Idiosyncratic risk and the cross-section of expected stock returns

Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.     

The relationship between risk and expected return in Europe

We employ MIDAS (mixed data sampling) to study the risk–expected return trade-off in several European stock indices. Using MIDAS, we report that in most indices there is a significant positive relationship between risk and expected return. This strongly contrasts with the result we obtain when we employ both symmetric and asymmetric GARCH models for conditional variance. We also find that asymmetric specifications of the variance process within the MIDAS framework improve the relationship between risk and expected return. As an additional application, we analyze the extent to which European stock markets are integrated, which is a particularly relevant issue, especially following the launch of the Euro in January 1999. Finally, we propose a bivariate MIDAS specification to test the pricing significance of the hedging component within an intertemporal risk–return trade-off with multiple European market indices.     

The intertemporal capital asset pricing model with dynamic conditional correlations

The intertemporal capital asset pricing model of Merton (1973) is examined using the dynamic conditional correlation (DCC) model of Engle (2002). The mean-reverting DCC model is used to estimate a stock’s (portfolio’s) conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock’s (portfolio’s) expected return. The risk-aversion coefficient, restricted to be the same across assets in panel regression, is estimated to be between two and four and highly significant. The risk premium induced by the conditional covariation of assets with the market portfolio remains positive and significant after controlling for risk premia induced by conditional covariation with macroeconomic, financial, and volatility factors.     

Additional evidence on transparency and bank financial performance

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book‐to‐market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E‐GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.     

An Intertemporal International Asset Pricing Model: Theory and Empirical Evidence

We extend Campbell's (1993) model to develop an intertemporal international asset pricing model (IAPM). We show that the expected international asset return is determined by a weighted average of market risk, market hedging risk, exchange rate risk and exchange rate hedging risk. These weights sum up to one. Our model explicitly separates hedging against changes in the investment opportunity set from hedging against exchange rate changes as well as exchange rate risk from intertemporal hedging risk. A test of the conditional version of our intertemporal IAPM using a multivariate GARCH process supports the asset pricing model. We find that the exchange rate risk is important for pricing international equity returns and it is much more important than intertemporal hedging risk.     

Cross-sectional forecasts of the equity premium

If investors are myopic mean-variance optimizers, a stock's expected return is linearly related to its beta in the cross-section. The slope of the relation is the cross-sectional price of risk, which should equal the expected equity premium. We use this simple observation to forecast the equity-premium time series with the cross-sectional price of risk. We also introduce novel statistical methods for testing stock-return predictability based on endogenous variables whose shocks are potentially correlated with return shocks. Our empirical tests show that the cross-sectional price of risk (1) is strongly correlated with the market's yield measures and (2) predicts equity-premium realizations, especially in the first half of our 1927–2002 sample.     

Conditional Properties of Hedge Funds: Evidence from Daily Returns*

Using daily returns on a set of hedge fund indices, we study (i) the properties of the indices' conditional density functions and (ii) the presence of asymmetries in conditional correlations between hedge fund indices and other investments and between hedge fund indices themselves. We use the SNP approach to obtain estimates of conditional densities of hedge fund returns and then proceed to examine their properties. In general, a nonparametric GARCH(1,1) model appears to provide the best fit for all strategies. We find that the conditional third and fourth moments are significantly affected by changes in the current volatility of returns on hedge fund indices. We examine changes in the conditional probability of tail events and report significant changes in the probability of extreme events when the conditioning information changes. These results have important implications for models of hedge fund risk that rely on probability of tail events. We formally test for the presence of asymmetries in conditional correlations to determine if there is contagion between hedge funds and other investments and between various hedge fund indices in extreme down markets versus extreme up markets. We generally do not find strong evidence in support of asymmetric correlations.     

International asset pricing models and currency risk: Evidence from Finland 1970–2004

In this paper we investigate whether global, local and currency risks are priced in the Finnish stock market using conditional international asset pricing models. We take the view of a US investor. The estimation is conducted using a modified version of the multivariate GARCH framework of [De Santis, G., Gérard, B., 1998. How big is the premium for currency risk? Journal of Financial Economics 49, 375–412]. For a sample period from 1970 to 2004, we find the world risk to be time-varying. While local risk is not priced for the USA, the local component is significant and time-varying for Finland. Currency risk is priced in the Finnish market, but is not time-varying using the De Santis and Gérard specification. This suggests that the linear specification for the currency risk may not be adequate for non-free floating currencies.     

Risk and the January effect

We use a time-series GARCH framework with the conditional variance/covariance as proxies for systematic risk to reexamine the proposition by Rozeff and Kinney (1976) and Rogalski and Tinic (1986) that the January effect may be a phenomenon of risk compensation in the month. We find no clear evidence that either conditional volatility or unconditional volatility in January is predominantly higher across the sampling years. Hence, against the proposition, the January effect is not due to risk per se. Rather, we find strong evidence that the January effect is due to higher compensation for risk in the month. This may be possible if investors have an increasing RRA utility function. Although many studies find that volatility tends to be higher in January, we find it to be period-specific and mostly in value-weighted return series, but not in equal-weighted return series. This is true both for the unconditional and conditional return volatility.     

STOCK RETURNS AND VOLATILITY ON CHINA'S STOCK MARKETS

We examine time‐series features of stock returns and volatility, as well as the relation between return and volatility in four of China's stock exchanges. Variance ratio tests reject the hypothesis that stock returns follow a random walk. We find evidence of long memory of returns. Application of GARCH and EGARCH models provides strong evidence of time‐varying volatility and shows volatility is highly persistent and predictable. The results of GARCH‐M do not show any relation between expected returns and expected risk. Daily trading volume used as a proxy for information arrival time has no significant explanatory power for the conditional volatility of daily returns. JEL classification: G15     

Optimal Asset Allocation Over the Business Cycle

Utilizing a broadly diversified portfolio of nine equity and debt assets, we show our portfolio's in-sample Markowitz return/risk profile considerably improved by keying asset proportions to cyclical changes in economic activity. For comparative purposes, we use the same assets in a hypothetical buy-and-hold benchmark portfolio. We find the variance/covariance structure of our portfolio to be considerably altered by the phase of the business cycle, with the diversification benefits enjoyed during expansions substantially diluted during recessions. Thus, cyclical reallocation appears to be more important in maintaining Markowitz efficiency during recessions vis-a-vis expansions. In the latter case we find expansion reallocation producing a 3.53% increase in our portfolio's return-to-risk ratio (relative to a buy-and-hold position), while for recessions optimal reallocation leads to a 79.14% increase.     

ASYMMETRIC COVARIANCE,VOLATILITY, AND THE EFFECT OF NEWS

We propose that covariance (rather than beta) asymmetry provides a superior framework for examining issues related to changing risk premiums. Accordingly, we investigate whether the conditional covariance between stock and market returns is asymmetric in response to good and bad news. Our model of conditional covariance accommodates both the sign and magnitude of return innovations, and we find significant covariance asymmetry that can explain, at least in part, the volatility feedback of stock returns. Our findings are consistent across firm size, firm leverage, and temporal and cross‐sectional aggregations.     

Time Variation in the Covariance between Stock Returns and Consumption Growth

The conditional covariance between aggregate stock returns and aggregate consumption growth varies substantially over time. When stock market wealth is high relative to consumption, both the conditional covariance and correlation are high. This pattern is consistent with the “composition effect,” where agents' consumption growth is more closely tied to stock returns when stock wealth is a larger share of total wealth. This variation can be used to test asset‐pricing models in which the price of consumption risk varies. After accounting for variations in this price, the relation between expected excess stock returns and the conditional covariance is negative.     

The risk-return tradeoff: A COGARCH analysis of Merton's hypothesis

We analysed daily returns of the CRSP value weighted and equally weighted indices over 1953-2007 in order to test for Merton's theorised relationship between risk and return. Like some previous studies we used a GARCH stochastic volatility approach, employing not only traditional discrete time GARCH models but also using a COGARCH — a newly developed continuous-time GARCH model which allows for a rigorous analysis of unequally spaced data. When a risk-return relationship symmetric to positive or negative returns is postulated, a significant risk premium of the order of 7-8% p.a., consistent with previously published estimates, is obtained. When the model includes an asymmetry effect, the estimated risk premium, still around 7% p.a., becomes insignificant. These results are robust to the use of a value weighted or equally weighted index.The COGARCH model properly allows for unequally spaced time series data. As a sidelight, the model estimates that, during the period from 1953 to 2007, the weekend is equivalent, in volatility terms, to about 0.3-0.5 regular trading days.     

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.     

The World Price of Covariance Risk

In a financially integrated global market, the conditionally expected return on a portfolio of securities from a particular country is determined by the country's world risk exposure. This paper measures the conditional risk of 17 countries. The reward per unit of risk is the world price of covariance risk. Although the tests provide evidence on the conditional mean variance efficiency of the benchmark portfolio, the results show that countries' risk exposures help explain differences in performance. Evidence is also presented which indicates that these risk exposures change through time and that the world price of covariance risk is not constant.     

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.     

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.     

The intraday behaviors and relationships with its underlying assets: evidence on option market in Taiwan

In this paper, we use daily data to investigate the information asymmetric effects and the relationships between the trading volume of options and their underlying spot trading volume. Our results reveal that options with higher liquidity are near-the-money and expiration periods with 2 to 4 weeks have higher trading activity. We classify them into two parts with the ARIMA model: the expected trading activity impact and the unexpected trading activity impact. Using the bivariate generalized autoregressive conditional heteroscedasticity (GARCH) model, we investigate the trading activity effect and information asymmetric effect. In conclusion, the trading volume volatility of the spot and options markets move together, and a greater expected and unexpected trading volume volatility of the spot (options) market is associated with greater volatility in the options (spot) market. However, both markets generate higher trading volume volatility when people expect such an impact rather than when they do not. We also find that there are feedback effects within these two markets. Furthermore, when the spot (options) market has negative innovations, it generates a greater impact on the options (spot) market than do positive innovations. Finally, the conditional correlation coefficient between the spot and the option markets changes over time based on the bivariate GARCH model.     

Asymmetric effect of basis on dynamic futures hedging: Empirical evidence from commodity markets

The dynamic minimum variance hedge ratios (MVHRs) have been commonly estimated using the Bivariate GARCH model that overlooks the basis effect on the time-varying variance–covariance of spot and futures returns. This paper proposes an alternative specification of the BGARCH model in which the effect is incorporated for estimating MVHRs. Empirical investigation in commodity markets suggests that the basis effect is asymmetric, i.e., the positive basis has greater impact than the negative basis on the variance and covariance structure. Both in-sample and out-of-sample comparisons of the MVHR performance reveal that the model with the asymmetric effect provides greater risk reduction than the conventional models, illustrating importance of the asymmetric effect when modeling the joint dynamics of spot and futures returns and hence estimating hedging strategies.