary Business S t a t i s t i c s : The Modern Approach, (Prentice-Hall, Inc., Englewood C l i f f s , New Jersey, 1964) . Harnett, Donald L., Introduction to S t a t i s t i c a l Methods, (Addison-Wesley Publishing Company, Inc., 1970). Hasley, M.A., The Importance of Pension Planning in the Economy, in Pension Planning in Canada, The Canadian Inst i t u t e of Chartered Accountants, Toronto, 1970. Hays, William L. and Robert L. Winkler, S t a t i s t i c s : P robability, Inference, and Decision, (Holt, Rinehart and Winston, Inc., New York, 1971). Pedoe, Arthur, L i f e Insurance, Annuities and Pensions, (University of Toronto Press, Toronto, Canada, 1970). 28 Appendix A Formula For Calculation Of Weighted Means i f x = the pension fund group y = the non-pension fund group l e t Wix = Ni and wiy = Ni ."i Ni Ni where: Ni = the number of s e c u r i t i e s in the i t h p o r t f o l i o , 1 ^ 1/ m m 9 9 5 then W x = ^  wix X i and Wy = wiy Y i and _ 5 o _ Var(wx) = j> (Wix) ^ Var x i Var(Wy) = ^ ( w i y ) 2 V a r y i and Z = Wx - Wy yvar(Wx) + Var (Wy) 

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