The intertemporal relation between expected returns and risk

This paper explores the time-series relation between expected returns and risk for a large cross section of industry and size/book-to-market portfolios. I use a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) model to estimate a portfolio's conditional covariance with the market and then test whether the conditional covariance predicts time–variation in the portfolio's expected return. Restricting the slope to be the same across assets, the risk-return coefficient is highly significant with a risk–aversion coefficient (slope) between one and five. The results are robust to different portfolio formations, alternative GARCH specifications, additional state variables, and small sample biases. When conditional covariances are replaced by conditional betas, the risk premium on beta is estimated to be in the range of 3% to 5% per annum and is statistically significant.     

Good News,Bad News,Volatility, and Betas

We investigate the conditional covariances of stock returns using bivariate exponential ARCH (EGARCH) models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., “leverage” effects. Using monthly data, we find strong evidence of conditional heteroskedasticity in both market and non-market components of returns, and weaker evidence of time-varying conditional betas. Surprisingly while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk.     

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.     

The Effect of US Stock Market Uncertainty on Emerging Market Returns

We investigate the effects of US stock market uncertainty (VIX) on the stock returns in Latin America and aggregate emerging markets before, during, and after the financial crisis. We find that increases in VIX lead to significant immediate and delayed declines in emerging market returns in all periods. However, changes in VIX explained a greater percentage of changes in emerging market returns during the financial crisis than in other periods. The higher US stock market uncertainty exerts a much stronger depressing effect on emerging market returns than their own-lagged and regional returns. Our risk transmission model suggests that a heightened US stock market uncertainty lowers emerging market returns by both reducing the mean returns and raising the variance of returns. The VIX fears raise the volatility of emerging market returns through generalized autoregressive conditional heteroskedasticity (GARCH)-type volatility transmission processes.     

Sentiment-scaled CAPM and market mispricing

This study explores the conditional version of the capital asset pricing model on sentiment to provide a behavioural intuition behind the value premium and market mispricing. We find betas (β) and the market risk premium to vary over time across different sentiment indices and portfolios. More importantly, the state β derived from this sentiment-scaled model provides a behavioural explanation of the value premium and a set of anomalies driven by mispricing. Different from the static β–return relation that gives a flat security market line, we document upward security market lines when plotting portfolio returns against their state βs and portfolios with higher state βs earn higher 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.     

On the distribution and conditional heteroscedasticity in Taiwan stock prices

This paper studies the distribution and conditional heteroscedasticity in stock returns on the Taiwan stock market. Apart from the normal distribution, in order to explain the leptokurtosis and skewness observed in the stock return distribution, we also examine the Student-t, the Poisson–normal, and the mixed-normal distributions, which are essentially a mixture of normal distributions, as conditional distributions in the stock return process. We also use the ARMA (1,1) model to adjust the serial correlation, and adopt the GJR–generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model to account for the conditional heterscedasticity in the return process. The empirical results show that the mixed–normal–GARCH model is the most probable specification for Taiwan stock returns. The results also show that skewness seems to be diversifiable through portfolio. Thus the normal–GARCH or the Student-t–GARCH model which involves symmetric conditional distribution may be a reasonable model to describe the stock portfolio return process¹.     

Is the Market Portfolio a Dynamic Factor? Evidence from Individual Stock Returns

This paper uses a factor model to test whether the market portfolio is a dynamic factor in the sense that individual stock returns contain a premium linked to the conditional risk of the market portfolio. The market conditional risk is based on a decomposition of the market variance into a time-varying trend component and a transitory component. The evidence shows that the conditional market premium is rising when the permanent trend rises relative to the conditional variance. The evidence for individual stock returns supports the notion that the market portfolio is a dynamic factor. Individual stock return autocorrelations are fully explained by the time variation in the market premium. The risk premia attributed to static factors are statistically insignificant.     

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.     

Cross-sectional analysis of Swedish stock returns with time-varying beta: the Swedish stock market 1983–96

This paper analyses the ability of beta and other factors, like firm size and book-to-market, to explain cross‐sectional variation in average stock returns on the Swedish stock market for the period 1983–96. We use a bivariate GARCH(1,1) process to estimate time-varying betas for asset returns. The estimated variances of these betas, derived from a Taylor series approximation, are used for correcting errors in variables. An extreme bound analysis is utilized for testing the sensitivity of the estimated coefficients to changes in the set of included explanatory variables.
Our results show that the estimated conditional beta is a more accurate measure of the true market beta than the beta estimated by OLS. The coefficient for beta is not significantly different from zero, while the variables book-to-market and leverage have significant coefficients, and the latter coefficients are also robust to model specification. Excluding the down turn 1990–92 from the sample shows that the significance of the risk premium for leverage might be considered as an industry effect during this extreme period. Finally, we find a close dependence between the risk premium for beta and that for size and book-to-market. The omission of each of these variables may cause statistical bias in the estimated coefficient for beta.     

Time Varying Beta Risk: An Analysis of Alternative Modelling Techniques

This paper investigates the performance of three different approaches to modelling time-variation in conditional asset betas: GARCH models, the extended market model of Schwert and Seguin (1990) and the Kalman Filter algorithm. Using daily UK industry returns, we find the simple market model beta to be as efficient as the more complicated GARCH type models. However, the Kalman Filter algorithm incorporating a random walk parameterisation dominates all other models under the mean-square error criterion. Finally, we provide strong evidence that a combination of the methods under investigation may lead to considerably more powerful estimators of the time-variation in conditional beta.     

Constructing Asset Pricing Models With Specific Factor Loadings

We demonstrate how one can build pricing formulae in which factors other than beta may be viewed as determinants of asset returns. This is important conceptually as it demonstrates how the additional factors can compensate for a market portfolio proxy that is mis‐specified, and also shows how such a pricing model can be specified ex ante. The procedure is implemented by first selecting an ‘orthogonal’ portfolio which falls on the mean‐variance efficient frontier computed from the empirical average returns, variances and covariances on the equity securities of a large sample of firms. One then determines the inefficient index portfolio which leads to a vector of betas that when multiplied by the average return on the orthogonal portfolio, and which when subtracted from the vector of average returns for the firms comprising the sample, yields an error vector that is equal to the vector of numerical values for the variables that are to form the basis of the asset pricing formula. There will then be a perfect linear relationship between the vector of average returns for the firms comprising the sample, the vector of betas based on the inefficient index portfolio and such other factors that are deemed to be important in the asset pricing process. We illustrate computational procedures using a numerical example based on the quality of information contained in published corporate financial statements.     

Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management

This paper derives the closed form solution for multistep predictions of the conditional means and covariances for multivariate ARMA-GARCH models. These predictions are useful e.g. in mean-variance portfolio analysis when the rebalancing frequency is lower than the data frequency. In this situation the conditional mean and the conditional covariance matrix of the cumulated higher frequency returns are required as inputs in the mean-variance portfolio problem. The empirical value of the result is evaluated by comparing the performance of quarterly and monthly rebalanced portfolios using monthly MSCI index data across a large set of GARCH models. Using correct multistep predictions generally results in lower risk and higher returns.     

The Correlation Structure of Unexpected Returns in U.S. Equities

We examine the correlations between unexpected market moves and unexpected equity portfolio moves conditional on market performance. We derive unexpected returns from a two-stage regime switching model. The model allows for time-varying expected returns where the market portfolio alone dictates the regime switching process. Portfolios exhibit a natural hedge where correlations during extreme unexpected market downturns are generally negative. During unexpected market upswings, correlations increase. Using the unconditional analysis would lead to overhedging during market downturns and underhedging during market upswings. The adjustments to the unconditional hedging strategy conditional on extreme market movements frequently exceed ±10%.     

MACROECONOMIC VARIABLES AND SEASONAL MEAN REVERSION IN STOCK RETURNS

In this paper I investigate whether seasonal mean reversion in stock portfolio returns is related to common macroeconomic risk factors. I decompose excess returns into explained and unexplained returns using a multifactor pricing model. The explained excess returns exhibit January mean reversion; the unexplained excess returns do not. The mean reversion can be attributed to the components of return related to unexpected inflation, bond default premium, and market risk. The results do not depend on the time-series properties of the portfolio betas. Bond default premia and excess market returns are mean reverting in January.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

Macroeconomic risks and REITs returns: A comparative analysis

We study the relationship between the excess returns of REITs and volatilities of macroeconomic factors in developing markets (Bulgaria and South Africa) and a ‘benchmark’ developed market (USA). As expected, our results generally indicate that conditional volatilities of macroeconomic risks, extracted through the GARCH (1,1) process, are time-varying. GARCH coefficients are largely significant for excess returns and retained principal components implying conditional time-varying volatility. We use the GMM to examine the linkage between volatilities of macroeconomic variables and REITs returns. The general result here is that macroeconomic risk cannot explain excess returns on REITs. However, we document a positive relationship between variability in REITs returns and the real economy for the US. US REITs portfolio managers and investors should be wary of fluctuations in these variables as they may accentuate volatility in REITs returns.     

Size,time-varying beta,and conditional heteroscedasticity in UK stock returns

The purpose of this study is to examine the relationship between firm size and time-varying betas of UK stocks. We extend the Schwert and Seguin (1990)(Journal of Finance 45, 1120–1155) methodology by explicitly modeling conditional heteroscedasticity in the market model residual returns. Our results show that the time-varying coefficient is not statistically significant for both small and large firm stock indexes. We also find that accounting for GARCH effects in the Schwert-Seguin market model yields beta estimates that are markedly differently from those when conditional heteroscedasticity is ignored. Event studies that ignore conditional heteroscedasticity may bias the abnormal returns of small and large firms, thereby leading to a different conclusion regarding the significance of an information event.     

Analysis of Dynamic Correlation of Japanese Stock Returns with Network Clustering

In this paper, the dynamic correlation of Japanese stock returns is estimated by using the dynamic conditional correlation (DCC–GARCH) model to study their correlation dynamics empirically. It is difficult to fit the model to the whole stock market jointly at the same time; therefore, a network-based clustering is applied for the dimensionality reduction of the sample data. Two types correlation structures are estimated: homogeneous groups of stocks in a balanced size are created by clustering to observe within-group correlation, while a single portfolio that comprises group portfolio returns is also created to observe between-group correlation. The estimation result reveals dynamic changes in correlation intensity represented by the largest eigenvalue of the estimated correlation matrix. A higher level of correlation intensity and volatility are observed during the crisis periods, namely after both the Lehman collapse and the Great East Japan Earthquake, for the between- and within-group correlations. It is also confirmed that the pattern of correlation change is significantly different between the groups. The proposed method is useful for monitoring dynamic correlation of asset returns efficiently in a large scale of portfolio.     

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.