TIME VARIATIONS IN RISK PREMIA,VOLATILITY, AND REWARD-TO-VOLATILITY

In this paper I relate the risk premia in the stock and bond markets to the conditional volatility of returns and time-varying reward-to-volatility variables. I find that the relation between the expected returns on the stocks and bonds and the volatility of returns is time varying. I provide an approach for evaluating the relative importance of the time-varying volatility of returns and reward-to-volatility variables to explain the predictability of risk premia for stock and bond returns. I show that changing reward-to-volatility variables explain more predictable variation in the risk premia for stocks and bonds than changing volatility of returns.     

A conditional higher-moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926–2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs.     

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.     

The effect of time-varying covariances on asset risk premia

In this article we examine an intertemporal capital asset pricing model (CAPM) that allows for time-varying conditional covariances that are assumed to follow a multivariate integrated generalized autoregressive conditional heteroscedastic (IGARCH) process. The resulting pricing equation includes idiosyncratic risk premia in addition to the usual market beta. Empirical analysis based on ten size and ten industry portfolios reveals significant idiosyncratic premia for most portfolios. Overall, we reject the static CAPM in favor of the intertemporal CAPM.     

Macrofactor Conditional Volatilities, Time-Varying Risk Premia and Stock Return Behavior

An Arbitrage Pricing Model is estimated in which the risk premia vary in proportion to the conditional volatilities of the macroeconomic innovations which follow an autoregressive specification. The conditional volatilities of the macroeconomic innovations exhibit strong timevariation from month to month. For size-ranked portfolios of all the shares traded on the Toronto Stock Exchange over the period from March 1962 through March 1988, five macrofactors (namely, the lag of industrial production, the Canadian index of 10 leading indicators, the U.S. composite index of 12 leading indicators, the exchange rate and the residual market factor) have time-varying and priced risk premia. The small-firm effect is absent in the risk-adjusted returns, and a significant portion of the observed January seasonality is explained by the model with time-varying risk premia.     

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.     

Time-varying risk premia in foreign exchange and equity markets: evidence from Asia–Pacific countries

This paper examines the validity of the risk premia hypothesis in explaining deviations from Uncovered Interest Parity (UIP) and the role of deviations from Purchasing Power Parity (PPP) in the pricing of foreign exchange rates and equity securities in five Asia–Pacific countries and the US. Using weekly data from 1 January, 1988 to 27 February, 1998, I find that conditional variances are not related to the deviations from UIP in any statistical sense based on an univariate GARCH(1,1)-M model. As I consider both foreign exchange and equity markets together and test a conditional international CAPM (ICAPM) in the absence of PPP, I cannot reject the model based on the J-test by Hansen (Econometrica 50 (1982), 1029–1054) and find significant time-varying foreign exchange risk premia present in the data. This empirical evidence supports the notion of time-varying risk premia in explaining the deviations from UIP. It also supports the idea that the foreign exchange risk is not diversifiable and hence should be priced in both markets.     

Testing the CAPM with Time-Varying Risks and Returns

This paper draws on Engle's autoregressive conditionally heteroskedastic modeling strategy to formulate a conditional CAPM with time-varying risk and expected returns. The model is estimated by generalized method of moments. A CAPM that allows mean excess returns to shift in January survives generalized method of moments specification tests for a number of omitted variables. However, a residual dividend yield component is found to remain in the excess returns of smaller firms. We find significant monthly and quarterly components in the risk premia and beta estimates.     

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.     

The components of the illiquidity premium: An empirical analysis of US stocks 1927–2010

This paper implements a conditional version of the liquidity adjusted CAPM (LCAPM). The conditional LCAPM allows for a time-varying decomposition of the total illiquidity premium into a level component and three risk components. The estimated average annual total illiquidity premium for US stocks 1927–2010 is 1.74–2.08%, which is substantially lower than in most previous studies. The contributions from illiquidity level and illiquidity risk are 1.25–1.28% and 0.46–0.83%, respectively. Of the three illiquidity risk components, risk related to the hedging of wealth shocks is the most important, while commonality risk is the least important. The illiquidity premia are clearly time-varying, with peaks in downturns and crises, but with no general tendency to decrease over time. The level premium and the risk premium are significantly positively correlated, at around 0.35; indicating that in periods of turbulence both illiquidity cost and illiquidity risk premia tend to be high.     

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.     

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.     

Is the foreign exchange market ‘risky’? Some new survey-based results

In this paper we examine the evidence in favour of time-varying risk premia for four foreign exchange markets. The main novelty in our work is that we use survey-based expectations data to generate risk premia, rather than exploiting the rational expectations assumption. In contrast to the perceived wisdom on the existence of a foreign exchange risk premium, we present positive evidence for the view that risk is an important variable in foreign exchange markets.     

Time-varying market,interest rate,and exchange rate risk premia in the US commercial bank stock returns

This paper examines the role of market, interest rate, and exchange rate risks in pricing a sample of the US Commercial Bank stocks by developing and estimating a multi-factor model under both unconditional and conditional frameworks. Three different econometric methodologies are used to conduct the estimations and testing. Estimations based on nonlinear seemingly unrelated regression (NLSUR) via GMM approach indicate that interest rate risk is the only priced factor in the unconditional three-factor model. However, based on ‘pricing kernel’ approach by Dumas and Solnik [(1995). J. Finance 50, 445–479], strong evidence of exchange rate risk is found in both large bank and regional bank stocks in the conditional three-factor model with time-varying risk prices. Finally, estimations based on the multivariate GARCH in mean (MGARCH-M) approach where both conditional first and second moments of bank portfolio returns and risk factors are estimated simultaneously show strong evidence of time-varying interest rate and exchange rate risk premia and weak evidence of time-varying world market risk premium for all three bank portfolios, namely those of Money Center bank, Large bank, and Regional bank.     

Out-of-sample density forecasts with affine jump diffusion models

We conduct out-of-sample density forecast evaluations of the affine jump diffusion models for the S&P 500 stock index and its options’ contracts. We also examine the time-series consistency between the model-implied spot volatilities using options & returns and only returns. In particular, we focus on the role of the time-varying jump risk premia. Particle filters are used to estimate the model-implied spot volatilities. We also propose the beta transformation approach for recursive parameter updating. Our empirical analysis shows that the inconsistencies between options & returns and only returns are resolved by the introduction of the time-varying jump risk premia. For density forecasts, the time-varying jump risk premia models dominate the other models in terms of likelihood criteria. We also find that for medium-term horizons, the beta transformation can weaken the systematic effect of misspecified AJD models using options & returns.     

The role of time-varying jump risk premia in pricing stock index options

This paper examines out-of-sample option pricing performances for the affine jump diffusion (AJD) models by using the S&P 500 stock index and its associated option contracts. In particular, we investigate the role of time-varying jump risk premia in the AJD specifications. Our empirical analysis shows strong evidence in favor of time-varying jump risk premia in pricing cross-sectional options. We also find that, during a period of low volatility, the role of jump risk premia becomes less pronounced, making the differences across pricing performances of the AJD models not as substantial as during a period of high volatility. This finding can possibly explain poor pricing perfomances of the sophisticated AJD models in some previous studies whose sample periods can be characterized by low volatility.     

Macroeconomic Sources of Risk in the Term Structure

We develop a new way of modeling time variation in term premia, based on the stochastic discount factor model of asset pricing. The joint distribution of excess U.S. bond returns of different maturity and the observable fundamental macroeconomic factors is modeled using multivariate GARCH with conditional covariances in the mean to capture the term premia. By testing the assumption of no arbitrage we derive a specification test of our model. We estimate the contribution made to the term premia at different maturities through real and nominal sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the reported failures of the rational expectations hypothesis can be attributed to an omitted time-varying term premium.     

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.     

The impact of (global) business cycle risk on the German and British stock markets: Evidence from the first age of globalization

In the period from 1880 to 1913, time-varying German and British stock market returns are related to business cycle variables such as the deviation of industrial production from trend. Common British and German business cycle dynamics Granger cause stock returns and explain more than 20% of time variation in one-year ahead stock market returns. The link between business cycle variables and stock returns is less pronounced in the modern era of financial globalization. A potential explanation for this finding is the fact that during the first globalization period stock indices were dominated by industrial companies and stock prices varied in line with dividends. In the modern era of globalization stock price dynamics predominantly reflect time-varying risk premia.     

Explaining the Poor Performance of Consumption-based Asset Pricing Models

We show that the external habit-formation model economy of Campbell and Cochrane (1999) can explain why the Capital Asset Pricing Model (CAPM) and its extensions are betterapproximate asset pricing models than is the standard onsumption-based model. The model economy produces time-varying expected eturns, tracked by the dividend–price ratio. Portfolio-based models capture some of this variation in state variables, which a state-independent function of consumption cannot capture. Therefore, though the consumption-based model and CAPM are both perfect conditional asset pricing models, the portfolio-based models are better approximate unconditional asset pricing models.