The performance of Mutual funds In The period 1945-1964 Michael C. Jensen Harvard Business School MJensen(hbs. edu ABSTRACT In this paper I derive a risk-adjusted measure of portfolio performance (now known as returns. The measure is based on the theory of the pricing of capital assets by Sharpe (1964), Lintner(1965a)and Treynor(Undated). I apply the measure to estimate the predictive ability of 115 mutual fund managers in the period 1945-1964-that is their ability to earn returns which are higher than those we would expect given the level of risk of each of the portfolios. The foundations of the model and the properties of the performance measure suggested here are discussed in Section ll The evidence on mutual fund performance indicates not only that these 115 mutual funds were on average not able to predict security prices well enough to outperform a buy-the-market and-hold policy, but also that there is very little evidence that any individual fund was able to do significantly better than that which we expected from mere random chance. It is also important to ote that these conclusions hold even when we measure the fund returns gross of management expenses(that is assume their bookkeeping, research, and other expenses except brokerage commissions were obtained free). Thus on average the funds apparently were not quite successful enough in their trading activities to recoup even their brokerage expenses Keywords: Jensens Alpha, mutual fund performance, risk-adjusted returns, forecasting ability, predictive ability Journal of Finance, Vol. 23, No. 2(1967)389-416 CM. C. Jensen 1967 This document is available on the ocial Science Research Network(SSRN) Electronic Library athttp://papers.ssrn.com/abstract=244153 Created. August 02
Created: August 2002 The Performance Of Mutual Funds In The Period 1945-1964 Michael C. Jensen Harvard Business School MJensen@hbs.edu ABSTRACT In this paper I derive a risk-adjusted measure of portfolio performance (now known as "Jensen's Alpha") that estimates how much a manager's forecasting ability contributes to the fund's returns. The measure is based on the theory of the pricing of capital assets by Sharpe (1964), Lintner (1965a) and Treynor (Undated). I apply the measure to estimate the predictive ability of 115 mutual fund managers in the period 1945-1964—that is their ability to earn returns which are higher than those we would expect given the level of risk of each of the portfolios. The foundations of the model and the properties of the performance measure suggested here are discussed in Section II. The evidence on mutual fund performance indicates not only that these 115 mutual funds were on average not able to predict security prices well enough to outperform a buy-the-marketand-hold policy, but also that there is very little evidence that any individual fund was able to do significantly better than that which we expected from mere random chance. It is also important to note that these conclusions hold even when we measure the fund returns gross of management expenses (that is assume their bookkeeping, research, and other expenses except brokerage commissions were obtained free). Thus on average the funds apparently were not quite successful enough in their trading activities to recoup even their brokerage expenses. Keywords: Jensen's Alpha, mutual fund performance, risk-adjusted returns, forecasting ability, predictive ability. Journal of Finance, Vol. 23, No. 2 (1967) 389-416. © M. C. Jensen 1967 This document is available on the Social Science Research Network (SSRN) Electronic Library at: http://papers.ssrn.com/ABSTRACT=244153
The performance of Mutual funds In The period 1945-1964= Michael C. Jensen Harvard Business school Miensen@hbs. edu I Introduction A central problem in finance(and especially portfolio management) has been that of evaluating the"performance"of portfolios of risky investments. The concept of portfolio"performance"has at least two distinct dimensions 1) The ability of the portfolio manager or security analyst to increase returns on the portfolio through successful prediction of future security prices, and 2) The ability of the portfolio manager to minimize (through"efficient diversification) the amount of"insurable risk"born by the holders of the portfolio The major difficulty encountered in attempting to evaluate the performance of a portfolio in these two dimensions has been the lack of a thorough understanding of the nature and measurement of"risk. Evidence seems to indicate a predominance of risk aversion in the capital markets, and as long as investors correctly perceive the"riskiness of various assets this implies that "risky"assets must on average yield higher returns than less"risky"assets. Hence in evaluating the"performance"of portfolios the effects of differential degrees of risk on the returns of those portfolios must be taken into account Assuming, of course, that investors expectations are on average correct. s This paper has benefited from comments and criticisms by G. Benston, E. Fama, J. Keilson, H Weingartner, and especially M. Scholes
* This paper has benefited from comments and criticisms by G. Benston, E. Fama, J. Keilson, H. Weingartner, and especially M. Scholes. The Performance Of Mutual Funds In The Period 1945-1964* Michael C. Jensen Harvard Business School Mjensen@hbs.edu I. Introduction A central problem in finance (and especially portfolio management) has been that of evaluating the “performance” of portfolios of risky investments. The concept of portfolio “performance” has at least two distinct dimensions: 1) The ability of the portfolio manager or security analyst to increase returns on the portfolio through successful prediction of future security prices, and 2) The ability of the portfolio manager to minimize (through “efficient” diversification) the amount of “insurable risk” born by the holders of the portfolio. The major difficulty encountered in attempting to evaluate the performance of a portfolio in these two dimensions has been the lack of a thorough understanding of the nature and measurement of “risk.” Evidence seems to indicate a predominance of risk aversion in the capital markets, and as long as investors correctly perceive the “riskiness” of various assets this implies that “risky” assets must on average yield higher returns than less “risky” assets.1 Hence in evaluating the “performance” of portfolios the effects of differential degrees of risk on the returns of those portfolios must be taken into account. 1 Assuming, of course, that investors’ expectations are on average correct
Jensen Recent developments in the theory of the pricing of capital assets by Sharpe (1964), Lintner(1965a)and Treynor(Undated) allow us to formulate explicit measures of a portfolio s performance in each of the dimensions outlined above. These measures are derived and discussed in detail in Jensen(1967). However, we shall confine our attention here only to the problem of evaluating a portfolio manager's predictive ability-that is his ability to earn returns through successful prediction of security prices which are higher than those which we could expect given the level of riskiness of his portfolio. The foundations of the model and the properties of the performance measure suggested here(which is somewhat different than that proposed in Jensen(1967))are discussed in Section II. The model is illustrated in Section Ill by an application of it to the evaluation of the performance of 115 open end mutual funds in the period 1945-1964 A number of people in the past have attempted to evaluate the performance of portfolios(primarily mutual funds), but almost all of these authors have relied heavily on relative measures of performance when what we really need is an absolute measure of performance. That is, they have relied mainly on procedures for ranking portfolios For example, if there are two portfolios A and b, we not only would like to know whether A is better (in some sense)than b, but also whether a and b are good or bad relative to some absolute standard. The measure of performance suggested below is such an absolute measure. It is important to emphasize here again that the word"performance is used here only to refer to a fund manager's forecasting ability. It does not refer to a portfolios"efficiency"in the Markowitz-Tobin sense A measure of"efficiency and its relationship to certain measures of diversification and forecasting ability is derived and discussed in detail in Jensen(1967). For purposes of brevity we confine ourselves here to an examination of a fund manager's forecasting ability which is of interest in and of itself See for example( Cohen and Pogue, 1967; Dietz, 1966; Farrar, 1962: Friend et al., 1962: Friend and Vickers, 1965; Horowitz, 1965; Sharpe, 1966; Treynor, 1965) 3 It is also interesting to note that the measure of performance suggested below is in many respects quite closely related to the measure suggested by Treynor(1965
Jensen 2 1967 Recent developments in the theory of the pricing of capital assets by Sharpe (1964), Lintner (1965a) and Treynor (Undated) allow us to formulate explicit measures of a portfolio’s performance in each of the dimensions outlined above. These measures are derived and discussed in detail in Jensen (1967). However, we shall confine our attention here only to the problem of evaluating a portfolio manager’s predictive ability—that is his ability to earn returns through successful prediction of security prices which are higher than those which we could expect given the level of riskiness of his portfolio. The foundations of the model and the properties of the performance measure suggested here (which is somewhat different than that proposed in Jensen (1967)) are discussed in Section II. The model is illustrated in Section III by an application of it to the evaluation of the performance of 115 open end mutual funds in the period 1945-1964. A number of people in the past have attempted to evaluate the performance of portfolios2 (primarily mutual funds), but almost all of these authors have relied heavily on relative measures of performance when what we really need is an absolute measure of performance. That is, they have relied mainly on procedures for ranking portfolios. For example, if there are two portfolios A and B, we not only would like to know whether A is better (in some sense) than B, but also whether A and B are good or bad relative to some absolute standard. The measure of performance suggested below is such an absolute measure.3 It is important to emphasize here again that the word “performance” is used here only to refer to a fund manager’s forecasting ability. It does not refer to a portfolio’s “efficiency” in the Markowitz-Tobin sense. A measure of “efficiency” and its relationship to certain measures of diversification and forecasting ability is derived and discussed in detail in Jensen (1967). For purposes of brevity we confine ourselves here to an examination of a fund manager’s forecasting ability which is of interest in and of itself 2 See for example (Cohen and Pogue, 1967; Dietz, 1966; Farrar, 1962; Friend et al., 1962; Friend and Vickers, 1965; Horowitz, 1965; Sharpe, 1966; Treynor, 1965). 3 It is also interesting to note that the measure of performance suggested below is in many respects quite closely related to the measure suggested by Treynor (1965)
Jensen (witness the widespread interest in the theory of random walks and its implications regarding forecasting success) In addition to the lack of an absolute measure of performance, these past studies of portfolio performance have been plagued with problems associated with the definition of"risk"and the need to adequately control for the varying degrees of riskiness among portfolios. The measure suggested below takes explicit account of the effects of"risk"or the returns of the portfolio. Finally, once we have a measure of portfolio"performance e also need to estimate the measures sampling error. That is we want to be able to measure its "significance in the usual statistical sense, Such a measure of significance also is suggested below I。 The model The Foundations of the Model -As mentioned above, the measure of portfolio performance summarized below is derived from a direct application of the theoretical results of the capital asset pricing models derived independently by Sharpe (1964), Lintner (1965a)and Treynor (Undated). All three models are based on the assumption that(1)all investors are averse to risk, and are single period expected utility of terminal wealth maximizers, (2)all investors have identical decision horizons and homogeneous expectations regarding investment opportunities, (3)all investors are able to choose among portfolios solely on the basis of expected returns and variance of returns, (4)all trans-actions costs and taxes are zero, and (5)all assets are infinitely divisible. Given the dditional assumption that the capital market is in equilibrium, all three models yield the following expression for the expected one period return ER ) on any security(or portolIo) )=R+p[E(R)-8] Defined as the ratio of capital gains plus dividends to the initial of the securit
Jensen 3 1967 (witness the widespread interest in the theory of random walks and its implications regarding forecasting success). In addition to the lack of an absolute measure of performance, these past studies of portfolio performance have been plagued with problems associated with the definition of “risk” and the need to adequately control for the varying degrees of riskiness among portfolios. The measure suggested below takes explicit account of the effects of “risk” on the returns of the portfolio. Finally, once we have a measure of portfolio “performance” we also need to estimate the measure’s sampling error. That is we want to be able to measure its “significance” in the usual statistical sense. Such a measure of significance also is suggested below. II. The Model The Foundations of the Model.—As mentioned above, the measure of portfolio performance summarized below is derived from a direct application of the theoretical results of the capital asset pricing models derived independently by Sharpe (1964), Lintner (1965a) and Treynor (Undated). All three models are based on the assumption that (1) all investors are averse to risk, and are single period expected utility of terminal wealth maximizers, (2) all investors have identical decision horizons and homogeneous expectations regarding investment opportunities, (3) all investors are able to choose among portfolios solely on the basis of expected returns and variance of returns, (4) all trans-actions costs and taxes are zero, and (5) all assets are infinitely divisible. Given the additional assumption that the capital market is in equilibrium, all three models yield the following expression for the expected one period return,4 E j (R ˜ ), on any security (or portfolio) j: E j (R ˜ ) = RF + b j E M [ (R ˜ ) - RF] (1) 4 Defined as the ratio of capital gains plus dividends to the initial price of the security
Jensen where the tildes denote random variables and the one-period risk free interest rate β cov(R RM)=the measure of risk(hereafter called systematic risk) which the asset pricing model implies is crucial in determining the E(RM)=the expected one-period return on the"market portfolio"which consists of investment in each asset in the market in proportion to its fraction of the t value of all assets in the market Thus eq. (1)implies that the expected return on any asset is equal to the risk free rate plus a risk premium given by the product of the systematic risk of the asset and the risk premium on the market portfolio. The risk premium on the market portfolio is the difference between the expected returns on the market portfolio and the risk free rate Cquation (1) then simply tells us what any security (or portfolio)can be expected to earn given its level of systematic risk, B,. If a portfolio manager or security analyst able to predict future security prices he will be able to earn higher returns than those implied by eq (1)and the riskiness of his portfolio. We now wish to show how(1)can be adapted and extended to provide an estimate of the forecasting ability of any portfolio manager. Note that(1)is stated in terms of the expected returns on any security or portfolio j and the expected returns on the market portfolio. Since these expectations are strictly unobservable we wish to show how(1)can be recast in terms of the objectively measurable realizations of returns on any portfolio j and the market portfolio M In Jensen(1967) it was shown that the single period models of Sharpe, Lintner, and Treynor can be extended to a multiperiod world in which investors are allowed s Note that since o(RA)is constant for all securities the risk of any security is just cov(R, RM) But since cov(R, RM)=0(RM)the risk of the market portfolio is just o(R), and thus we really measuring the riskiness of any security relative to the risk of the market portfolio. Hence the systematic risk of the market portfolio, cov(R, RM)/o(R/), is unity, and thus the dimension of the measure of systematic risk has a convenient intuitive interpretatio
Jensen 4 1967 where the tildes denote random variables, and RF = the one-period risk free interest rate. b j = † cov j R ˜ , M ( R ˜ ) 2 s M R ˜ = the measure of risk (hereafter called systematic risk) which the asset pricing model implies is crucial in determining the prices of risky assets. E M (R ˜ ) = the expected one-period return on the “market portfolio” which consists of an investment in each asset in the market in proportion to its fraction of the total value of all assets in the market. Thus eq. (1) implies that the expected return on any asset is equal to the risk free rate plus a risk premium given by the product of the systematic risk of the asset and the risk premium on the market portfolio.5 The risk premium on the market portfolio is the difference between the expected returns on the market portfolio and the risk free rate. Equation (1) then simply tells us what any security (or portfolio) can be expected to earn given its level of systematic risk, b j . If a portfolio manager or security analyst is able to predict future security prices he will be able to earn higher returns than those implied by eq. (1) and the riskiness of his portfolio. We now wish to show how (1) can be adapted and extended to provide an estimate of the forecasting ability of any portfolio manager. Note that (1) is stated in terms of the expected returns on any security or portfolio j and the expected returns on the market portfolio. Since these expectations are strictly unobservable we wish to show how (1) can be recast in terms of the objectively measurable realizations of returns on any portfolio j and the market portfolio M. In Jensen (1967) it was shown that the single period models of Sharpe, Lintner, and Treynor can be extended to a multiperiod world in which investors are allowed to 5 Note that since 2 s M (R ˜ ) is constant for all securities the risk of any security is just cov j R ˜ , M ( R ˜ ). But since cov j R ˜ , M ( R ˜ ) = 2 s M (R ˜ ) the risk of the market portfolio is just 2 s M (R ˜ ), and thus we are really measuring the riskiness of any security relative to the risk of the market portfolio. Hence the systematic risk of the market portfolio, cov j R ˜ , M ( R ˜ )/ 2 s M (R ˜ ), is unity, and thus the dimension of the measure of systematic risk has a convenient intuitive interpretation