This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the Fama-French three-factor model on portfolios sorted by size and book-to-market characteristics. The conditional consumption CAPM can account for the difference in returns between low-book-to-market and high-bookto-market portfolios and exhibits little evidence of residual size or book-to-market effects. We are grateful to Eugene Fama and Kenneth French for graciously providing the

An integrated econometric view of maximum likelihood methods and more traditional two-pass approaches to estimating beta-pricing models is presented. Several aspects of the well-known “errors-in-variables problem ” are considered, and an earlier conjecture concerning the merits of simultaneous estimation of beta and price of risk parameters is evaluated. The traditional inference procedure is found, under standard assumptions, to overstate the precision of price of risk estimates and an asymptotically valid correction is derived. Modifications to accommodate serial correlation in market-wide factors are also discussed Sharpe (1964) and Lintner (1965) demonstrate that, in equilibrium, a financial asset’s expected return must be positively linearly related to its “beta, ” a measure of systematic risk or co-movement with the market portfolio return: 1 This article is an extension of the second chapter of my doctoral dissertation at Carnegie Mellon University. Recent versions were presented in seminars

Four decades later, the CAPM is still widely used in applications, such as estimating the cost of capital for firms and evaluating the performance of managed portfolios. It is the centerpiece of MBA investment courses. Indeed, it is often the only asset pricing model taught in these courses. 1 The attraction of the CAPM is that it offers powerful and intuitively pleasing predictions about how to measure risk and the relation between expected return and risk. Unfortunately, the empirical record of the model is poor – poor enough to invalidate the way it is used in applications. The CAPM’s empirical problems may reflect theoretical failings, the result of many simplifying assumptions. But they may also be caused by difficulties in implementing valid tests of the model. For example, the CAPM says that the risk of a stock should be measured relative to a comprehensive “market portfolio ” that in principle can include not just traded financial assets, but also consumer durables, real estate, and human capital. Even if we

In this paper, I set up scenarios where the mean-variance capital asset pricing model is true and where it is false. Then I investigate whether the coefficients from regressions of population expected excess returns on population betas, and expected excess returns on betas and size, allow us to distinguish between the scenarios. I show that the coefficients from either ordinary least squares or generalized least squares regressions do not allow us to tell whether the model is true or false. EACH OF THE FOLLOWING FIVE statements has implications for how we might judge whether the Sharpe ~1964!–Lintner ~1965! mean-variance capital asset pricing model ~MV CAPM! is true or false. First, the market portfolio is MV efficient. Second, there is at least one positively weighted efficient portfolio. Third, in the riskless asset version of the model, the market portfolio is the tangency portfolio—it is the point of tangency between a ray emanating from the riskless interest rate and the minimum-variance frontier of

We use information contained in yield spreads to recover investors ’ ex ante required rates of return on corporate securities, and then use these ex ante returns to study the pricing of risky assets. Differently from the standard approach, our asset pricing tests do not rely on the use of ex post average equity returns as proxies for expected equity returns. We find that: (i) the market beta plays a significant role in the cross-section of expected equity returns, and its role persists even after size and book-to-market factors are accounted for; (ii) the risk premia associated with size and book-to-market are positive, significant, and countercyclical; and (iii) there is little evidence on positive momentum profits. We also find that systematic risk, as captured by common equity factors, is the main driver of the cross-sectional variation in bond yield spreads. JEL Classification: G12, E44

Abstract not found

Our main purpose in this paper is to derive the generalized equilibrium relationship between risk and return under the assumption that the asset returns follow a joint symmetric ff-stable distribution, with 1 ! ff ! 2. In order to justify such an investigation, we start by empirically evidencing the fractal structure of stocks market through extensive tests of self-similarity and stability. These tests allow us to model price changes with ff-stable distributions. We then show that equilibrium rates of return on all risky assets are functions of their covariation with the market portfolio. The "stable" CAPM highlights a new measure of the quantity of risk which may be interpreted as a generalized beta coefficient.

We employ analysts ’ expected rates of return and provide evidence on the relation between these expectations and firm attributes. The assumption that these expectations are unbiased estimates of market-wide expected rates of return allows us to circumvent the use of realized rates of return and provide evidence on the predictions emanating from traditional asset pricing models. We find a positive and robust relation between expected return and market beta and a

The emerging sub#eld of econophysics explores the degree to which certain concepts and methods from statistical physics can be appropriately modi#ed and adapted to provide new insights into questions that have been the focus of interest in the economics community. Here we give a brief overview of two examples of research topics that are receiving recent attention. A #rst topic is the characterization of the dynamics of stock price #uctuations. For example, we investigate the relation between trading activity -- measured by the number of transactions N#t -- and the price change G#t for a given stock, over a time interval [t; t +#t]. We relate the time-dependent standard deviation of price #uctuations -- volatility -- to two microscopic quantities: the number of transactions N#t in #t and the variance W #t of the price changes for all transactions in #t. Our work indicates that while the pronounced tails in the distribution of price #uctuations arise from W#t , the long-range correlations found in |G#t | are largely due to N#t .We also investigate the relation between price #uctuations and the number of shares Q#t traded in #t. We #nd that the distribution of Q#t is consistent with a stable L#evy distribution, suggesting aL#evy scaling relationship between Q#t and N#t , which would provide one explanation for volume-volatility co-movement. A second topic concerns cross-correlations between the price #uctuations of di#erent stocks. We adapt a conceptual framework, random matrix theory (RMT), #rst used in physics to interpret statistical properties of nuclear energy spectra. RMT makes predictions for the statistical properties of matrices that are universal, that is, do not depend on the interactions between the elements comprising the system. In physics systems, deviat...

This paper explores the ability of theoretically-based asset pricing models such as the CAPM and the consumption CAPM#referred to jointly as the (C)CAPM#to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the threefactor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumpti...