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On the relationship between stock prices and the quantity of money Martinoff, Michael 1970

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ON THE RELATIONSHIP BETWEEN STOCK PRICES AND THE QUANTITY OF MONEY by MICHAEL MARTINOFF B.A., University of B r i t i s h Columbia, 1969 A Thesis Submitted i n P a r t i a l Fulfilment of the Requirements for the Degree of MASTER OF BUSINESS ADMINISTRATION i n the Faculty of Commerce and Business Administration We accept this as conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA September, 1970 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Bri t i s h Columbia, I agree that the Library shall make it freely available for reference and study. I further agree tha 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 September 22,, 197Q. ABSTRACT The old Quantity Theory of the Value of Money can be expressed as the "Equation of Exchange," MV=PT, i n which M i s the quantity of money, V i s the v e l o c i t y of c i r c u l a t i o n of money, P i s the p r i c e l e v e l , and T i s the t o t a l number of transactions during the period under con-s i d e r a t i o n . The major shortcoming of the old Quantity Theory was that v e l o c i t y (V) was taken to be numerically constant, which i t i s not. The new Quantity Theory i s a theory of the demand f o r money as an asset, productive c a p i t a l y i e l d i n g a stream of income i n the form of convenience, s e c u r i t y , and so on. According to t h i s theory, people hold p o r t f o l i o s containing money, bonds, e q u i t i e s , and other assets, and they adjust t h e i r p o r t f o l i o s so that they obtain the maximum returns therefrom. The demand f o r money can be expressed i n terms of the demand fo r other assets ( i n r e a l terms), the behaviour of the general p r i c e l e v e l , people's u t i l i t y preferences, and t h e i r t o t a l wealth. Given a function describing t o t a l income, an equation describing the v e l o c i t y of c i r c u l a t i o n of money can be w r i t t e n as the quotient of the income function divided by the demand f o r money function. This i s the d i f -ference between the new and old Quantity Theories: under the o l d , the v e l o c i t y of money was considered to be a numerical constant; under the new i t i s described as a function of income and the demand f o r money. In accordance with the above theory, when a monetary disturbance i s introduced by the cen t r a l bank, people w i l l want to adjust t h e i r portfolios in such a way as to compensate for the disturbance. The i n i t i a l impact of the monetary disturbance i s in the markets for the most l i q u i d assets: the f i n a n c i a l markets. This idea was tested by correlation analysis on Canadian data of money supply and stock prices and variants thereof for the years 1924 - 1967. Even after the influence of trend had been removed from the data, s t a t i s t i c a l support was found for the above theory, but only after the influence of random variation had been reduced by six-month moving averaging. However, the evidence—a s i g n i f i c a n t correlation of .259 between percent change i n money and percent change i n stock prices—suggests that monetary change accounts for only about 6.7 percent of the variation i n stock prices. But this conclusion must be tempered by the r e a l i s a t i o n that variable lags of the same nature as those that exist between monetary change and change i n the l e v e l of business a c t i v i t y can be expected to exist between monetary change and change i n the l e v e l of stock prices. Thus i t can be argued that the results of correlation analysis tend to understate the actual impact of monetary change on stock prices. TABLE OF CONTENTS CHAPTER Page I. Introduction 1 II. The Quantity Theory of the Value of Money 3 III. Data, S t a t i s t i c a l Tests, and Results Thereof 16 IV. Analysis of the Results 20 V. Conclusions 25 Bibliography 26 Appendix: The Computer Programme Used 27 CHAPTER I INTRODUCTION A competent economist wrote: Both monetary change and stock prices lead business cycle turning points, and both series can, therefore, be cl a s s i f i e d as leading indicators of economic a c t i v i t y . But since monetary changes have a longer lead over business cycle turning points than do stock prices, i t follows that monetary change leads stock prices. It was an awareness of these simple leading relationships that was responsible for sparking the i n v e s t i -gations .. .which have turned up additional evidence bearing on the pervasive influence of monetary change.^ Sprinkel examined data of stock prices and monetary growth i n the United States. For money he used currency plus demand deposits, because this definition yielded better results than did any other. Sprinkel said that a positive relationship exists between stock prices and changes i n monetary growth, and he presented evidence i n support of his claim; he did not perform s t a t i s t i c a l tests. The purpose of this paper i s to see i f there i s a relationship between stock prices and the quantity of money. A positive relation-ship between stock prices and changes i n monetary growth—confirmation of Sprinkel's work—would be expected. Beryl W. Sprinkel, Money and Stock Prices (Homewood, 111. Richard D. Irwin, Inc., 1964), p. 115. Since the Bank of Canada controls the quantity of money i n Canada, the quantity of money i s taken to be exogenously determined. Thus interest i s focused on two areas: f i r s t l y , a p r i o r i reasons why stock prices should respond to changes i n the quantity of money; and secondly, empirical evidence of such a relationship. Empirical evidence cannot, of course, provide proof, which i s possible only through l o g i c ; however, i t i s assuring to find empirical support for one's a p r i o r i reasoning. In Chapter II the Quantity Theory of the Value of Money i s d i s -cussed. Both the old Quantity Theory and the new are described, and the deficiencies of the old are seen. The theory of how monetary d i s -turbance affects f i r s t the f i n a n c i a l markets and l a t e r the markets for goods and services i s described. In Chapter III the s t a t i s t i c a l tests performed and the results thereof are presented. In Chapter IV the results are analysed. Chapter V contains the conclusions. CHAPTER II THE OUANTITY THEORY OF THE VALUE OF MONEY In this chapter both the old Quantity Theory and the new are described, and the deficiencies of the old are seen. The theory of how monetary disturbance affects f i r s t the f i n a n c i a l markets and l a t e r the markets for goods and services i s described. Though he was not the f i r s t to write about the old Quantity Theory of the Value of Money, Fisher"'' expressed the idea of the old Quantity Theory i n his "Equation of Exchange," MV=PT, i n which, during a given period of time, M i s the quantity of money (cash plus demand deposits), V i s the velocity of money, which i s the average rate of turnover of money i n i t s exchange for goods and services, P i s the average of the prices struck i n a l l transactions i n the economy, and T i s the number of transactions. This equation i s written as an identity because i t i s true by de f i n i t i o n . However, before the identity can be applied to the real world to y i e l d p r a c t i c a l results i t must be reformulated as an hypothesis explaining a relationship between dependent and independent variables, for example: T r PT MV V = — or P = — . Irving Fisher, The Purchasing Power of Money, The Controversy over the Quantity Theory of Money, Studies i n Economics, ed. by Edwin Dean (Boston: D.C. Heath and Company, 1965), p. 9-28. The former formula can be considered a d e f i n i t i o n of velocity; the l a t t e r , a theory about prices. It i s i n this l a t t e r form that the Quantity Theory was usually considered. It may be argued that M, V, and T are the independent variables for the following reasons: M i s determined by the monetary authorities; T i s determined by the l e v e l of real production i n the economy, because a l l exchanges are r e a l l y exchanges of real goods and services—money i s only an intermediary; V i s determined by i n s t i t u t i o n a l factors, such as the frequency of payment of wages. Therefore P turns out to be the dependent variable, as would be expected from the microeconomic theory of perfect competition, according to which prices always adjust to equate quantity supplied to quantity demanded, and thus clear the market. Thus there are three independent variables: M, V, and T. A change i n M or V produces a proportional change i n P; a change i n T produces an inversely proportional change i n P. If M drops 50 percent overnight, then the next morning a l l prices w i l l drop 50 percent, and a l l factors of production w i l l remain f u l l y employed. However, i t doesn't appear to work that way. Prices are not that f l e x i b l e ; markets are not that perfect. Changes i n M produce changes i n V and T as well as i n P. For example, as the rate of expansion of M declines, V tends to increase because the interest rate has tended to r i s e , causing firms to try to reduce their holdings of cash. Factors other than M are at work as well. For example, i t has been found that 5. as real incomes r i s e people tend to hold more than proportionately greater amounts of money; consequently V has shown a long-term secular decline. Thus i s can be seen that although the old Quantity Theory i s necessarily b a s i c a l l y sound, (because i t i s based on an iden t i t y , MV=PT) i n this basic form i t i s i n s u f f i c i e n t l y comprehensive to be able to be applied to the real world to y i e l d p r a c t i c a l results. This short-3 coming was remedied i n the new Quantity Theory." The new Quantity Theory i s a theory of the demand for money. Here money i s treated as an asset, productive cap i t a l yielding a stream of "income." In the context of this theory, t o t a l wealth includes a l l sources of consumable services, even the productive capacity of human beings, "Income" here i s a net concept; that i s , an allowance must have been made for maintaining productive capacity intact. Income may also be considered to be the l e v e l of consumption of services that could be maintained i n d e f i n i t e l y . Wealth i s equal to income divided by the rate of interest. Various forms of wealth are available to the wealth-holder. These forms of wealth d i f f e r from each other not only i n their market See Milton Friedman, The Demand for Money: Some Theoretical and Empirical Results, i n his The Optimum Quantity of Money and Other Essays (Chicago: Aldine Publishing Company, 1970), pp. 111-139. 3 See Milton Friedman, The Quantity Theory of Money: A Restatement, Ibid., pp. 51-67. prices, but also i n the forms and sizes of the income streams they y i e l d . Wealth may be held as: 1) money, claims that are generally accepted i n payment of debts at a fixed nominal value; 2) bonds, claims to time streams of payments that are fixed i n nominal units; 3) equities, shares i n the returns of enterprises; 4) physical non-human goods, such as consumer durables; and 5) human c a p i t a l . Each of these forms of wealth yields a return. Money yields a r e t u r n — a s e r v i c e — i n the form of convenience and security. The real value of this return depends, of course, on the quantity of real goods and services that a given amount of money can buy; that i s , i t depends on the general price l e v e l . This i s true of other forms of wealth as well; the price l e v e l affects the real value of their y ields. The real return from holding wealth in the form of a bond depends on three things: the periodic (coupon) payment, fixed in nominal amount; the change in the price of the bond over time; and, as above, the price l e v e l . Equities are similar to bonds; that i s , the real value of their y i e l d i s based on the same considerations, except that the periodic pay-ment i s not fixed in nominal amount; indeed, to the extent that the return on an equity rises with the price l e v e l , .an equity may be considered to y i e l d an income stream of constant real value. 7. Physical capital goods y i e l d a return i n kind. The nominal value of this y i e l d , l i k e the y i e l d on equities, depends on the price l e v e l . So also does human capit a l y i e l d a return i n kind. In a non-slave society i t i s not possible to specify market prices of human cap i t a l , and obstacles exist to investment and disinvestment i n human cap i t a l . However, direct investment i n a human can take place under some circumstances; for instance, a man can invest i n himself through education. Thus far six considerations have been introduced; the price l e v e l and the real values of the rates of return on the fi v e forms of wealth. Two more considerations remain to be introduced. The quantity of each form of wealth i n a wealth holder's port-f o l i o w i l l be influenced by his u t i l i t y preferences (he w i l l want to maximise expected u t i l i t y ) and by his t o t a l wealth. Recall that t o t a l wealth may be considered to be equal to t o t a l income divided by the interest rate, where income i s considered to be the return to a l l forms of wealth, including the non-monetary returns arising from the holding of money, physical capital goods, and human ca p i t a l . Eight considerations have been introduced; these considerations determine the quantity of each form of wealth that a wealth holder w i l l hold i n his p o r t f o l i o . Thus the quantity of money which wealth holders w i l l hold can be expressed as a function of the seven other considera-tions: 8. real return on bonds real return on equities re a l return on physical cap i t a l goods Demand for money = f real return on human capital behaviour of the general price l e v e l u t i l i t y preferences t o t a l wealth simplified, M = f (X) Observe that although the above matters were introduced i n the context of the individual wealth holder as a person, analogous considera-tions apply to business enterprises as wealth holders; the l a t t e r are concerned with the cost of productive services, the cost of substitute productive services, and the value of the product yielded by productive services. Notice that i f income (Y = PT) i s given, then dividing Y by M yie l d s an equation describing the velocity of money i n terms of the determinants of the demand for money: * Y Y M = fOO = v ( x ) * Thus the "Equation of Exchange" i n which the old Quantity Theory was cast can be seen to be a limited application of equation *, a limited application i n which the velocity of money was considered to be i f not constant at least numerically stable. 9. At this point the same question that arose with respect to the old Quantity Theory again arises: how can this theory be applied to the real world to yie l d practical results? The s t a b i l i t y and importance of the demand function for money and the independence of the factors affecting demand for and supply of money must be considered. Of what use i f the new Quantity Theory i f the demand for money i s a highly unstable f u n c t i o n , or i f the factors affecting demand for and supply qf money are interrelated? Consider the la%%er- point f i r s t . Under a fractional reserve banking system the total amount of money i n circulation i s equal to the monetary base (in a f i a t money system, the l i a b i l i t i e s of the central bank; sold, under a pure gold standard) plus the demand deposits created by the banking system through fractional reserve operation, Thus i f the reserve ratio i s r, and the monetary base i s Z, then the total amount of money in circulation i§ equal to Z/r, The legal reserve ratio i s prescribed. However, because reserves required as legal reserves cannot be used as operating reserves, banks keep actual reserves in excess of legal reserves. Consequently the actual reserve ratio i s somewhat larger than the legal reserve r a t i o , and the amount of money actually i n circulation i s somewhat smaller than .the amount which would be i n c i r -culation i f the banks were to keep only reserves legally required, The amount of excess reserves to be kept i s in the banks' dis-cretion. Thus i t can be seen that even i f the central bank holds the monetary base constant, the money supply can vary i n accordance with the bank's inclinations %§ hold excess reserves, During an upswing in 10. business a c t i v i t y , when the demand for money increases, and interest rates r i s e , banks should be inclined to reduce their excess reserves, due to the higher opportunity cost of holding them. This policy w i l l cause the effective money supply to rise (in response to an increase i n the demand for money) even i f the central bank holds the monetary base constant. Notice that a monetary base of Z can be expanded into a money supply of Z/r only i f a l l Z of the monetary base i s put into the banking system. But currency i s part of the monetary base, and people tend to want to hold currency, because of i t s l i q u i d i t y . Furthermore, the ratio of currency to deposits that they w i l l hold varies according to their inclinations. It can be seen that by varying their holdings of currency the people can cause the money supply to vary even i f the central bank holds the monetary base constant. The same process, mutatis mutandis, can cause monetary contrac-tion, i n response to a decrease in the demand for money, or to an increase in the banks' demand for excess reserves, or to an increase in the people's demand for currency. Indeed, the great depression was caused not really by the Fed's contracting the monetary base, but rather by the banks' reducing the money supply by trying to increase their excess reserves and by the people's contracting the money supply by 4 increasing their currency holdings. Milton Friedman, The Great Contraction 1929 - 1933 (Princeton, New Jersey: Princeton University Press, 1965), p. 46. 11. The onset of the [ f i r s t ] banking c r i s i s i s clearly marked i n a l l three proximate determinants but p a r t i c u l a r l y i n the deposit ra t i o s . From a peak of 11.9 i n October 1930, the ratio of deposits to currency declined s h a r p l y — a decline that was to carry the r a t i o , with only minor interruptions along the way, to a low of 4.4 i n March 1933. The deposit-reserve ra t i o likewise began a decline that was to carry i t from a l e v e l of 12.9 i n October 1930—the a l l -time high was 13.4 i n A p r i l 1929—to a l e v e l of 8.4 i n March 1933. These declines brought the deposit-currency ra t i o back to i t s l e v e l i n 1912. They thus wiped out the whole of the much heralded spread i n the use of deposits and 'economy' i n reserves achieved under the Reserve System.^ It can be seen that the supply of money can vary i n response to the demand for i t ; however, should the central bank not want the money supply to vary, i t can, through open market operations, cause the monetary base to vary i n such a way as to offset other changes such as changes i n the deposit-currency and deposit-reserve ratios which would otherwise cause the money supply to vary, as described above. Thus possible variations i n the deposit-reserve ratio and i n the deposit-currency ratio present no obstacle to the application of the new Quantity Theory. Consider now the former point. Of what use i s the new Quantity Theory i f the demand for money i s a highly unstable function? Very l i t t l e . But the demand for money has been shown empirically to be highly stable; Friedman mentions several studies. One cannot read Lerner's description of the effects of mone-tary reform i n the Confederacy i n 1864 without recognizing that at least on occasion the supply of money can be a largely autono-mous factor and the demand for money highly stable even under 5 I b i d . See Friedman, Optimum Quantity, pp. 64-65. 12, extraordinarily unstable circumstances. After three years of war, after widespread destruction and military reverses, i n the face of impending defeat, a monetary reform that succeeded in reducing the stock of money halted and reversed for some months a rise in prices that had been going on at the rate of 10 per cent a month most of the war! It would be hard to con-struct a better controlled experiment to demonstrate the c r i t i -cal importance of the supply of money.7 In summary thus far, the new Quantity Theory is a theory of the demand for money as a productive asset. The demand for money has been g found empirically to be highly stable. An equation describing the velocity of money can be derived from the demand for money. This i s the difference between the new Quantity Theory and the old: under the old the velocity of money was considered to be stable, a numerical constant; under the new i t i s considered to be a stable function. The old Quantity Theory was unduly simple. Of what use i s the new Quantity Theory? It can be used to provide a means of relating monetary change, change i n stock prices, and 9 change i n the level of business a c t i v i t y . Consider an economy i n which real wealth and real GNP remain, for the sake of simplicity, constant, but i n which the money supply has been expanding at an annual rate of 5 percent for some time, producing a continuous increase i n the price level at an annual rate of 5 percent. The people have f u l l y adjusted to this annual rate of price increase, and expect i t to continue. ^Ibid., p. 64. 8 I b i d . , pp. 64-65. 9 I b i d . , pp. 229-235. 13. The people hold real wealth i n various forms: money, bonds, equities, physical capital goods, and human capital. Notice that i t i s real wealth that matters; the people's nominal money holdings, for example, increase at an annual rate of 5 percent, but the real value of these money holdings—the amount of real goods and services which can be received in exchange for these money holdings—remains constant, since the price level i s increasing at an annual rate of 5 percent. Suppose now that the central bank does not make i t s regular purchase of bonds, which would have enabled the money supply to con-tinue to grow; i t has introduced a monetary disturbance which, i t w i l l be seen, w i l l travel through the financial markets and eventually cause readjustment in the market for real goods and services. It i s assumed that the people already held the desired propor-tions of real assets i n their portfolios. Had the central bank made i t s regular purchase of bonds, the nominal value of the total stock of bonds i n the hands of the people would have continued to rise at an annual rate of 5 percent, and the real values of both the t o t a l stock of bonds and the total stock of money would have remained constant. However, now i t i s the nominal value of the money stock which remains constant; because of the 5 percent annual rate of increase i n the price l e v e l , the real value of the stock of money has begun to f a l l at an annual rate of 5 percent. Thus the actual proportions of real wealth which the people hold in their portfolios become different from the desired proportions. The people w i l l take action to restore equality between actual and desired real amounts of assets in their portfolios; 14. they w i l l s e l l bonds—driving down the prices of bonds—and buy money in order to reduce the relative amount of real bonds held and to increase the relative amount of real money held. But they are not s e l l i n g their bonds to the central bank (because i t isn't buying); consequently the money supply i s not growing. They are able to approach the desired ratio of the real value of their money holdings to the real value of their holdings of other assets only by s e l l i n g some of their other assets. After bonds, equities are most readily marketable, so they are sold as well as bonds. Disinvesting i n other assets, such as physical capital goods, i s not as easy as disinvesting i n bonds and equities, so these bear most of the burden of adjustment. As the nominal value of the money supply continues to remain constant—and thus the real value of the money supply continues to f a l l — the adjustment process which began i n the financial markets spreads to the markets for other assets. The prices of, for example, physical capital goods begin to f a l l . At this point the prices of the f i n a l goods and services provided by the physical capital goods (and human capital) are seen to be too high i n relation to the prices of the capital which is their source, and so the demand for these f i n a l goods and services f a l l s . Workers who choose to price their services above the market become unemployed. But now the monetary disturbance i s beginning to affect the f i n a l prices of goods and services. In time price r i g i d i t i e s (which i n this hypothetical economy meant annual price increases of 5 percent) are overcome, and the rate of increase inthe price level drops to zero. Now a new equilibrium Is reached i n which real and nominal values of assets are equivalent. 14a, To the extent that prices of a l l assets i n the economy did not adjust quickly to the decline i n the real value of the money stock, the burden of adjustment was borne excessively by the more l i q u i d assets. As the prices of the less l i q u i d assets and of f i n a l goods and services were brought into l i n e , a recovery i n the prices of the more l i q u i d assets was enabled. ...we should expect i t [monetary disturbance] to have i t s f i r s t impact on the financial markets, and there, f i r s t on bonds, and only later on equities, and only s t i l l l ater on actual flows of payments for real resources. This i s of course the actual pattern. The financial markets tend to revive well before the trough. His-t o r i c a l l y , railroad bond prices have risen very early i n the process. Equity markets start to recover later but s t i l l generally before the business trough. Actual expenditures on purchases of goods and services r i s e s t i l l later.10 In summary, then, this i s what happened i n the economy under consideration: 1) The economy was in equilibrium; actual holdings of real assets were equal to desired holdings. 2) A monetary disturbance was introduced; the real value of the stock of money began to decline. 3) In order to maintain the desired ratio of real money to other real wealth people began to s e l l l i q u i d assets, driving down their prices. 4) In time the process of adjustment spread to the markets for less l i q u i d assets, and recovery i n the financial markets was enabled, as the economy approached a new equilibrium. Ibid., pp. 231-232. 1 5 . Of course i n p r a c t i c e , given that neither the Bank of Canada nor the Fed has pursued a p o l i c y of constant monetary expansion, e q u i l i b r i u m has not been reached: rather, the economy has been required to adjust to disturbance a f t e r disturbance. Now i t i s possible to state the hypothesis to be tested i n t h i s paper: that, on the basis of the above new Quantity Theory, a s t a t i s -t i c a l l y t e s t a b l e r e l a t i o n s h i p e x i s t s between the behaviour of the money supply and the behaviour of stock p r i c e s . More s p e c i f i c a l l y , a p o s i t i v e c o r r e l a t i o n between money and stock p r i c e s , and between stock p r i c e s and changes i n monetary growth, would be expected. CHAPTER I I I DATA, STATISTICAL TESTS, AND RESULTS THEREOF In this chapter the s t a t i s t i c a l tests performed are b r i e f l y described, and the results thereof are presented. More detailed analy-sis follows i n Chapter IV. Data describing stock prices and seasonally adjusted cash and 1 demand deposits i n Canada for the years 1924-1967 were collected. Correlation analyses on several pairs of variables, l i s t e d i n Table I and described below and further explained i n Chapter IV, were run; lags 2 of up to +120 to -120 months were introduced, i n order to see i f better-results could be obtained i n this way than without lags. Since a lag exists between the beginning of a monetary disturbance and the beginning """Money supply was considered to be cash plus demand deposits. The Dominion Bureau of Statis t i c s index of total common stock prices was used for Stock prices. Data on cash, demand deposits, and stock prices were taken from the Dominion Bureau of Statis t i c s S t a t i s t i c a l Summary Supplements. Periodically there were discontinuities i n the series; at each of these points an adjustment ratio was calculated and the data were adjusted accordingly. The adjustment ratio was calcu-lated i n this fashion: at a point at which the two discontinuous parts of the series overlapped the datum for the new part and the datum for the earlier part were observed and the ratio new datum'old datum was calculated. The earlier data were then multiplied by this ratio. 2 Each test was run i n i t i a l l y with lags of +24 to -24 months; i t was thought that longer lags were a. p r i o r i unreasonable. However, in those tests i n which trend was an influence—explained further in this chapter and i n the following chapter.—the highest correlations appeared at the longest lags. Consequently, these tests were re-run with progressively longer lags, up to 120 months. 17. of a reaction i n the level of business a c t i v i t y , a lag might also be expected to exist between the beginning of a monetary disturbance and the beginning of a reaction i n the stock market. Test //l was quite straightforward: money vs. stock prices. The correlation results of test #1 were high throughout the whole range of lags of +120 to -120 months; this i s the results of comparing what are essentially two trends. The idea behind test //2 was to eliminate the trends i n both money and stock prices by constructing exponential trend l i n e s , measuring percent deviations of the actual data from the trends, and correlating these deviations. For the purposes of test #2 i t was assumed that money supply grew at a constant annual rate u per time period t , as: M(t) = M 8 y t o It was assumed that stock prices grew similarly. For the pur-poses of the test U was calculated, as was 9, the corresponding para-meter for stock prices. Then the series of data describing exponential growth—at the above calculated r a t e s — i n stock prices and i n money were calculated; that i s , the trend lines were constructed. Then each datum was divided by the corresponding trend datum, from which result 1.0 was subtracted, yielding the percent deviation from trend. These are the data that were correlated in that test. 18, TABLE I Test Best Cor-relation (s) Lag of l a t t e r Variable Over Former Result Significant at Better Than the Level #1 Stock prices vs. money #2 Percent devia-tion from trend of exponentially normalised stock prices vs. simi-l a r l y treated money //3 Stock prices vs. f i r s t differences i n log. money #4 Stock prices vs. 6-month moving averages of f i r s t differences i n log. money #5 F i r s t differences in log. stock prices vs. f i r s t differences i n log. money #6 6-month moving averages of f i r s t differences i n log. stock prices vs. 6-month moving averages of f i r s t d i f -ferences i n log. money .957 .965 -118 mo. +120 mo. ,811 -112 mo. ,005 .005 ,005 Not sig n i f i c a n t l y different from zero Not signifi c a n t l y different from zero Not significantly different from zero .259 -2 mo. .005 19. F i r s t differences i n the natural logarithms of the data of a series are equivalent to percent changes in those data. These were used i n several combinations in the remaining tests. Because of erratic fluctuations i n the money series, Sprinkel recommends, "...computing a current annualized rate of change for each month but averaging the most recent six months' rates. The resulting' series removes most short-run erratic movements but retains f a i r sen-3 s i t i v i t y to average recent developments." Annualizing having no effect on correlation, six-month moving averages of natural logarithms of both series were tried i n test #6. In contrast to tests #1 and to some extent #2, the correlation results of test #6 did not remain high throughout, but f e l l rapidly and decide-dly on both sides of the peak. Sprinkel, 0p_. C i t . , p. 45. CHAPTER IV ANALYSIS OF THE RESULTS Given that i t i s desired to see whether or not a relationship exists between money and stock prices, one might ask, "Which are the relevant variables to be correlated: the level of stock prices, or change i n stock prices vs. the level of the money supply, or change i n the money supply, or perhaps change i n change in the money supply?" Observe f i r s t that the " l e v e l " of the money supply and the " l e v e l " of stock prices are not necessarily comparable magnitudes; the former i s a quantity of wealth; the l a t t e r , an average of prices. These are not the same dimensions. But what does i t matter what the dimensions are? What is being sought i s a s t a t i s t i c a l l y sound relationship. A time series can be considered to contain four elements: a trend, plus c y c l i c a l , seasonal, and random fluctuations. Thus, given a time series, the choice of which variation thereupon i s to be s t a t i s -t i c a l l y tested depends on which element of the time series i s to be examined. Since the data used in these tests are seasonally adjusted, seasonal variation i s taken to be eliminated. Thus the results of test #1, the test of stock prices vs. money, contain the influence of the remaining three elements: trend, c y c l i c a l variation, and random variation. That the correlation results are high throughout the range of lags of -120 months to +120 months suggests 21. that the influence of trend on these results i s very powerful, Of what use i s the information that both money supply and stock prices exhibit r i s i n g trends? Not much. Suppose the money supply has been ri s i n g for some time and i s expected to continue to rise at an annual rate of x percent, where x percent i s greater than the annual rate of increase necessary to satisfy people's increasing demand to hold real money. Then the price level w i l l have been rising at an annual rate of y percent, and i t expected to continue to rise at that rate. Consequently, the nominal interest rate w i l l be equal to the real interest rate plus y percentage points, in order that the rise in the price level be discounted by the market. The price of a bond which retained interest and paid compound interest thereon would rise at the nominal interest rate compounded, as would, i n the absence of discriminatory taxation, an equity of equal r i s k which retained a l l i t s earnings. Here there i s no opportunity for profit beyond a normal rate of return on investment. Consider now test #2, the theory of which—the removal of a hypothetical exponential growth trend—was described i n Chapter I I , Th results of this test are much more appealing, because i n contrast to those of test #1, the correlations do not remain high over a l l the lags rather, they decline quite smoothly from the peak value of .811 (where money leads stock prices by 112 months) to zero in the area around zero lag. This lends the inference that the test reveals more than just the results of correlating two trends. However, why was the lag—112 month so long? The answer i s that i n this test deviations were taken about a 22. hypothetical long-run growth trend, though i n r e a l i t y many shorter trends surely existed over the time period tested. Consequently what was examined was a congeries of c y c l i c a l influences and trends, and the trends certainly produced their impact i n the form of the long lag. In the remaining four tests, i n order to remove the influence of trend from the data, monthly percent differences, that i s , f i r s t d i f -ferences i n the natural logarithms of the data, were introduced. Tests #3 and #4 produced results not signifi c a n t l y different from zero, as might be expected because the influence of trend was s t i l l present, i n stock prices. Six-month moving averages were used i n test #4 (to no avail) as i n test #6 (to some avail) i n order to reduce the influence of random fluctuations. The propriety of the use of six-month moving averages might well be questioned. On the one hand i t may be argued that i n monthly data there exists a substantial random element, which ought to be removed by six-month moving-averaging, but on the other hand i t may be argued that one can moving-average one's way down to a straight l i n e for each series. However, the results of test #6 do not show high correlations over various lags, the result characteristic of the correlation of two somewhat straight l i n e s , that i s , two trends; rather, the correlation results of test #6 f e l l rapidly and decidedly on both sides of the peak. The peak correlation, .259 was obtained with money leading stocks by two months; the adjacent correlations were as in Table I I . 23. TABLE II g (months) Correlation -8 .080 -7 .093 -6 .118 -5 .168 -4 .200 -3 .228 -2 .259 -1 .258 0 .248 1 .218 2 .184 3 .165 4 .123 5 .128 6 .117 7 .099 8 .084 In both directions away from the peak the correlations dropped smoothly to zero and remained there. It w i l l be noted that although the correlation of .259 was found to be significant at better than the .005 l e v e l , an r of .259 implies 2 an r of only 6.7; that i s , only 6.7 percent of the variation i n s i x -month moving averages of percent changes i n stock prices can be accounted for by six-month moving averages of percent changes i n money. Williams writes: So rapid can be the velocity of circulation of money i n both the stock market and the real estate market that neither stocks nor real estate need ever wait for an increase in the quantity of money i n order to rise i n price, and no shortage of money need ever keep prices down i n these markets.1 John Burr Williams, The Theory of Investment Value (New York: Augustus M. Kelley, 1965), p. 49. 24, Sprinkel admits; It must be remembered too that infrequently the stock market experiences a cycle a l l i t s own, apparently unrelated to the business cycle. In 1939 and 1940 when war broke out i n Europe and for a while went badly for the A l l i e s , the U.S. stock mar-ket broke sharply despite strong underlying monetary and economic trends. Again i n 1962, the market suffered a sharp break even though a recession did not follow shortly. However, favorable l i q u i d i t y trends restored most of the losses within several months; and stock prices eventually rose to new highs before l i q u i d i t y trends became unfavorable,2 Thus i t seems that money may not be very important to the stock market. However, with reference to the low correlation, .259, obtained above, i t should be pointed out that since there exists a variable lag between the beginning of a monetary disturbance and the beginning of a reaction i n the level of business a c t i v i t y , a variable lag might also be expected to exist between the beginning of a monetary disturbance and the beginning of a reaction i n the stock market, Such a variable lag would preclude the use of correlation analysis as a means of detecting a relationship between money and stock prices; indeed, i f i t were given that v a r i a b i l i t y exists i n the lag, then the correlation of .259 could be considered quite high, Sprinkel performed no correlation analysis; rather he plotted graphs of stock prices and six-month moving averages of percent changes i n money and, f i t t i n g trend lines by eye, produced results considerably 3 more encouraging than a correlation of .259. Sprinkel, 0p_. Cit. , p, 116, Sprinkel, Ibid,, p, 5, CHAPTER V CONCLUSIONS The theory of how monetary disturbance ought to affect finan-c i a l markets was seen i n Chapter I. Recall that, according to the theory, monetary disturbance affects the amounts of various assets that wealth-holders wish to hold, causing them to adjust their port-f o l i o s , f i r s t with respect to their most l i q u i d assets. Even after the influence of trend had been removed from the data, s t a t i s t i c a l support was found for the above theory, but only after the influence of random variation had been reduced by s i x -month moving averaging. However, the evidence—a significant cor-relation of .259—suggests that monetary change accounts for only about 6.7 percent of the variation i n stock prices. But this result must be tempered with the realisation that variable lags of the same nature as those that exist between monetary change and change i n the level of business a c t i v i t y can be expected to exist between monetary change and change i n the level of stock prices. Thus i t can be argued that the discovered results of correlation analysis tends to understate the actual impact of monetary change on stock prices. 26 BIBLIOGRAPHY Dean, E. (ed.). The Controversy Over the Quantity Theory, of Money; Studies i n Economics. Boston: D.C. Heath and Company, 1965. Friedman, M. The Optimum Quantity of Money and Other Essays. Chicago Aldine Publishing Company, 1970. Friedman, M. The Great Contraction 1929-1933. Princeton, New Jersey: Princeton University Press, 1965. Sprinkel, B. W. Money and Stock Prices. Homewood, 111.: Richard D. Irwin, Inc., 1964. Williams, J. B. The Theory of Investment Value. New York: Augustus M. Kelley, 1965. A A * A A A / A X A A A A A A A A A A A A A A A A A A A ; .«A \ 11 x A x A A A i A A .1 A A A A A A * i. K x w w w m w w . K x. A ,i A A A A wxrimmm&m&mmrm*mm*W***W**1*W******* P F S NO. 77481? UMIVFRSITY OF 3 C COMPUTING CENTRE MTS(AN12C) 15:01:34 #***WE ARE HAVING MANY HARDWARE PROBLEMS—SORRY**3* + ,.••».«*****.******+***** THIS JOE SUBMITTED THROUGH FRONT DESK READER ******************** tSIGNON WFJW T = 2tC P = 5C C0PIFS=4 •:#LAST S1GNON WAS: 21:34:09 09-09-70 USER "WFJW" SIGNED ON AT 15:01:36 ON 09-11-70 $LIST * SOURCE* 1 tRUN *WATFOR 5=*S0URCE* 6=*SINK* 2 tCGMPILF __3 SUBROUTINE CORLTN(X.Y) 4 DIMENSION X ( 5 2 8 ) , Y{528) 5 DO 1 K=6,78 6 XYSUM = C O 7 XSUM = C O 8 YSUM = 0.0 9 XSQSUM= 0.0 10 YSQSUM= 0.0 11 DO 2 1=42,488 12 J=K+I~42 13 XYSUM = XYSUM +• X ( I ) * Y ( J ) 14 X SUM = X SUM + X( I ) 15 YSUM = YSUM + Y ( J ) 16 XSQSUM=XSQSUMAX( I ) * X! I ) 17 2 Y SO SUM = YSQSUM + Y ( J ) *Y ( J ) 18 Z=S0RT((500.0*XSOSUM-XSUM*XSUM)*(500.0*YSQSUM-YSUM*YSUM>) 19 IF( Z.LT .0 .001 ) 0,0 TO 3 20 R = ( 5 0 C 0*XYSUM-XSUM*YSUM)/Z 21 N = K-42 22 WRITE(6,21l N, R 23 21 F OR MAT ( I X , 1 5 , F 1 C 4 ) 24 GO TO 1 25 3 WRITE(6,22) 26 22 F0RMATQ6HZ LESS THAN .001) .27 1 CONT IMUE _ 28 RETURN 29 F|\|D 30 C 31 REAL M, LOGM, LOGS A 32 DIMENSION C( 528) , 0 0 ( 5 2 8 ) , STKAVGI528), M!528 ) , 33 1 CUNAJ( 528) .DDUNAJ ( 528) , SAUNAJ( 528) , 34 3 L0GM(528), CHL0GNM528), AVCLM(528), DUMF(528), 35 4 L 0 G S A ( 5 2 8 ) , CHLOGS(528), AVCLS(528),OUMF(528) 36 DO 500 1=1,528 37 READ (5,11) D D U N A J ( I ) , C U N A J ( I ) , SAUNAJ(I) 38 11 FORMAT (F8.1,F8.1,F8.1.F8.3) 39 5 00 CONTINUE 40 C 41 C 42 C INSTRUCTIONS TO ACJUST DATA 43 C 44 A=1.0 45 B - L C , — 46 CC=1.0 47 00 30 1=1,528 48 K=529-I 49 IFCT.EQ. 28) A=2262.0/2325.0*A 50 I F I I . E Q . 39) B=4425.0/5847.0*6 _5J IFU.FQ. 74) CC = ],39 ,9/326.3*CC 52 IFU.EQ.135) B=3764 .0/3846.0*B 53 I F ( I . E Q . 1 7 2 ) B=3292 .0/315C.0*B 54 I F d . E Q . 267) A=lC69.5/998.8*A 55 I F d . E Q . 3 2 6 ) C O 74. 5/8 1. 7*CC 56 I F d . F Q . 3 3 9 ) A=251.0/248.7*A J L Z I F I I . F Q . 4 0 9 ) CC=75.3/72.2*CC 5 8 3 1 ~T(K)=CUNAJ<K)*A ~ ~ ' 59 D0(K)=D0UNAJ(K)*8 6C 3<j STKAVG(K)=SAUNAJ(K)*CC 61 DO 12 1=1,528 62 M ( I ) = C ( I ) + D 0( I ) 63 L0GSA( d = AL0G( STKAVGI I) ) 64 12 LOGM(I)=AL0G(M(I)) *5 DO 13 1=1,527 66 CHLOGM(1 + 1 )=LO0M( 1 + 1 )-L0GM( I) 67 13 C H t O G S U H )=L0GSAd+l ) - L 0 G S A d ) 68 CHLOGM( 1 I=0 . C j_9 CHLOGS ( 1 )=Q .0 70 DUMF(4 )=CHL0GM(2 ) +CHL0GM (3 ! +CHLOGM ( 4) +CHL OGfTilT+CHLOGM ( 6 ) +C HL OGM ( 7 71 1 ) 72 DUME(4 ) = CHLOGS< 2)+CHLQGSI3)+CHLOGS( 4 )+CHL0GSI 5>+CHL0G S< 6 )+CHLCG S < 7 73 1) 74 AVCLM(4 ) = DUMF(4)/6.0 _75 AVCLS(4)=DUME(4)/6.0 76 DO 11C 1=4,524 77 J= 1-2 7 8 DUMF(I + 1 ) =DUMF( I I -CHLOGM(J)+CHLOGM(J+6) 79 DUMF(dl)=DUME( I ) -CHLOG S ( J ) +CHLOGS ( J +6 ) 80 AVCLS(1+ 1 >=0UME( 1+1 ) l b . C J l 110 AVCLM( I + l ) = DIJMFd+l I/6.C 82 AVCLM(l)=o.O 83 AVCLM(2 ( = 0 . 0 84 AVCLM<3)=0.0 85 A VC L M ( 52 61=0.0 86 AVCLM<527 ) = 0.0 87 AVCLM( 528 ) =0.0 . 88 AVCLS( 1) = 0.0 89 AVCLS ( 2 ) = '? .0 90 AVCLS(3)=O.C 91 AVCLS(526)=0.0 92 AVCLS(527 ) = 0 .0 93 AVCLS( 528) =0. 0 95 C 96 C NOW WE WILL PRINT CUT ALL THE DATA 97 C 98 201 WR[TE(6,41) 99 41 FORMAT! //// I X , 19H 1 UNADJUSTED CASH, / J_ TOO F l X , 17H 2 ADJUSTED CASH, / 101 21X, 30H 3 UNADJUSTED DEMAND DEPOSITS, / 102 31X, 28H 4 ADJUSTED DEMAND DEPOSITS, / 103 41X, 29H 5 MONEY, FROM ADJUSTED DATA, / 104 51X, 13H 6 LOG MCNEY,/ 105 51X, 28H 7 FIRST DIFFERENCES IN ( 6 ) , / 106 61X, 35H 8 SIX-MONTH MOVING AVERAGE OF (7!,/ 107 91X, 29H 9 UNADJUSTED STOCK AVERAGES, / 108 11X, 27H10 ADJUSTED STOCK AVERAGES, / 1C9 21X, 23H11 LOG STOCK AVERAGES,/ U<1 31X, 30H12 FIRST DIFFERENCES IN ( 1 1 ) , / 111 41X, 38H13 SIX-MONTH MOVING A VER A GF S OF [ IZUl 112 hRITE<6,99) 113 99 FORMAT ( 10X , 1H1 ,6X, 1H2, 6X, 1H3, 6X,lH4,tX,lH5,6;< IH6 .6X,1H7,6X,1H8, 114 1 6X , 1 H9, 6X, 2H10, 5X, 2 H H , 5X, 2hl2,5X, 2H13) 115 NYFAR=1923 116 00 43 J = l , 4 4 117 NYEAR=NYEAR+1 118 NRITE(6,44I NYE AR 119 44 FORMAT (// I X , 14) 12C K=J-1 121 L=K*12 122 00 43 N = l , 12 JLZ2 V=l±h l ? A WRITF(6,46)CUNAJ(I) ,C( I ) ,DDUNAJ(I ) ,OD(I),C< I) , LOGM<I),CHLOGM < I) 1 2 5 1AVCLM(I),SAUNAJ( 1),STKAVG(I),LOGSA( I I , ChLOGSI I),AVCLS(I) 46 FCRMATl 6X, 5(F7.1 I ,3(F7 .2 ) ,2<F7 .1 ) ,3(FT.2 I ) 126 127 43 CONTINUE 128 C 129 C 130 WRITE(6, 1~5~) 131 15 FORKAT (////53HSTOCK PRICES VS MONEY, MONEY LAGGED -36 TO +36 MONT 132 2HS//) 133 CALL CORLTN(STKAVG,M ) 134 WRITE(6,16) 135 16 FORMAT <//// 64H STOCK PRICES VS FIRST DIFFERENCES IN LOG MONEY, L 136 3AGGED AS ABOVE //) 137 CALL CORLTN(STKAVG,CHLOGM) 138 WRITE(6,17) 139 17 FORMAT <//// 93h STOCK PRICES VS SIX-TONTH MOVING AVERAGES OF FIRS 140 4T DIFFERENCES IN LOG MONEY, LAGGED AS ABOVE II) 141 CALL CORLTN ( STKAVG, AVCLM) 142 WRITE(6,l8) 143 18 FORMAT(//// 89H FIRST DIFFERENCES IN LOG STOCK PRICES VS FIRST DIF 144 5FERENCES IN LOG MONEY, LAGGED AS ABOVE //) 145 CALL CORLTNfCHLCGS,CHLOGMI 146 WR1TE(6,19) _14J7 L5 FORMAT (//// 1 H H SIX-MONTH MOVING AVERAGES UF_ tig ST DIFFERENCES IN 6 L 0 G S T O C K P R I C E S VS S I M I L A R L Y T R E AT ETJMUN EY, LAGGED AS A B O V E //) 148 -149 CALL CORLTNIAVCLS,AVCLM) 150 C 151 C 152 STOP 1 5 3 END 154 $DATA END OF FILE RFS NO. 7743 12 UNIVERSITY OF B C COMPUTING CENTRE MTS(AN12C> 15:01:34 USER: WFJW DEPARTMENT: COMM i I i « i i CN AT 15 :C l :36 OFF AT 15 :G1:38 ELAPSED TIME 1.3 SEC. CPU TINE USED .385 SEC . #### STORAGE USED 1.5? PAGE-SEC CARDS READ 159 LINES PRINTED 708 PAGES PRINTED 16 CARDS PUNCHED r DRUM READS A RATE FACTOR 1.0 # & # APPROX. COST OF THIS RUN C$1.15 ^ *: i£ i,< FILE STORAGE 169 PG-HR. C$.06 v*LAST SIGNON WAS: 21:34:09 09-09-70 MMMMM MMMMMM MMMMMMM K M M M M M M M MMMMMMMMM MMMMMMMMMM MMMMM TTTTTTTTTTTTTTTTTTTTTTTTT MMMMMM TTTTTTTTTTTTTTTTTTTTTTTTT MMMMMMM TTTTTTTTTTTTTTTTTTTTTTTTT MMMMMMMM TTTTT MPMMMMMMM TTTTT M MM MMMMMMM . JTTTT sssssssss sssssssssssss sssssssssssssssss ssssss sssssss sssss sssss sssss MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMMMMMMMM MM MM MMMMM MMMMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM TTTTT TTTTT TTTTT TTTTT TTTTT - J I I T T ssssss sssssssssssss sssssssssssss sssssssssssss sssssss sssss MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM fMfrfMM MMM MMMMM MMMMM MMMMM MMMMM MMMMM MMMMM TTTTT T T J T T TTTTT TTTTT TTTTT J I I J T sssss sssss sssss sssssss sssssss sssssssssssssssss sssssssssssss sssssssss 

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