CAPM over the long run: 1926–2001

A conditional one-factor model can account for the spread in the average returns of portfolios sorted by book-to-market ratios over the long run from 1926 to 2001. In contrast, earlier studies document strong evidence of a book-to-market effect using OLS regressions over post-1963 data. However, the betas of portfolios sorted by book-to-market ratios vary over time and in the presence of time-varying factor loadings, OLS inference produces inconsistent estimates of conditional alphas and betas. We show that under a conditional CAPM with time-varying betas, predictable market risk premia, and stochastic systematic volatility, there is little evidence that the conditional alpha for a book-to-market trading strategy is different from zero.     

Expected Returns,Time-varying Risk,and Risk Premia

A new empirical model for intertemporal capital asset pricing is presented that allows both time-varying risk premia and betas where the latter are identified from the dynamics of the conditional covariance of returns. The model is more successful in explaining the predictable variations in excess returns when the returns on the stock market and corporate bonds are included as risk factors than when the stock market is the single factor. Although changes in the covariance of returns induce variations in the betas, most of the predictable movements in returns are attributed to changes in the risk premia.     

Are the Latent Variables in Time-Varying Expected Returns Compensation for Consumption Risk?

Multibeta asset pricing models are examined using proxies for economic state variables in a framework which exploits time-varying expected returns to estimate conditional betas. Examples include multiple consumption-beta models and models where asset returns proxy for the state variables. When the state variables are not specified, the tests indicate two or three time-varying expected risk premiums in the sample of quarterly asset returns. Conditional betas relative to consumption generate less striking evidence against the model than betas relative to asset returns, but both the consumption and the market variables fail to proxy for the state variables.     

Conditional Risk Premiums of Asian Real Estate Stocks

This paper uses a multi-factor latent variable model to examine the time variation of expected returns on Asian property stocks. Using data from 1990 to 1997, we found strong evidence of time-varying risk premium, suggesting property development based on constant discount rate may underestimate the cost of capital. A further study using a multi-country model suggests that conditional excess returns of many crisis-stricken economies appear to move quite closely with each other. This supports the hypothesis that the risk premiums in these Asian markets move closely over time As a result, they provide a partial explanation of market contagion in the region.     

A Cross-Sectional Empirical Test of a Dual-State Multi-Factor Pricing Model

During empirical testing of the Capital Asset Pricing Model an assumption is typically made that risk is intertemporally constant. However, prior research finds that risk changes over time. We empirically test a conditional dual-state cross-sectional model allowing risk to change through prior identification of different market and economic states. We examine relationships between returns and conditional market and economic-factor betas, size, book-to-market equity, and earnings-price ratios. We find that relationships shift across regimes, suggesting the importance of a conditional, as opposed to unconditional, model. Relationships also change in January.     

Efficiency in the Pricing of the FTSE 100 Futures Contract

This paper studies the pricing efficiency in the FTSE 100 futures contract by linking the predictable movements in futures returns to the time-varying risk and risk premia associated with prespecified factors. The results indicate that the predictability of the FTSE 100 futures returns is consistent with a conditional multifactor model with time-varying moments. The dynamics of the factor risk premia, combined with the variation in the betas, capture most of the predictable variance of returns, leaving little variation to be explained in terms of market inefficiency. Hence the predictive power of the instruments does not justify a rejection of market efficiency.     

Stock prices, news, and business conditions

Previous research finds that fundamental macroeconomic newshas little effect on stock prices. We show that after allowingfor different stages of the business cycle, a stronger relationshipbetween stock prices and news is evident. In addition to stockprices, we examine the effect of real activity news on proxiesfor expected cashflows and equity discount rates. We find thatwhen the economy is strong the stock market responds negativelyto news about bigger real economic activity. This negative relationis caused by the larger increase in discount rates relativeto expected cashflows.     

Testing Conditional Asset Pricing Models Using a Markov Chain Monte Carlo Approach

We use Markov Chain Monte Carlo (MCMC) methods for the parameter estimation and the testing of conditional asset pricing models. In contrast to traditional approaches, it is truly conditional because the assumption that time variation in betas is driven by a set of conditioning variables is not necessary. Moreover, the approach has exact finite sample properties and accounts for errors‐in‐variables. Using S&P 500 panel data, we analyse the empirical performance of the CAPM and the Fama and French (1993) three‐factor model. We find that time‐variation of betas in the CAPM and the time variation of the coefficients for the size factor (SMB) and the distress factor (HML) in the three‐factor model improve the empirical performance. Therefore, our findings are consistent with time variation of firm‐specific exposure to market risk, systematic credit risk and systematic size effects. However, a Bayesian model comparison trading off goodness of fit and model complexity indicates that the conditional CAPM performs best, followed by the conditional three‐factor model, the unconditional CAPM, and the unconditional three‐factor model.     

Time-Varying Expected Returns in International Bond Markets

This article examines the predictable variation in long-maturity government bond returns in six countries. A small set of global instruments can forecast 4 to 12 percent of monthly variation in excess bond returns. The predictable variation is statistically and economically significant. Moreover, expected excess bond returns are highly correlated across countries. A model with one global risk factor and constant conditional betas can explain international bond return predictability if the risk factor is proxied by the world excess bond return, but not if it is proxied by the world excess stock return.     

The Variation of Economic Risk Premiums in Real Estate Returns

We examine the predictable components of returns on stocks, bonds, and real estate investment trusts (REITs). We employ a multiple-beta asset pricing model and find that there are varying degrees of predictability among stocks, bonds, and REITs. Furthermore, we find that most of the predictability of returns is associated with the economic variables employed in the asset pricing model. The stock market risk premium is highly important in capturing the predictable variation in stock portfolios, and the bond market risk premiums (term and risk structure of interest rates) are important in capturing the predictable variation in bond portfolios. For REITs, however, both the stock and bond market risk premiums capture the predictable variation in returns. REITs have comparable return predictability to stock portfolios. We conclude that there is an important economic risk premium for REITs that are not captured by traditional multiple-beta asset pricing models.     

Estimating Systematic Risk Using Time Varying Distributions

This article proposes a dynamic vector GARCH model for the estimation of time-varying betas. The model allows the conditional variances and the conditional covariance between individual portfolio returns and market portfolio returns to respond asymmetrically to past innovations depending on their sign. Covariances tend to be higher during market declines. There is substantial time variation in betas but the evidence on beta asymmetry is mixed. Specifically, in 50% of the cases betas are higher during market declines and for the remaining 50% the opposite is true. A time series analysis of estimated time varying betas reveals that they follow stationary mean-reverting processes. The average degree of persistence is approximately four days. It is also found that the static market model overstates non-market or, unsystematic risk by more than 10%. On the basis of an array of diagnostics it is confirmed that the vector GARCH model provides a richer framework for the analysis of the dynamics of systematic risk.     

Implementing Fischer Black's Simple Discounting Rule

Corporate managers typically estimate the value of capital projects by discounting the project's expected future net cash flows at the cost of capital. The capital asset pricing model (CAPM) is generally used to estimate that cost. But, as anyone who has worked on the finance or business development staff of a public company can attest, there are major challenges in applying the CAPM, including largely unresolved questions about what constitutes the “market portfolio,” how to estimate market risk premiums, and how to estimate the betas of projects. In a short article published in Financial Management in 1988, Fischer Black proposed a valuation “discounting rule” that avoids all these problems—one that involves discounting a relatively certain (as opposed to an expected or average) level of operating cash flows at the risk-free rate. But Black's article does not address the question of how to calculate these “certainty equivalent” or “conditional” cash flows. In this article, the authors propose a way of implementing Black's rule that involves estimating the “conditional” cash flows in a three-step procedure:

• • Find a benchmark security that correlates with the project's cash flows;
• • Estimate the percentiles of the distribution in which the benchmark return equals the risk-free rate over different investment horizons;
• • Use information from corporate managers to assess the cash flows that define the same percentiles in the cash flow distributions.

As the authors point out, the virtue of Black's rule is that it shifts the focus of the analyst away from the assessment of discount factors and puts it squarely on the more challenging, and arguably more relevant, problem of estimating the project's cash flows.     

Tests of Asset Pricing with Time-Varying Expected Risk Premiums and Market Betas

Tests of asset-pricing models are developed that allow expected risk premiums and market betas to vary over time. These tests exploit the relation between expected excess returns and current market values. Using weekly data for 1963 through 1982 on ten common stock portfolios formed according to equity capitalization, a single-risk-premium model is not rejected if the expected premium is time varying and is not constrained to correspond to a market factor. Conditional mean-variance efficiency of a value-weighted stock index is rejected, and the rejection is insensitive to how much variability of expected risk premiums is assumed.     

The predictability of returns on equity REITs and their co-movement with other assets

Recent evidence suggests that the variation in the expected excess returns is predictable and arises from changes in business conditions. Using a multifactor latent variable model with time-varying risk premiums, we decompose excess returns into expected and unexpected excess returns to examine what determines movements in expected excess returns for equity REITs are more predictable than all other assets examined, due in part to cap rates which contain useful information about the general risk condition in the economy. We also find that the conditional risk premiums (expected excess returns) on EREITs move very closely with those of small cap stocks and much less with those of bonds.     

Equity Risk Premium

Abstract

The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.

The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about ?1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.

This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926–2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered.     

The Risk and Predictability of International Equity Returns

We investigate predictability in national equity market returns,and its relation to global economic risks. We show how to consistentlyestimate the fraction of the predictable variation that is capturedby an asset pricing model for the expected returns. We use amodel in which conditional betas of the national equity marketsdepend on local information variables, while global risk premiadepend on global variables. We examine single- and multiple-betamodels, using monthly data for 1970 to 1989. The models capturemuch of the predictability for many countries. Most of thisis related to time variation in the global risk premia.     

Changes in Expected Security Returns,Risk, and the Level of Interest Rates

Regressions of security returns on treasury bill rates provide insight about the behavior of risk in rational asset pricing models. The information in one-month bill rates implies time variation in the conditional covariances of portfolios of stocks and fixed-income securities with benchmark pricing variables, over extended samples and within five-year subperiods. There is evidence of changes in conditional “betas” associated with interest rates. Consumption and stock market data are examined as proxies for marginal utility, in a general framework for asset pricing with time-varying conditional covariances.     

The Importance of Cash-Flow News for Financially Distressed Firms

Previous studies have shown that stock prices are moved primarily by news about discount rates (expected returns). I argue that when a firm experiences financial distress, news about cashflows becomes more dominant in driving its stock returns. Applying Campbell's (1991) variance decomposition framework to financially distressed firms supports this argument. Furthermore, I find that more bankruptcies occur after negative shocks to expected cashflows than after positive shocks to discount rates; and that stock prices of distressed firms are less sensitive than those of sound firms to changes in equity risk.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

Unconditional Tests of Linear Asset Pricing Models with Time‐Varying Betas

In conditional affine factor models, estimated risk prices should satisfy certain unconditional constraints. Specifically, a cross‐sectional estimate of the unconditional slope associated with a risk factor should equal the average price of risk of the factor. The estimated slope associated with the product of a risk factor and an instrument should be equal to the covariance of the factor risk premium with the instrument. We show that the constraints only apply to the conditional models with time‐varying betas. We identify an unconditional constraint on unconditional betas for time‐varying beta models and incorporate it into model tests. We show that imposing this unconditional constraint changes estimates of unconditional betas and risk prices significantly.