Tests of the Relations Among Marketwide Factors,Firm-Specific Variables,and Stock Returns Using a Conditional Asset Pricing Model

In this article we generalize Harvey's (1989) empirical specification of conditional asset pricing models to allow for both time-varying covariances between stock returns and marketwide factors and time-varying reward-to-covariabilities. The model is then applied to examine the effects of firm size and book-to-market equity ratios. We find that the traditional asset pricing model with commonly used factors can only explain a small portion of the stock returns predicted by firm size and book-to-market equity ratios. The results indicate that allowing time-varying covariances and time-varying reward-to-covariabilities does little to salvage the traditional asset pricing models.     

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.     

Can stochastic discount factor models explain the cross-section of equity returns?

We propose a multivariate test of the capital asset pricing model (C-CAPM) of the cross-sectional variation in equity returns in which we compare cross-sectional variation in equity returns to the cross-sectional variation in their conditional covariance with stochastic discount factors. We use a multivariate generalized heteroskedasticity in mean model to estimate 25 portfolios that are formed on size and the book-to-market ratio. Each portfolio is allowed to have its own no-arbitrage condition. We find that although the conditional covariances of returns with consumption exhibit negative variation across size, they do not vary across the book-to-market ratio. Thus, C-CAPM can capture the size effect, but not the value effect. The fit is, however, improved by allowing the coefficients on the consumption covariances to be different. The value effect appears to be associated with the book-to-market ratio as well as size. On its own the book-to-market ratio does not generate additional information about average returns to C-CAPM. A possible explanation for these findings is that both small and low book-to-market ratio firms are expected to have higher rates of growth.     

INTERTEMPORAL ASSET PRICING WITHOUT CONSUMPTION DATA: EMPIRICAL TESTS

In this paper I conduct tests of an intertemporal asset pricing model using variables that forecast stock returns as the risk factors. I document that the forecasting variables are priced so that expected excess returns are related to their conditional covariances with the forecasting variables. The variability in the covariance risk fails to explain the cross-sectional and time-series variation in expected stock returns. Evidence rejects restrictions on the prices of covariance risk imposed by the model with constant volatilities. I also find that an extended model that allows time-varying conditional volatilities is misspecified.     

Option pricing when correlations are stochastic: an analytical framework

In this paper we develop a novel market model where asset variances–covariances evolve stochastically. In addition shocks on asset return dynamics are assumed to be linearly correlated with shocks driving the variance–covariance matrix. Analytical tractability is preserved since the model is linear-affine and the conditional characteristic function can be determined explicitly. Quite remarkably, the model provides prices for vanilla options consistent with observed smile and skew effects, while making it possible to detect and quantify the correlation risk in multiple-asset derivatives like basket options. In particular, it can reproduce and quantify the asymmetric conditional correlations observed on historical data for equity markets. As an illustrative example, we provide explicit pricing formulas for rainbow “Best-of” options.     

INFLATION MEASUREMENT,INFLATION RISK,AND THE PRICING OF TREASURY BILLS

One explanation for the high real interest rates on Treasury bills during the period from 1980 to 1985 is that the risk premium had risen. A procedure for testing this hypothesis is to apply the Black version of the capital asset pricing model to real Treasury bill returns. This paper examines that procedure in detail. The main conclusion is that nonstationarity and measurement error, which are always impediments to empirical implementation of the CAPM, are particularly difficult to handle when estimating changes in Treasury bill risk premiums. Furthermore, the behavior of the premium depends on the index used to measure inflation.     

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.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

A reduced PDE method for European option pricing under multi-scale,multi-factor stochastic volatility

The number of tailor-made hybrid structured products has risen more prominently to fit each investor’s preferences and requirements as they become more diversified. The structured products entail synthetic derivatives such as combinations of bonds and/or stocks conditional on how they are backed up by underlying securities, stochastic volatility, stochastic interest rates or exchanges rates. The complexity of these multi-asset structures yields lots of difficulties of pricing the products. Because of the complexity, Monte-Carlo simulation is a possible choice to price them but it may not produce stable Greeks leading to a trouble in hedging against risks. In this light, it is desirable to use partial differential equations with relevant analytic and numerical techniques. Even if the partial differential equation method would generate stable security prices and Greeks for single asset options, however, it may result in the curse of dimensionality when pricing multi-asset derivatives. In this study, we make the best use of multi-scale nature of stochastic volatility to lift the curse of dimensionality for up to three asset cases. Also, we present a transformation formula by which the pricing group parameters required for the multi-asset options in illiquid market can be calculated from the underlying market parameters.     

International Asset Pricing and Portfolio Diversification with Time-Varying Risk

We test the conditional capital asset pricing model (CAPM) for the world's eight largest equity markets using a parsimonious generalized autoregressive conditional heteroskedasticity (GARCH) parameterization. Our methodology can be applied simultaneously to many assets and, at the same time, accommodate general dynamics of the conditional moments. The evidence supports most of the pricing restrictions of the model, but some of the variation in risk-adjusted excess returns remains predictable during periods of high interest rates. Our estimates indicate that, although severe market declines are contagious, the expected gains from international diversification for a U.S. investor average 2.11 percent per year and have not significantly declined over the last two decades.     

Modelling and forecasting short-term interest rate volatility: A semiparametric approach

This paper employs a semiparametric procedure to estimate the diffusion process of short-term interest rates. The Monte Carlo study shows that the semiparametric approach produces more accurate volatility estimates than models that accommodate asymmetry, level effect and serial dependence in the conditional variance. Moreover, the semiparametric approach yields robust volatility estimates even if the short rate drift function and the underlying innovation distribution are misspecified. Empirical investigation with the U.S. three-month Treasury bill rates suggests that the semiparametric procedure produces superior in-sample and out-of-sample forecast of short rate changes volatility compared with the widely used single-factor diffusion models. This forecast improvement has implications for pricing interest rate derivatives.     

The World Price of Foreign Exchange Risk

Departures from purchasing power parity imply that different countries have different prices for goods when a common numeraire is used. Stochastic changes in exchange rates are associated with changes in these prices and constitute additional sources of risk in asset pricing models. This article investigates whether exchange rate risks are priced in international asset markets using a conditional approach that allows for time variation in the rewards for exchange rate risk. The results for equities and currencies of the world's four largest equity markets support the existence of foreign exchange risk premia.     

Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

Stock Return Predictability and Asset Pricing Models

This article develops an asset allocation framework that incorporatesprior beliefs about the extent of stock return predictabilityexplained by asset pricing models. We find that when prior beliefsallow even minor deviations from pricing model implications,the resulting asset allocations depart considerably from andsubstantially outperform allocations dictated by either theunderlying models or the sample evidence on return predictability.Under a wide range of beliefs about model pricing abilities,asset allocations based on conditional models outperform theirunconditional counterparts that exclude return predictability.     

Stock returns and the term structure

In monthly U.S. data for 1959–1979 and 1979–1983, the state of the term structure of interest rates predicts excess stock returns, as well as excess returns on bills and bonds. This paper documents this fact and uses it to examine some simple asset pricing models. In 1959–1979, the data strongly reject a single-latent-variable specification of predictable excess returns. There is considerable evidence that conditional variances of excess returns change through time, but the relationship between conditional mean and conditional variance is reliably positive only at the short end of the term structure.     

Composition of wealth,conditioning information,and the cross-section of stock returns

Value stocks covary with aggregate consumption more than growth stocks during periods when financial wealth is low relative to consumption. However, the conditional value premium does not exhibit such countercyclical behavior. Consequently, a one-factor conditional consumption-based asset pricing model can be rejected without making any arbitrary assumptions on the dynamics of the price of risk or the conditional moments. Empirical evidence is somewhat more consistent with a consumption-based model augmented with an aggregate wealth growth factor, which can be motivated by either recursive preferences or relative wealth concerns.     

Pricing currency risk in the stock market: Evidence from Finland and Sweden 1970-2009

We investigate the role of currency risk on stock markets in two interlinked Nordic countries exhibiting a gradual move from fixed to floating exchange rates. We apply the Ding and Engle (2001) covariance stationary specification in a multivariate GARCH-M setup to test a conditional international asset pricing model. Using a sample period from 1970 to 2009, we find that the currency risk is priced in both stock markets, and that the price and the risk premium are lower after the floatation of the currencies, especially for Finland. We also find the cross-country exchange rate shock from Finland to affect the price of currency risk in Sweden, but not vice versa. Finally, we discuss some of the potential issues in applying multivariate GARCH-M specifications in tests of asset pricing models.     

An International Asset Pricing Model with Time-Varying Hedging Risk

This paper employs a two-factor international equilibrium asset pricing model to examine the pricing relationships among the world's five largest equity markets. In addition to the traditional market factor premium, a hedging factor premium is included as the second factor to explain the relationship between risks and returns in the international stock markets. Moreover, a GARCH parameterization is adopted to characterize the general dynamics of the conditional second moments. The results suggest that the additional hedging risk premium is needed to explain rates of return on international equities. Furthermore, the restriction that the coefficient on the hedge-portfolio covariance is one smaller than the coefficient on the market-portfolio covariance can not be rejected. This suggests that the intertemporal asset pricing model proposed by Campbell (1993) can be used to explain the returns on the five largest stock market indices.     

Sorting, Firm Characteristics, and Time-varying Risk: An Econometric Analysis

We show that sorting reveals the time-varying market risk exposuresof the firm-specific investment opportunity set. Sorting onthe basis of firm characteristics uncovers information on firm-specificdistress or growth, and this leads to more efficient estimationof conditional risk sensitivity. We demonstrate the effectivenessof the sorting methodology with an empirical exercise that teststhe conditional capital asset pricing model (CAPM). When measuredproperly using sorting and firm characteristics, conditionalbetas, along with size and the book-market ratio, are significantdrivers of expected returns.     

Testing conditional asset pricing models: An emerging market perspective

The CAPM as the benchmark asset pricing model generally performs poorly in both developed and emerging markets. We investigate whether allowing the model parameters to vary improves the performance of the CAPM and the Fama–French model. Conditional asset pricing models scaled by conditioning variables such as Trading Volume and Dividend Yield generally result in small pricing errors. However, a graphical analysis reveals that the predictions of conditional models are generally upward biased. We demonstrate that the bias in prediction may be the consequence of ignoring frequent large variation in asset returns caused by volatile institutional, political and macroeconomic conditions. This is characterised by excess kurtosis. An unconditional Fama–French model augmented with a cubic market factor performs the best among some competing models when local risk factors are employed. Moreover, the conditional models with global risk factors scaled by global conditioning variables perform better than the unconditional models with global risk factors.