Mutual Fund Performance TORIO William F. Sharpe The Journal of Business, Vol 39, No. 1, Part 2: Supplement on Security Prices (Jan 1966),pp.119-138 Stable uri http://links.jstor.org/sici?sici=0021-9398%028196601%0293993a1%03c119%03amfp903e2.0.co%03b2-6 The Journal of Business is currently published by The University of Chicago Press Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://uk.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyouhave obtained prior permission, you may not download an entire issue of a joumal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://ukjstor.org/joumals/ucpress.html Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmiss JstOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support @jstor. org http://ukjstor.org Thu oct1918:08:442006
MUTUAL FUND PERFORMANCE WILLIAM F. SHARPET ture studies of mutual fund performance W TitHIN the last few years consider- has appeared. Drawing on results ob- made in tained in the field of hree closely related areas-the Jack L. Treynor has suggested a new theory of portfolio selection, the theory predictor of mutual fund performance4- of the pricing of capital assets under con- one that differs from virtually all those ditions of risk, and the general behavior used previously by incorporating the vol- in all three areas are relevant for evalu- meaningful manner. ating mutual fund performance. Unfor This paper attempts to extend Trey tunately, few of the studies of mutual nor's work by subjecting his proposed funds have taken advantage of the sub- measure to empirical test in order to stantial backlog of theoretical and em- evaluate its predictive ability. But we pirical material made available by recent will also attempt to do something more studies in these related areas. However, -to make explicit the relationships be. one paper pointing the direction for fu- tween recent developments in capital theory and alternative models of mutual I am grateful to Norman H. Jones, of the fund performance and to subject the elpful comments alternative models to empirical test. suggestions. t Associate professor of economics and operations II IMPLICATIONS OF RECENT DEVEL- tion. Any views expressed in this paper are those of the author. They should A. PORTFOLIO ANALYSIS THEORY5 fecting the views of the The theory of portfolio analysis is es- oration or the official opinion or policy of any sentially normative; it describes efficient of its governmental or private research sponsors. I The original work in the feld was that of H. techniques for selecting portfolios on the Markowitz; see his"Portfolio Selection, "Journal of basis of predictions about the perform Finance, XII (March, 1952), 71-91, or the subse- ance of individual securities. The key ficient Diversification of Investments(New York: element in the portfolio analyst's view A Simplified Model for Portfolio Analysis, Gy of the world is his emphasis on both ex- agement Science, IX January, 1963), 277-93, and pected return and risk. The selection of Eugene F. Fama,"Portfolio analysis in a Stable a preferred combination of risk and ex- Paretian Market, 'Management Science, XI(anu- pected return must, in the final analysis ary,1965),404-19 depend on the preferences of the investor a See, e. g, my"Capital Asset Prices: A Theory of and cannot be made solely by the Market Journal of Finance, XIX (September, 1964), 425-4 mary of this work see Eugene F. unds, harvard Business Review, XLIlI (anu Journal of business, XXXVIII January, 1965), 34- s The material in this section is based on the
THE JOURNAL OF BUSINESS nician. However, the technician can(and followed in practice, involves merely a should) attempt to find efficient portfo. description of the general degree of risk lios-those promising the greatest ex- planned for the fund's portfolio; the fund pected return for any given degree of then simply attempts to select the effi- risk. The portfolio analyst's tasks are thus cient portfolio for that degree of risk(i.e (1)translating predictions about security the one with the greatest expected re- performance into predictions of portfolio turn performance, and (2) selecting from Portfolio analysis theory per se makes among the large number of possible port- no assumptions about the pattern of se folios those that are efficient. The security curity prices or the skill of investment analyst's task is to provide the required managers. Thus few implications can be dictions of security performance(in- drawn concerning the results obtained by cluding the interrelationships among the different mutual funds. Performance ex performances of securities). The inves- post might vary in two respects.First tor's task is to select from among the different funds could exhibit different efficient portfolios the one that he con- degrees of variability in return, due siders most desirable, based on his par- either to conscious selection of different ticular feelings regarding risk and ex- degrees of risk or to erroneous predictions pected return of the risk inherent in particular portfo- What tasks are implied for the mutual lios. Second, funds holding portfolios fund by this view of the investment with similar variability in return might process? Certainly those of security anal- exhibit major differences in average re ysis and portfolio analysis. The emphasis turn, due to the inability of some manag in mutual fund advertising on diversifica- ers to select incorrectly priced securities tion and the search for incorrectly priced and or to diversify their holdings prop- securities reflects the importance accord- erly. In short, if sound mutual fund man ed these aspects of the process. Portfolio agement requires the selection of incor analysis theory, unfortunately, does not rectly priced securities, effective diversi make clear the manner in which the third fication, and the selection of a portfolio unction should be performed. A mutual in the chosen risk class, there is ample fund cannot practically determine the room for major and persisting differences preference patterns of its investors di- in the performance of different funds. rectly. Even if it could, there might be substantial differences among them. TH B. THE BEHAVIOR OF STOCK-MARKET PRICES process must work in the other direction, Recent work on the general behavior with the mutual fund management se- of stock-market prices has raised serious lecting an attitude toward risk and ex- questions concerning the importance of pected return and then inviting investors one of the functions of mutual fund man- with similar preferences to purchase agement. The theory of random walks shares in the fund. At one extreme, the asserts that the past behavior of a secu- fund might attempt to describe an entire rity' s price is of no value in predicting its pattern of relative preference for expect- future price. The impressive evidence ed return vis-a-vis risk (i. e, a pattern supporting this theory suggest that it of indifference curves). A much more likely method, and one that seems to be "The Behavior of Stock-Market Prices, "op cit
MUTUAL FUND PERFORMANCI may be very difficult(and very expen- has shown that the task of diversification sive) to detect securities that are incor- may be much simpler than formerly sup ctly priced. If so, it is not because se- posed, requiring only the spreading curity analysts are not doing their job of holdings among standard industri properly, but because they are doing it classes. 7 If so, most funds are likely to very well. However, if this is the case, hold portfolios that are efficient ex ante it may not pay the manager of a particu- Any differences in efficiency ex post are lar fund to devote extensive resources to thus probably transitory. The only basis the search for incorrectly priced securi- for persistently inferior performance ties;and the fund that does so may pro- would be the continued expenditure of vide its investors a poorer net perform- large amounts of a funds assets on the ance(after costs) than one that does not. relatively fruitless search for incorrectly Under these conditions what are the valued securities tasks of the mutual fund? Broadly de fined, they still include security analysis C. THE THEORY OF CAPITAL-ASSET PRICES UNDER CONDITIONS OF RISK portfolio in the desired risk class. But Empirical work on the behavior of sis is directed more toward evaluating new information affecting the value of that the market responds very rapidly to the interrelationships among securities- the extent to which returns are correlat- securities. A natural reaction to these ed. And portfolio analysis is concerned results is the construction of a model of the manner suggested by portfolio analy- diversified portfolio will be efficient; the sis theory. Such an approach has been mutual fund manager must select from described elsewhere only the major fea among alternative diversified portfolios tures will be given here the one with the appropriate degree of The predicted performance of a port- risk folio is described with two measures: the Strictly speaking, the implications of expected rate of return(E)and the pre this view of the world for mutual fund dicted variability or risk, expressed as performance do not differ from those of the standard deviation of return (a) the theory of portfolio analysis. Ex post, All investors are assumed to be able to funds can be expected to exhibit differ- invest funds at a common risk-free in ences in variability of return, due to in- terest rate and to borrow funds at the tentional or unintentional selection of same rate(at least to the desired extent) different risk classes. And the portfolios At any point of time, all investors share of some funds may be more efficient than the same predictions concerning the fu others(i. e,, give greater average return ture performance of securities(and thus at the same level of variability)if manag- portfolios). Under these conditions all ef ers differ in their ability to diversify 7See Benjamin F. King,"Market and Industry effectively. However, the likelihood that Factors in Stock Price Behavior, "Journal of busi persistent differences in efficiency will ness, XXXIX, No. 1, Part I(Supplement,Janu- ary, 1966) occur is greatly reduced. Recent work & In my"Capital Asset Prices.,"op cit
122 THE JOURNAL OF BUSINESS ficient portfolios will fall along a straight portfolios should lie along a straight line line of the form° with higher values of Vi associated with E;=p十 higher values of A. Because there is risk in the stock market, the points will not here p is the pure (riskless)interest lie precisely along such a line, even if th rate and b is the risk premium. Since in- model is completely correct. But the vestors are assumed to be risk-averse,b lationship should be present, visible, and will be positive statistically significant These results follow immediately from The implications of this model for a relationship first described by James tual fund performance are relatively Tobin.0 If an investor can borrow or straightforward. If all funds hold proper lend at some riskless interest rate p and/ ly diversified portfolios and spend the or invest in a portfolio with predicted appropriate amount for analysis and ad- performance (Ei, o i), then by allocating ministration, they should provide rates his funds between the portfolio and bor- of return giving A V: values lying gen rowing or lending he can attain any erally along a straight line. Points that point on the line diverge from the underlying relationship E=P+(=2) should reflect only transitory effects and differences in perfo Any portfolio will thus give rise to On the other hand. if some funds complete (linear)boundary of E, o com- diversify properly, or spend too much on binations. The best portfolio will be the research and/or administration, they one giving the best boundary; clearly it will, persistently give rates of return is the one for which(E: -/o: is the yielding inferior A, V: values. Their per- greatest. If more than one portfolio is to formance will be poorer and can be ex be efficient, all must lie along a common pected to remain so line and give identical values of this ratio The capital-market model described III PERFORMANCE OF 34 OPEN-END here deals with predictions of future per MUTUAL FUNDS, 1954-63 formance. Since the predictions cannot To test some of the implications drawn be obtained in any satisfactory manner, in the previous section, the annual rates the model cannot be tested directly. In- of return for thirty-four open-end mutual stead, ex post values must be used-the funds during the period 1954-63 were average rate of return of a portfolio must analyzed in the manner described above. be substituted for its expected rate of The annual rate of return for a fund is return,and the actual standard deviation based on the sum of dividend payments, of its rate of return for its predicted risk. capital gains distributions, and changes We denote these measures by Ai and vi in net asset value: it is thus a measure (the latter for variability) of met performance--gross yield less the The capital-market model implies that expenses of management and adminis- x post values for 4; and V for efficient tration. The latter range from 0.25 per By definition, for inefficient portfolios: Ei< 办十b 1 The funds used for this and all subsequent analyses were which annual rates of return 10 In his "Liquidity Preference as Behavior were given by Weisenberger for at least the last 20 years. All data are from Arthur Weisenberger ( February,1958),65-86 Co., Investment Companies(1953, 1962, 1964 eds)
MUTUAL FUND PERFORMANCE 123 cent of net assets per year to 1.5 per cent ernment bond at a price that would have per year Most funds also charge e an guaranteed a return of slightly less than tial fee of approximately 8.5 per cent for 3 per cent if held to maturity. Using 3 selling costs when shares are purchased; per cent as the estimate of p for the annual rates of return are not net of such period, Boston Fund, shown by point y costs n Figure 1, plus borrowing or lending The average annual rate of return(ao) could have provided any combination of and the standard deviation of annual average return and variability lying rate of return Vi for each fund along line PYZ Incorporate shown in Figure 1; the values are listed shown by point Q, could have provided in Table 1. The relationship predicted by any combination lying along line Pe the theory of capital asset prices is clear- Clearly the for ly present-funds with large average re- latter, since for any level of risk it offered turns typically exhibit greater variability er average return. Indeed, the than those with small average returns. steepness of the line associated with a Moreover, the relationship is approxi- fund provides a useful measure of per mately linear and significant. 2 However, formance--one that incorporates both there are differences in efficiency; a num- risk and average return. We define this ber of funds are actually dominated (i.e., as the reward-to-variability ratio: For some other fund provided both a greater Boston Fund the ratio is equal to the value of At and a smaller value of vi. distance XP on Figure 1 divided by the To analyze the differences, we need a distance XY. The larger the ratio, the single measure of performance; once such better the performance a measure is specified, any persistent An alternative interpretation of the differences can be investigated by testing ratio gives rise to the name---reward-to- alternative measures for predicting per- variability ratio (R/V). The numerator formance shows the difference between the funds An intuitively appealing and theoreti- average annual return and the pure in cally meaningful measure of performance terest rate; it is thus the reward provided is easily derived from the Tobin effect. the investor for bearing risk. The denom- With substitution of the ex post meas- inator measures the standard deviation ures (A and V) for the ex ante measures of the annual rate of return: it show (E and o), the formula described in Sec- amount of risk actually borne. The ratio tion ii becomes is thus the reward per unit of variability. The final column of Table 1 shows the A=P+ alues of the R/v ratio for the thirty- four funds. They vary considerably By investing in fund i and borrowing or from almost 078(the Boston Fund)to lending at the riskless rate p, an investor slightly over 0.43(Incorporated Inves could have attained any point along the tors). Those who view the market as line given by this formula. In 1953 it was nearly perfect and managers as goo possible to purchase a ten-year U.S. gov- diversifiers would argue that the differ 1 The results of statistical tests on these data tangent of the angle made by the line Journal of Finance, nother way, the reciprocal of the slope September, 1965, pp. 416-22. (dA/dv)equals the R/V ratio
26% 18 16 H 10 8 FIG. 1. -Average return and variability, 34 open-end mutual funds, 1954-63
MUTUAL FUND PERFORMANCE 125 ences are either transitory or due to ex- IV. THE PERSISTENCE OF DIFFER- cessive expenditures by some funds. ENCES IN PERFORMANCE Others would argue that the differences to determine the extent to which dif are persistent and can be attributed (at ferences in performance continue through least partially)to differences in manage- time, the returns from the thirty-four ment skill. The remainder of this pape funds during the period 1944-53 were attempts to test these alternative ex planations,using pre-1954 data to pre- used to compute R/V ratios for the dec- dict performance from 1954 to 1963, and ade preceding the one previously investi in the tradition of empirical studies of gated. 14, The funds were ranked in each mutual funds, provides comparisons with 14 Since the long-term interest rate during this the performance of the securities used to period was somewhat lower than that prevailing in compute the Dow-Jones Industrial Av. the latter period, a pure interest rate of 2.5 per cent as used in the calculations(this was approximately rage the yield on a ten-year U.s. government bond in TABLE 1 PERFORMANCE OF 34 MUTUAL FUNDS, 1954-63 Mutual Fund eturn (Per Cent)(Per Cent) 12.0 ock F Broad Street Investing 14.8 70329 19.3 mmonwealth Investment Company Dividend fund 14,4 Eaton and Howard, Stock Fund 14.6 16.4 14.5 ities, Common Stock Fu 1 of americ 17.4 mis-Sales Mutual Fun Massachusetts Investors Trust 20.8 tts investors -growth Stod 18.3 12,4 New England Fund Scudder, Stevens& Clark Balanced Fund Wisconsin Fund 0.64091 * R/V ra caLios obtained from the rounded data shown routed from cent)/variability. The ratios sh
126 THE JOURNAL OF BUSINESS period, from 1-the fund with the high- perfect, there is a general upward trend est( best)R/V ratio, to 34the fund suggesting that funds ranking low in the with the lowest(worst)R/V ratio. Fig- early period tend to rank low in the later ure 2 plots the rankings in the two peri- period, while those ranking high in the ods. Although the relationship is far from early period tend to rank high in the later period. The value of Spearmans 1943): Although different assumptions regarding the rank correlation coefficient(+360)bears affect the rankings of individual funds, the this out as does the count of points in redictive ability of the measures con- the four quadrants(shown in the lower this paper is not significantly he assumed rates over a considerable 1s The standard error for the sample size used in this and all subsequent calculations is 0. 174. +2aH,9H39g+c0v°兰 15 Rank based on the Reward-to-Variability Ratio, 1944-1953 Rank correlation coefficient =.360 worst FIG. 2.--Predictions based on the reward-to-variability ratio
MUTUAL FUND PERFORMANCE 127 portion of the figure). Put rather crudely, pute the Dow-Jones Industrial Average the latter shows that an investor select- moreover, as shown in Figure 3, the per ing one of the seventeen best funds in centage was quite similar for most of the the first period would have an 11: 6 thirty-four funds. Treynor has taken ad chance of holding one of the seventeen vantage of this relationship by using the best in the second period. Conversely, if volatility of a fund as a measure of its he had selected one of the seventeen risk instead of the total variability used worst in the first period he would have in the R/V ratio. Since the returns on an 11: 6 chance of holding one of the all diversified portfolios move with the seventeen worst in the second period. market, the extent to which changes simple regression analysis using the ac- the market are reflected in changes in a tual values of the R/v ratios gives simi- funds rate of return can stand as a good lar results: the correlation coefficient is measure of the total variability of the + 3157 and the b-value for the slope co- funds return over time. By observing efficient+1.88 this relationship over some past period, a These results show that differences in reasonably good estimate of volatility- performance can be predicted, although the change in the rate of return on a fund imperfectly. However, they do not indi- associated with a 1 per cent change in cate the sources of the differences. Equal- the rate of return on, say, the Dow-Jones ly important, there is no assurance that portfolio--can be obtained.We will use past performance is the best predictor of B to represent this value for the ith future performance. We consider next fund.17 the alternative measu The measure that we will term eynor Treynor Index(TI)can be obtained TREYNOR INDEX simply substituting volatility for varia- In a perfect capital market no securi bility in the formula for the R/V ratio ties would be incorrectly priced. Thu Ai-p one function of the mutual fund (finding ch securities)would be eliminated leaving only the tasks of diversification Stated in this manner, the relationship and selecting the appropriate risk class. between the two measures is clear. And Moreover, under such conditions it has the extent of the contribution of volatil- been shown that truly diversified ity to over-all variability makes the portfolios will move with the over-all ranking of funds on the basis of the Trey- market, giving high returns when the nor Index very close to that based on market in general provides high returns the R/V ratio. Figure 4 shows the rank and low returns when the market pro- ings using the two measures for the peri vides low returns. The data bear out this od 1954-63. Since the mutual funds in hypothesis. During the period 1954-63, our sample all hold highly diversified almost 90 per cent of the variance of the portfolios, the similarity of the rankings return on the typical fund in our sample is not surprising. And the cost of was due to its comovement with the re- the Treynor Index as a measure of turn on the thirty securities used to com- 17 To be consistent with the notation in my "A In my "Capital Asset Pric Simplified Model for Portfolio Analysis, " op