We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While considerable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Campbell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of future market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. Hence, stocks with different sensitivities to innovations in aggregate volatility should have different expected returns.The first goal of this paper is to provide a systematic investigation of how the stochastic volatility of the market is priced in the cross-section of expected stock returns. We want to both determine whether the volatility of the market * Ang is with Columbia University and NBER. Hodrick is with Columbia University and NBER.Yuhang Xing is at Rice University. Xiaoyan Zhang is at Cornell University. We thank Joe Chen, Mike Chernov, Miguel Ferreira, Jeff Fleming, Chris Lamoureux, Jun Liu, Laurie Hodrick, Paul Hribar, Jun Pan, Matt Rhodes-Kropf, Steve Ross, David Weinbaum, and Lu Zhang for helpful discussions. We also received valuable comments from seminar participants at an NBER Asset Pricing meeting,

We describe the joint dynamics of bond yields and macroeconomic variables in a Vector Autoregression, where identifying restrictions are based on the absence of arbitrage. Using a term structure model with inflation and economic growth factors, together with latent variables, we investigate how macro variables affect bond prices and the dynamics of the yield curve. We find that the forecasting performance of a VAR improves when no-arbitrage restrictions are imposed and that models with macro factors forecast better than models with only unobservable factors.Variance decompositions show that macro factors explain up to 85% of the variation in bond yields. Macro factors primarily explain movements at the short end and middle of the yield curve while unobservable factors still account for most of the movement at the long end of the yield curve.

Correlations between international equity market returns tend to increase in highly volatile bear markets, which has led some to doubt the benefits of international diversification. This article solves the dynamic portfolio choice problem of a U.S. investor faced with a time-varying investment opportunity set modeled using a regime-switching process which may be characterized by correlations and volatilities that increase in bad times. International diversification is still valuable with regime changes and currency hedging imparts further benefit. The costs of ignoring the regimes are small for all-equity portfolios but increase when a conditionally risk-free asset can be held.

No abstract

Stocks with high idiosyncratic volatility have low expected returns around the world. This effect is individually significant in each G7 country. Across 23 developed markets, the difference in average returns between the extreme quintile portfolios sorted on idiosyncratic volatility is -1.31% per month, after controlling for world market, size, and value factors. In the U.S., we rule out explanations based on trading frictions, information dissemination, and higher moments. There is strong comovement in the low returns to high idiosyncratic volatility stocks across countries, suggesting that broad, not easily diversifiable factors lie behind this phenomenon.