Testing the CAPM revisited

This paper re-examines the tests of the Sharpe–Lintner Capital Asset Pricing Model (CAPM). The null that the CAPM intercepts are zero is tested for ten size-based stock portfolios and for twenty five book-to-market sorted portfolios using five-year, ten-year and longer sub-periods during 1965–2004. The paper shows that the evidence for rejecting the CAPM on statistical grounds is weaker than the consensus view suggests, and highlights the pitfalls of testing multiple hypotheses with the conventional heteroskedasticity and autocorrelation robust (HAR) test with asymptotic P-values. The conventional test rejects the null for almost all sub-periods, which is consistent with the evidence in the literature. By contrast, the null is not rejected for most of the sub-periods by the new HAR tests developed by Kiefer et al. (2000), Kiefer and Vogelsang (2005), and Sun et al. (2008).     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

How to Discount Cashflows with Time-Varying Expected Returns

While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores time‐varying risk premiums and betas. We develop a model to consistently value cashflows with changing risk‐free rates, predictable risk premiums, and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large misvaluations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time variation in risk‐free rates and factor loadings.     

Tests of the CAPM with Time-Varying Covariances: A Multivariate GARCH Approach

This paper examines an asset pricing model in which the Sharpe-Lintner CAPM and the zero-beta CAPM are special cases. The model allows the ratio of expected market risk premium to market variance, the conditional expected excess returns, and the risks to change over time. The results are found to be sensitive to the choice of the portfolio formation techniques. Significant time variability is shown in the conditional expected excess asset returns and risks and also in the reward-to-risk ratio.     

Time-Varying Betas of German Stock Returns

The market model assumes stock returns to be a linear function of the market return. However, there is considerable evidence that the beta stability assumption commonly used when estimating the market model is invalid. In this paper we account for beta instability in German stock returns by allowing the coefficients to vary over time in estimation. For time-varying beta estimation we rely on the Flexible Least Squares approach, the Random Walk Model and Moving Window Least Squares. Due to our results time-varying estimation fits the data considerably better than time-invariant estimation and, hence, increases the efficiency of beta based risk measurement.Acknowledgements: The authors thank Stefan Mittnik, Christian Pigorsch, an anonymous referee and the editor for constructive comments.     

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.     

Testing the CAPM with broader market indexes: A problem of mean-deficiency

This study addresses a problem that can arise when a broader market index is used to test the CAPM: a return series used in the index can exclude part of an asset's return. If the excluded return is constant, then a test of mean-variance efficiency can be constructed, but an additional parameter must be estimated. This point is illustrated in tests with both broader market indexes and stocks-only indexes. The broader indexes exclude the rental return on real estate and durables. The excluded rental return is estimated under the assumption that the index portfolio is mean-variance efficient.     

Accounting for the Accuracy of Beta Estimates in CAPM Tests on Assets with Time-varying Risks

This paper advocates two ways to make more efficient use of available information in reducing the bias of the risk premium estimate in two-pass tests of the CAPM. First, explicit modelling of the time-variability of betas can improve the accuracy of the beta forecasts. Second, the cross-sectional information available can be exploited more efficiently using individual stocks instead of portfolios provided that noisy beta predictions are given a smaller weight than more accurate ones. This paper proposes an adjustment of the cross-sectional regressions of excess returns against betas to give larger weights to more reliable beta forecasts. A significant positive relationship between returns and the beta forecast is obtained when the proposed approach is applied to data from the Helsinki Stock Exchange, while the traditional Fama–MacBeth approach as such finds no relationship at all.     

Modeling Time-Varying Volatility and Expected Returns: Evidence from the GCC and MENA Regions

The aim of this study is to investigate empirically the underlying nexus of stock market returns and volatility in the Gulf Cooperation Council (GCC) countries and Middle East and North Africa (MENA) region by using the GARCH-M model. We find that volatility is time-varying in all countries, which indicates substantial variation in the degree of risk across time. However, we do not find empirical support that this time-varying volatility significantly explains expected returns, except in the case of Kuwait, United Arab Emirates, and the MENA region portfolio. Our findings show that stock return volatility is negatively correlated with stock returns in these three markets under the assumption of investor risk aversion. This lends some support to the hypothesis of a volatility-driven negative relationship in the literature. The policy implications of our results are discussed.     

投资收益与风险的正相关性和保险公司的两难选择

在一定的条件下，投资的收益与风险之间正相关性，这就使得保险公司不得不在高收益、高风险和低风险、低收益之间进行选择。然而，基于保险公司风险偏好的分析却表明，这两种极端的选择都不满足最优的条件，保险公司的正确选择应该是在收益和风险之间寻找到一种平衡。     

CAPM, Higher Co‐moment and Factor Models of UK Stock Returns

In this paper we examine the variables that explain the cross‐section of UK stock returns. Previous studies have found that the CAPM beta has moderate or even insignificant explanatory power once the Fama French factors are included. However, we control for different realised risk premia in up and down markets by using the same methodology as Pettengill, Sundaram and Mathur (1995). Unlike previous work, we find that beta is highly significant in explaining the cross‐section of UK stock returns and more importantly remains significant even when the Fama French factors are included in the cross‐sectional regressions. We also investigate whether higher co‐moments (co‐skewness and co‐kurtosis) have any explanatory power but find that empirical support is weaker.     

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.     

Testing Gaussianity and Linearity of Japanese Stock Returns

In this article, we first investigate the Gaussianity of Japanese stock return time series (214 daily, 18 weekly) by the Gaussianity test proposed by Kariya, Tsay, Terui and Li (1994) comprehensively and consistently. And it is observed that all the series are not Gaussian when the 6th order moment structures are taken into account. Up to the 4th order moments there are some series which are compatible with the Gaussianity. Secondly, we apply five well-known nonlinearity tests for stationary time series to the data set and examine the specific nonlinearity of the series. Some series strongly exhibit the specific types of nonlinearity. Typically the Nikkei daily index shows the TAR (Threshold Autoregressive) type nonlinearity. Comparing daily return series with weekly series, it is also shown that a central limit effect is working on the weekly stock returns, where daily information is accumulated over a week, in the sense that weekly returns are relatively closer to Gaussian.     

对冲基金投资收益与风险理论文献综述

另类投资领域中的对冲基金研究对于中国正在兴起的私募基金具有重要的理论和现实意义.本文系统回顾了对冲基金投资收益与风险研究的文献内容,收益的定价方法、收益数据的偏差研究、风险的估测方法、风险测量的不足、对冲基金对金融市场的稳定性影响等,研究发现对冲基金的风险未被正确认识而收益表现被高估.这为全面认识对冲基金的收益风险特征提供了理论基础.     

The Risks and Returns of Brady Bonds in a Portfolio Framework

This paper examines the risks and returns of Brady bonds for the period 1990–1995 in a Modern Portfolio Theory framework. We find: (1) that the realized returns of Brady bonds are lower than the realized returns of other asset classes such as US stocks or US bonds; and (2) Brady bonds exhibit higher volatility compared to the other asset classes. These findings are largely explained by the influence of Mexico's devaluation of the Peso in December 1994. In addition, Mexico's devaluation is found to have had a strong (adverse) contagion effect on the returns on Brady bonds of other countries. The paper also finds that Brady bonds exhibit low correlations with US stocks and bonds markets. Thus, we find that there are potentially positive diversification gains from including Brady bonds in a domestic (US investor's) portfolio.     

Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

CAPM and APT-like models with risk measures

The paper deals with optimal portfolio choice problems when risk levels are given by coherent risk measures, expectation bounded risk measures or general deviations. Both static and dynamic pricing models may be involved. Unbounded problems are characterized by new notions such as (strong) compatibility between prices and risks. Surprisingly, the lack of bounded optimal risk and/or return levels arises for important pricing models (Black and Scholes) and risk measures (VaR, CVaR, absolute deviation, etc.). Bounded problems present a Market Price of Risk and generate a pair of benchmarks. From these benchmarks we introduce APT and CAPM-like analyses, in the sense that the level of correlation between every available security and some economic factors explains the security expected return. The risk level non correlated with these factors has no influence on any return, despite the fact that we are dealing with risk functions beyond the standard deviation.     

考虑流动性的三阶矩资本资产定价的理论模型与实证研究

本文把流动性风险、偏态风险引进传统CAPM模型中,推导出基于流动性的三阶矩资本资产定价的理论模型。本文的模型表明,证券(组合)的收益依赖于它的期望流动性成本、其流动性成本和市场流动性成本的协方差以及其收益和市场收益的协方差与协偏态。本文采用我国A股市场的股票收益数据对模型进行了实证检验.检验结果表明,我国A股市场的证券(组合)的风险溢价在大盘升降区间体现了不同的特征,无论是在全样本区间还是两个子样本区间,基于流动性的三阶矩资本资产定价模型都能更好的拟合资产收益,说明了流动性和偏态因素在我国A股市场的资产定价中有重要影响。