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.

Turan G. Bali, Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate, The Journal of Financial and Quantitative Analysis, Vol. 35, No. 2 (Jun., 2000), pp. 191-215

This paper models the stochastic behavior of short-term interest rates, and determines the correct specification of the drift and diffusion functions of the spot rate process. A wide variety of one-factor diffusion and two-factor stochastic volatility models is compared in terms of their ability to capture the dynamics of interest rate volatility. The empirical evidence on the one-, three- and six-month Eurodollar deposit rates indicates that a new class of models with stochastic volatility is better than the single-factor diffusion models in forecasting the future volatility of interest rate changes. The paper extends the one-factor BDT term structure model to a two-factor setting, and presents the pricing implications for discount bonds. Monte Carlo simulation results for the implied yields of three- and six-month zero-coupon bonds imply that incorporating the so-called level and GARCH effects in volatility improves the pricing performance of the interest rate models.

While it is established that idiosyncratic volatility is negatively priced in the cross-section of stock returns, the relation between idiosyncratic volatility and hedge fund returns is largely unexplored. We document that hedge funds with high idiosyncratic volatility earn higher future risk-adjusted returns of 6 percent p.a. than hedge funds with low idiosyncratic volatility. The outperformance arises because hedge funds trade high idiosyncratic volatility stocks wisely. They pick high volatility stocks when they are underpriced and short-sell high volatility stocks when they are overpriced. Our results support the notion that hedge funds’ idiosyncratic volatility is a measure of managerial skill.

We investigate the pricing of risk-neutral skewness in the stock options market by creating skewness assets comprised of two option positions (one long and one short) and a position in the underlying stock. The assets are created such that exposure to changes in the underlying stock price (delta), and exposure to changes in implied volatility (vega) are removed, isolating the effect of skewness. We find a strong negative relation between risk-neutral skewness and the skewness asset returns, consistent with a positive skewness preference. The returns are not explained by well-known market, size, book-to-market, momentum, short-term reversal, volatility, or option market factors.

This paper examines the cross-sectional relation between idiosyncratic volatility and expected stock returns. The results indicate that i) the data frequency used to estimate idiosyncratic volatility, ii) the weighting scheme used to compute average portfolio returns, iii) the breakpoints utilized to sort stocks into quintile portfolios, and iv) using a screen for size, price, and liquidity play critical roles in determining the existence and significance of a relation between idiosyncratic risk and the cross section of expected returns. Portfoliolevel analyses based on two different measures of idiosyncratic volatility (estimated using daily and monthly data), three weighting schemes (value-weighted, equal-weighted, inverse volatility-weighted), three breakpoints (CRSP, NYSE, equal market share), and two different samples (NYSE/AMEX/NASDAQ and NYSE) indicate that no robustly significant relation exists between idiosyncratic volatility and expected returns.

This paper determines whether the world market risk, country-specific total risk, and country-specific idiosyncratic risk are priced in an international capital asset pricing model (ICAPM). Portfolio-level analyses, country-level cross-sectional regressions, stacked time-series, and pooled panel regressions indicate that the world market risk is not, but country-specific total and idiosyncratic risks are significantly priced in an ICAPM framework with partial integration. This result is robust to different methods for estimating risk measures, different investment horizons, and after controlling for the countries’ aggregate dividend yield, earnings-to-price ratios, inflation risk, exchange rate uncertainties, aggregate volatility risk, and past return characteristics. The main findings turn out to be insensitive to the choice of one-factor vs. multifactor models used to estimate systematic and idiosyncratic risk measures.

Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973–2003. We find evidence of cyclical components in both the catastrophic and operational risk measures obtained from the generalized Pareto distribution and the skewed generalized error distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions’ returns represent compensation for operational risk. However, depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events.

We introduce a new hybrid measure of stock return tail covariance risk, motivated by the underdiversified portfolio holdings of individual investors, and investigate its cross-sectional predictive power. Our key innovation is that this covariance is measured across the left tail states of the individual stock return distribution, and not across those of the market return as in standard systematic risk measures. We document a positive and significant relation between hybrid tail covariance risk (H-TCR) and expected stock returns, with an annualized premium of 9%, in contrast to the insignificant or negative results for purely stock-specific or systematic tail risk measures. (JEL G10, G11, C13)

Abstract Recent theoretical models underscore the potential asymmetric response of various behaviors, ranging from criminal activity to smoking. In this paper, we use state-level panel and individual-level panel data to document the previously unnoticed asymmetric response of crime to changes in the unemployment rate. The results have policy implications, and they have potentially widespread ramifications because similar asymmetries may also be prevalent in other domains, ranging from the relationship between income and health to peer quality and student outcomes.