Abacus

How to Cite

Dempsey, M. (2013), The Capital Asset Pricing Model (CAPM): The History of a Failed Revolutionary Idea in Finance. Abacus, 49: 723. doi: 10.1111/j.1467-6281.2012.00379.x

Abstract

The capital asset pricing model (CAPM) states that assets are priced commensurate with a trade-off between undiversifiable risk and expectations of return. The model underpins the status of academic finance, as well as the belief that asset pricing is an appropriate subject for economic study. Notwithstanding, our findings imply that in adhering to the CAPM we are choosing to encounter the market on our own terms of rationality, rather than the market’s.

Modern academic finance is built on the proposition that markets are fundamentally rational. The foundational model of market rationality is the capital asset pricing model (CAPM). The implications of rejecting market rationality as encapsulated by the CAPM are very considerable. In capturing the idea that markets are inherently rational, the CAPM has made finance an appropriate subject for econometric studies. Industry has come to rely on the CAPM for determining the discount rate for valuing investments within the firm, for valuing the firm itself, and for setting sales prices in the regulation of utilities, as well as for such purposes as benchmarking fund managers and setting executive bonuses linked to adding economic value. The concept of market rationality has also been used to justify a policy of arm’s-length market regulationon the basis that the market knows best and that it is capable of self-correcting. Nevertheless, we consider that in choosing to attribute CAPM rationality to the markets, we are imposing a model of rationality that is firmly contradicted by the empirical evidence of academic research.

In Fisher Black and the Revolutionary Idea of Finance. Mehrling (2007 ) considers the CAPM as the revolutionary idea that runs through finance theory. He recounts the first major step in the development of modern finance theory as the efficient markets hypothesis, followed by the second step, which is the CAPM. While the efficient market hypothesis states that at any time, all available information is imputed into the price of an asset, the CAPM gives content to how such information should be imputed. Simply stated, the CAPM says that investors can expect to attain a risk-free rate plus a market risk premium multiplied by their exposure to the market. Mehrling presents the model formally as:

where E (R_j ) is the expected return on asset j over a single time-period, r_f is the riskless rate of interest over the period, E (R _M ) is the expected return on the market over the period, and _j identifies the exposure of asset j to the market.

In Mehrling’s account, Black (1972 ) recognized that a rational market effectively requires the CAPM. As Black saw it, if the market of all assets offers investors a risk premium'[E (R _M ) r_f ]in compensation for bearing risk exposure, then, all else being equal, each individual stock, j. must rationally offer a risk premium equal to _j .[E (R _M ) r_f ], since _j measures the asset’s individual exposure to market risk. Market frictions (limited access to borrowing at the risk-free rate, for example) might imply adjustments, but, at the core, the CAPM must maintain (Black, 1972 ).

Nevertheless, we argue that the CAPM fails as a paradigm for asset pricing. To this end, we show, first, how a re-examination of the research of Black et al. (1972 ), which did much to lay the empirical foundation for the CAPM, reveals that the data do not actually provide a justification of the CAPM as claimed, but rather constitute confirmation of the null hypothesis, namely that investors impose a single expectation of return on assets. Researchers, however, did not wish to abandon the core paradigm of market rationality. Such paradigm, after all, justified the status of finance as a subject worthy of scientific inquiry. Second, we show that though the evidence now obliges academics to admit the ineffectiveness of beta, the impression remains that the CAPM (in some adjusted form) is core to the empirical behaviour of markets. Fama and French, for example, resolutely defend their three-factor model (which currently stands as the industry-standard alternative to the CAPM) as a multi-dimensional risk model of asset pricing. Nevertheless, they concede that the average return for an asset over multiple periods is insensitive to its beta. This fact alone suggests that markets might be unable to price risk differentially across assets.

There is a correspondence here with the observation of the scientific philosopher Thomas Kuhn (1962 ), who states that facts always serve to justify more activity without ever seriously being allowed to threaten the paradigm core. In Kuhn’s view, normal science generally consists of a protracted period of adjustments to the surrounding framework of a central paradigm with add-on hypotheses aimed at defending the central hypothesis against various anomalies. The continued defence of the CAPMadding more factors to the CAPM to explain more anomalieshas led the single-factor CAPM model to become the three-factor model of Fama and French. To this model are added additional factors for idiosyncratic volatility, liquidity, momentum, and so forth, all of which typify Kuhn’s articulation of normal science.

If the CAPM must be rejected, we are obliged to return to a view of markets as predating the introduction of the CAPM. Namely, that markets respond generally positively to good news, and negatively to bad news, but wherein Keynesian crowd psychology as each investor looks to other investors inevitably influences the reaction, which may take on a degree of optimism or pessimism that disconnects from the fundamental news. Markets may indeed be capable of self-correction in the long-term, but this may be of little compensation to members of society enduring losses and the negative impact on the economy in the meantime. Such a view of markets would imply that a research agenda aimed at understanding market fallibility and their potential for self-destruction, rather than aimed at enriching an account of markets in equilibrium, provides a more useful contribution to policy making. In effect, the paradigm of the CAPM and efficient markets may need to be replaced with a paradigm of markets as vulnerable to capricious behaviour.

1 Background

By the late 1950s, the prestige of the natural sciences had encouraged the belief that the modelling of decision-making and resource allocation problems could be identified through the elaboration of optimization models and the general extension of techniques from applied mathematics. Into this environment, Modigliani and Miller (1958. 1963 ) ushered their agenda for the modern theory of corporate finance. Thus the discipline was transformed from an institutional normative literaturemotivated by and concerned with topics of direct relevance to practitioners (such as technical procedures and practices for raising long-term finance, the operation of financial institutions and systems)into a microeconomic positive science centred about the formation and analysis of corporate policy decisions with reference to perfect capital markets. A capital market where prices provide meaningful signals for capital allocation is an important component of a capitalist system. When investors choose among the securities that represent ownership of firms’ activities, they can do so under the assumption that they are paying fair prices given what is known about the firm (Fama, 1976 ). The foundations of modern finance theory embrace such a view of capital markets. The underlying paradigm asserts that financial capital circulates to achieve those rates of return that are most attractive to its investors. In accordance with this principle, prices of securities observed at any time fully reflect all information available at that time so that it is impossible to make consistent economic profits by trading on such available information (e.g. Modigliani and Miller, 1958 ; Fama, 1976 ; or Weston, 1989 ).

The efficient market hypothesisthe notion that market prices react rapidly to new information (weak, semi-strong or strong form)is claimed to be the most extensively tested hypothesis in all the social sciences (e.g. Smith, 1990 ). Consistent with the efficient market hypothesis, detailed empirical studies of stock prices indicate that it is difficult to earn above-normal profits by trading on publicly available data because they are already incorporated into security prices. Fama (1976 ) reviews much of this evidence, though the evidence is not completely one-sided (e.g. Jensen, 1978 ). Yet even allowing that empirical research has succeeded in broadly establishing that successive share price movements are systematically uncorrelated, thus establishing that we are unable to reject the efficient market hypothesis, this does not describe how markets respond to information and how information is impounded to determine share prices. That is to say, the much-vaunted efficient market hypothesis does not in itself enable us to conclude that capital markets allocate financial resources efficiently. If we wish to claim allocative efficiency for capital markets, we must show that markets not only rapidly impound new information, but also meaningfully impound that information.

The variant of the efficient market hypothesis that encapsulates such efficient allocation is the capital asset pricing model (CAPM). The CAPM has dominated financial economics to the extent of being labelled the paradigm (Ross, 1978 ; Ryan, 1982 ). Since its inception in the early 1960s, it has served as the bedrock of capital asset pricing theory and its application to practitioner activities. The CAPM is based on the concept that for a given exposure to uncertain outcomes, investors prefer higher rather than lower expected returns. This tenet appears highly reasonable, and following the inception of the CAPM in the late 1960s, a good deal of empirical work was performed aimed at supporting the prediction of the CAPM that an asset’s excess return over the risk-free rate should be proportional to its exposure to overall market risk, as measured by beta.

The underlying intuition of the CAPM has appealed forcibly to practitioners in the fields of finance and accounting. At universities, future practitioners are inculcated with the notion of the CAPM and its attendant beta. Management accountants are likely to instinctively determine an acceptable discount rate in terms of the CAPM and a project beta when discounting. Corporate and fund management performances are measured in terms of abnormal returns, where abnormal is relative to a CAPM-determined return.

Early tests of the CAPM showed that higher stock returns were generally associated with higher betas. These finding were taken as evidence in support of the CAPM while findings that contradicted the CAPM as a completely adequate model of asset pricing did not discourage enthusiasm for the model.1 Miller and Scholes (1972 ), Black et al. (1972 ) and Fama and McBeth (1973 ) also demonstrate a clear relationship between beta and asset return outcomes. Nevertheless, the returns on stocks with higher betas are systematically less than predicted by the CAPM, while those of stocks with lower betas are systematically higher. In response, Black proposed a two-factor model (with loadings on the market and a zero-beta portfolio). Thus the claim was made that the CAPM could be fixed by substituting the risk-free rate in the model with the rate of return on a portfolio of stocks with zero beta.

Controversially, Fama and French (1992 ) show that beta cannot be saved. Controlling for firm size, the positive relationship between asset prices and beta disappears. Additional characteristics such as firm size (Banz, 1981 ), earnings yield (Basu, 1983 ), leverage (Bhandari, 1988 ), the firm’s ratio of book value of equity to its market value (Chan et al. 1991 ), stock liquidity (Amihud and Mendelson, 1986 ), and stock price momentum (Jegadeesh and Titman, 1993 ) now appear to be important in describing the distribution of asset returns at any particular time. The Fama and French (1996 ) three-factor model identifies exposures to differential returns across high and low book-to-market stocks and across large and small firms to the CAPM as proxies for additional risk factors. As is often remarked, the model derives from a fitting of data rather than from theoretical principles. Black (1993 ) considered the then fledgling Fama and French three-factor model as data mining. Although Fama and French have decried the capacity of beta, they nevertheless insist that their two factors are additional’designed to capture certain anomalies with the CAPM. Formally, their model is presented as a refinement in the spirit of the CAPM. The trend of adding factors to better explain observed price behaviours has continued to dominate asset pricing theory. Subrahmanyam (2010 ) documents more than 50 variables used to predict stock returns. Nevertheless, the CAPM remains the foundational conceptual building block for these models. The three-factor model of Fama and French (1993. 1996 ), and the Carhart model (1997 ) which adds momentum exposure as a fourth factor, are now academically mainstream.

2 Expectations Models in Finance

In what is generally recognized as the first methodologically satisfactory test of the CAPM, Black, Jensen and Scholes (1972 ) (hereafter, BJS) find that there is a positive relation between average stock returns and beta ( ) during the pre-1969 period. BJS, however, recognized that although this observation might be interpreted as encouraging support for the CAPM, it is not actually sufficient to substantiate the CAPM. Insightfully, they recognized that even if it were the case that beta is actually ignored by investors, beta would still be captured in the data of stock returns as _j .[R _M E (R _M )], where _j is the beta for a stock j. and [R _M E (R _M )] represents the actual market return (R _M ) over what it was expected to be (E (R _M )). To see where the _j .[R _M E (R _M )] term comes from, consider that a researcher wishes to test the null hypothesis that investors actually ignore beta and simply seek those stocks offering the highest returns, with the outcome that all stocks are priced to deliver the same expected return, say 10%, in a given year. Now, suppose that the actual market return for this year turns out to be 18%. In accordance with the null hypothesis model (all stocks are priced to deliver the same return), should the researcher now expect to find that outcome returns for this year are distributed around 18% and that beta has no explanatory role? Surprisingly, the answer is no. Consider, for example, that Stock A has a sensitivity to the market described by its beta of 1.5, and Stock B has a sensitivity to the market described by its beta of 0.5. BJS argue that the researcher should expect to find that each stock has achieved a return equal to the initial expectation (10%) plus the surprise additional market return (8% = 18% 10%) multiplied by that stock’s beta (defined as an asset’s return sensitivity to the market return). In other words, the researcher expects to find that the outcome return for Stock A is 10% + 1.5*8% = 22%, and for Stock B is 10% + 0.5*8% = 14%, even though both stocks were priced to give the same expected outcome of 10%.

Thus for BJS, the outcome regression equation to test a hypothesis for the expectation of return, E (R_j ), for assets j against the actual outcome returns, R_j . for the assets, becomes:

where E (R_j ) formulates the model to be tested (e.g. the right-hand side of the CAPM expression in equation ((1) ) and [R _M E (R _M )] is the unexpected excess market return multiplied by the asset beta (_j ) and _j allows an error term (cf. BJS, equation ((3) )). Note again that the _j term here does not depend on any assumptions regarding investor expectations.

In seeking to test the CAPM, BJS therefore formed their appropriate regression equation by substituting the CAPM equation for E (R_j ) as equation ((1) ) into equation ((2) ) to give:

The E (R _M ) terms cancel out and the required regression equation of the excess asset return R_j r_f on the excess market return (R _M r_f ) becomes:

A significant advantage of the regression equation is that its inputs are observable output data and not expectations.

BJS (1972 ) and Black (1993 ) apply equation ((3) ) to the data following a double-pass regression method so as to achieve a number of testable predictions. Thus they founded the elements of the methodology that underpins all subsequent tests of asset pricing models. The method can be explained briefly. In a first pass, equation ((3) ) is run as a time-series regression of each stock’s monthly excess return (R_j,t r_f ) at time t on the monthly excess market return (R _M,t r_f ) for that month so as to determine each stock’s beta (_j ) as the slope of the regression:

where _j denotes the intercept of the regression and _j,t are the regression error terms, which are expected to be symmetrically distributed about zero (cf. BJS, equation ((6) )). The stocks are then ranked by their beta and 10 decile portfolios are partitioned from lowest beta to highest beta stocks. In this way, an average intercept (_P ) and average slope (that is, beta, _P ) may be assigned to each portfolio. We can see that if the CAPM of equation ((1) ) is well specified in describing expectations, the intercepts _P for each portfolio should be close to zero. In the second pass, equation ((3) ) can now be run as a single cross-section regression of the excess portfolio returns (R_P r_f ) on the portfolio betas (_P ) (as determined in the prior time-series regression as the explanatory variable):

(cf. BJS, equation ((11) )). Again, if the CAPM of equation ((1) ) is well specified, the intercept ₀ term should be statistically indistinguishable from zero, and the coefficient ₁ on the _P ‘s should identify the average excess market return, (R _M r_f ).

In the time-series regressions, the BJS studies determine that the intercept _P s are consistently negative for the high-risk portfolios ( > 1) and consistently positive for the low-risk portfolios ( < 1). In the cross-sectional regression, they find that the intercept is positive and the slope is too low to be identified with an average excess market return, (R _M r_f ). Both pass regressions therefore contradict the CAPM.

As highlighted in Mehrling’s biography 2007 ), Black realized that without some meaningful version of the CAPM, markets cannot be held to be rational. As Black (1993 ) explained, if the market does not appropriately reward beta, no investor should invest in high-beta stocks. Rather, the investor should form a portfolio with the lowest possible beta stocks and use leverage to achieve the same market exposure but with a superior return performance as compared with a high-beta stock portfolio.

The simplest way to make the CAPM fit the data is to replace the risk-free rate, r_f (typically the return on short-term U.S. Treasury bonds) with some larger value, R _z. since that would adjust the intercepts and explain the lower slope of the cross-sectional regressions. In fact, BJS use the data to calculate the required substitute rate, R _z. that offers the best fit. As Mehrling’s biography recalls, the R _z term was a statistical fix in search of a theoretical explanation (p. 114). Accordingly, Black proposed his version of the CAPM as:

where R _z is postulated as representing the return on a portfolio that has zero covariance with the return on the market portfolio. Black argued that the model is consistent with relaxing the assumption of the existence of risk-free borrowing and lending opportunities.

The test of whether the data are being generated by the process of equation ((6) ) is that of whether the actual outcome returns are explained by the regression equation ((3) ) with the standard risk-free rate r_f replaced by R_z :

which (because we wish to maintain the regression format of a dependence of R_j r_f on R _M r_f as the independent variable) can be rewritten as:

That is, the first-pass time-series regressions of the excess return (R_j r_f ) on the excess market return (R _M r_f ) now has predicted intercepts _P for the portfolios as:

where R_z is the average excess mean return on the zero-beta portfolio over the period. Equation ((7) ) (and therefore equation ((6) )) could therefore be declared consistent with the JBS findings that the intercept _P s are increasingly negative (positive) with increasing (decreasing) betas from the base _P = 1. Additionally, the second-pass cross-section regressions of the portfolio returns (R_P ) on the portfolio betas (_P ) as equation (5) above:

which is consistent with the determinations of JBS of a positive intercept and a slope that understates the excess market return.

Suppose, however, that we insist on testing the possibility that investors contravene Black’s CAPM and can be modelled as adhering to our (heretical) null hypothesis that all assets j have the same expected rate of return, E (R_j ), which is then necessarily that of the market, E (R _M ):

How do the regressions separate the hypotheses as preferable explanations of the data? To test the equation ((10) ) hypothesis, we would form the regression equation (with equation ((2) )) as:

Note again how _j above identifies the drag of the excess market return on the return on asset j. Equation ((11) ) (again for the purpose of expressing a preferred regression dependence of R_j r_f on R _M r_f as the independent variable) can be rewritten as:

The first-pass time-series regressions should now have the intercept _P :

and the second-pass cross-section regressions (equation ((5) )):