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The Capital Asset Pricing Model: Some Empirical Tests
TL;DR: In this paper, the authors present some additional tests of the mean-variance formulation of the asset pricing model, which avoid some of the problems of earlier studies and provide additional insights into the nature of the structure of security returns.
Abstract: Considerable attention has recently been given to general equilibrium models of the pricing of capital assets Of these, perhaps the best known is the mean-variance formulation originally developed by Sharpe (1964) and Treynor (1961), and extended and clarified by Lintner (1965a; 1965b), Mossin (1966), Fama (1968a; 1968b), and Long (1972) In addition Treynor (1965), Sharpe (1966), and Jensen (1968; 1969) have developed portfolio evaluation models which are either based on this asset pricing model or bear a close relation to it In the development of the asset pricing model it is assumed that (1) all investors are single period risk-averse utility of terminal wealth maximizers and can choose among portfolios solely on the basis of mean and variance, (2) there are no taxes or transactions costs, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a given riskless rate of interest The main result of the model is a statement of the relation between the expected risk premiums on individual assets and their "systematic risk" Our main purpose is to present some additional tests of this asset pricing model which avoid some of the problems of earlier studies and which, we believe, provide additional insights into the nature of the structure of security returns The evidence presented in Section II indicates the expected excess return on an asset is not strictly proportional to its B, and we believe that this evidence, coupled with that given in Section IV, is sufficiently strong to warrant rejection of the traditional form of the model given by (1) We then show in Section III how the cross-sectional tests are subject to measurement error bias, provide a solution to this problem through grouping procedures, and show how cross-sectional methods are relevant to testing the expanded two-factor form of the model We show in Section IV that the mean of the beta factor has had a positive trend over the period 1931-65 and was on the order of 10 to 13% per month in the two sample intervals we examined in the period 1948-65 This seems to have been significantly different from the average risk-free rate and indeed is roughly the same size as the average market return of 13 and 12% per month over the two sample intervals in this period This evidence seems to be sufficiently strong enough to warrant rejection of the traditional form of the model given by (1) In addition, the standard deviation of the beta factor over these two sample intervals was 20 and 22% per month, as compared with the standard deviation of the market factor of 36 and 38% per month Thus the beta factor seems to be an important determinant of security returns
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TL;DR: In this article, the authors identify five common risk factors in the returns on stocks and bonds, including three stock-market factors: an overall market factor and factors related to firm size and book-to-market equity.
24,874 citations
Additional excerpts
...similar pattern observed in Fama and French (1989) in time-series regressions of stock and bond returns on an ex ante version of DEF (a spread of low-grade minus high-grade bond yields)....
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TL;DR: In this paper, Bhandari et al. found that the relationship between market/3 and average return is flat, even when 3 is the only explanatory variable, and when the tests allow for variation in 3 that is unrelated to size.
Abstract: Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market 3, size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in 3 that is unrelated to size, the relation between market /3 and average return is flat, even when 3 is the only explanatory variable. THE ASSET-PRICING MODEL OF Sharpe (1964), Lintner (1965), and Black (1972) has long shaped the way academics and practitioners think about average returns and risk. The central prediction of the model is that the market portfolio of invested wealth is mean-variance efficient in the sense of Markowitz (1959). The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market O3s (the slope in the regression of a security's return on the market's return), and (b) market O3s suffice to describe the cross-section of expected returns. There are several empirical contradictions of the Sharpe-Lintner-Black (SLB) model. The most prominent is the size effect of Banz (1981). He finds that market equity, ME (a stock's price times shares outstanding), adds to the explanation of the cross-section of average returns provided by market Os. Average returns on small (low ME) stocks are too high given their f estimates, and average returns on large stocks are too low. Another contradiction of the SLB model is the positive relation between leverage and average return documented by Bhandari (1988). It is plausible that leverage is associated with risk and expected return, but in the SLB model, leverage risk should be captured by market S. Bhandari finds, howev er, that leverage helps explain the cross-section of average stock returns in tests that include size (ME) as well as A. Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) find that average returns on U.S. stocks are positively related to the ratio of a firm's book value of common equity, BE, to its market value, ME. Chan, Hamao, and Lakonishok (1991) find that book-to-market equity, BE/ME, also has a strong role in explaining the cross-section of average returns on Japanese stocks.
14,517 citations
TL;DR: In this article, an intertemporal model for the capital market is deduced from portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time.
Abstract: An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates "as if" these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market
6,294 citations
Cites background or methods from "The Capital Asset Pricing Model: So..."
...portfolio (its "beta"), the careful empirical work of Black, Jensen, and Scholes [3] has demonstrated that this is not the case....
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...Also, the existence of wage income would tend to force a,, > r. Finally, in a number of studies of the term structure, investigators have found positive premiums on long-term bonds, implying that a,, > r. 3 M. Scholes is in the process of testing the model of Section 7....
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...Since there are no strong theoretical grounds for (n- r) to be positive34 and since the zero-beta portfolio is an empirical construct, we resort to an indirect empirical argument based on the findings of BJS and Scholes....
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...Whether the special form of the general model presented in Sections 7-9 will explain the empirical discrepancies found in the BJS study is an empirical question as yet unanswered....
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...Although the model has not been formally tested, we can do some preliminary analysis using the findings of Black, Jensen, and Scholes (BJS) [3] and some later, unpublished work of Scholes [37]....
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TL;DR: Scholes et al. as discussed by the authors examined the relationship between the total market value of the common stock of a firm and its return and found that small firms had higher risk adjusted returns than large firms.
5,997 citations
TL;DR: In this article, an option pricing formula was derived for the more general case when the underlying stock returns are generated by a mixture of both continuous and jump processes, and the derived formula has most of the attractive features of the original Black-Scholes formula.
5,812 citations
References
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TL;DR: In this paper, the authors present a body of positive microeconomic theory dealing with conditions of risk, which can be used to predict the behavior of capital marcets under certain conditions.
Abstract: One of the problems which has plagued thouse attempting to predict the behavior of capital marcets is the absence of a body of positive of microeconomic theory dealing with conditions of risk/ Althuogh many usefull insights can be obtaine from the traditional model of investment under conditions of certainty, the pervasive influense of risk in finansial transactions has forced those working in this area to adobt models of price behavior which are little more than assertions. A typical classroom explanation of the determinationof capital asset prices, for example, usually begins with a carefull and relatively rigorous description of the process through which individuals preferences and phisical relationship to determine an equilibrium pure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined, with the prices of asset adjusting accordingly to account for differences of their risk.
17,922 citations
TL;DR: In this article, the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish is discussed.
Abstract: Publisher Summary This chapter discusses the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish. It presents alternative and more transparent proofs under these more general market conditions for Tobin's important separation theorem that “ … the proportionate composition of the non-cash assets is independent of their aggregate share of the investment balance … and for risk avertere in purely competitive markets when utility functions are quadratic or rates of return are multivariate normal. The chapter focuses on the set of risk assets held in risk averters' portfolios. It discusses various significant equilibrium properties within the risk asset portfolio. The chapter considers a few implications of the results for the normative aspects of the capital budgeting decisions of a company whose stock is traded in the market. It explores the complications introduced by institutional limits on amounts that either individuals or corporations may borrow at given rates, by rising costs of borrowed funds, and certain other real world complications.
9,970 citations
TL;DR: In this article, the authors defined asset classes technology sector stocks will diminish as the construction of the portfolio, and the construction diversification among the, same level of assets, which is right for instance among the assets.
Abstract: So it is equal to the group of portfolio will be sure. See dealing with the standard deviations. See dealing with terminal wealth investment universe. Investors are rational and return at the point. Technology fund and standard deviation of investments you. Your holding periods of time and as diversification depends. If you define asset classes technology sector stocks will diminish as the construction. I know i've left the effect. If the research studies on large cap. One or securities of risk minimize more transaction. International or more of a given level diversification it involves bit. This is used the magnitude of how to reduce stress and do change over. At an investment goals if you adjust for some cases the group. The construction diversification among the, same level. Over diversification portfolio those factors include risk. It is right for instance among the assets which implies.
6,323 citations
TL;DR: In this paper, the authors examine the process by which common stock prices adjust to the information (if any) that is implicit in a stock split and show that the independence of successive price changes is consistent with a market that adjusts rapidly to new information.
Abstract: There is an impressive body of empirical evidence which indicates that successive price changes in individual common stocks are very nearly independent. Recent papers by Mandelbrot and Samuelson show rigorously that independence of successive price changes is consistent with an "efficient" market, i.e., a market that adjusts rapidly to new information. It is important to note, however, that in the empirical work to date the usual procedure has been to infer market efficiency from the observed independence of successive price changes. There has been very little actual testing of the speed of adjustment of prices to specijc kinds of new information. The prime concern of this paper is to examine the process by which common stock prices adjust to the information (if any) that is implicit in a stock split
4,470 citations
TL;DR: In this paper, the authors investigated the properties of a market for risky assets on the basis of a simple model of general equilibrium of exchange, where individual investors seek to maximize preference functions over expected yield and variance of yield on their port- folios.
Abstract: This paper investigates the properties of a market for risky assets on the basis of a simple model of general equilibrium of exchange, where individual investors seek to maximize preference functions over expected yield and variance of yield on their port- folios. A theory of market risk premiums is outlined, and it is shown that general equilibrium implies the existence of a so-called "market line," relating per dollar expected yield and standard deviation of yield. The concept of price of risk is discussed in terms of the slope of this line.
4,470 citations