# Research

## Published Papers

## Does idiosyncratic volatility proxy for risk exposure? (with Zhanhui Chen), 2014

We decompose aggregate market variance into an average correlation component and an average variance component. Only the latter commands a negative price of risk in the cross-section of portfolios sorted by idiosyncratic volatility. Portfolios with high (low) idiosyncratic volatility relative to the Fama-French model have positive (negative) exposures to innovations in average stock variance and therefore lower (higher) expected returns. These two findings explain the idiosyncratic volatility puzzle of Ang, et al. (2006, 2009). The factor related to innovations in average variance also reduces the pricing errors of book-to-market and momentum portfolios relative to the Fama-French (1993) model.

## Correlation Risk (with CNV Krishnan and Peter Ritchken), 2009

Investors hold portfolios of assets with different risk-reward profiles for diversification benefits. Conditional on the volatility of assets, diversification benefits can vary over time depending on the correlation structure among asset returns. The correlation of returns between assets has varied substantially over time. To insure against future "low diversification" states, investors might demand securities that offer higher payouts in these states. If this is the case, then investors would pay a premium for securities that perform well in regimes in which the correlation is high. We empirically test this hypothesis and find that correlation carries a significantly negative price of risk, after controlling for asset volatility and other risk factors.

## The expected value premium (with Long Chen and Lu Zhang), 2007

Fama and French (2002) estimate the equity premium using dividend growth rates to measure the expected rate of capital gain. We use similar methods to study the value premium. From 1941 to 2002, the expected HML return is on average 5.1% per annum, consisting of an expected-dividend-growth component of 3.5% and an expected dividend-to-price component of 1.6%. The ex-ante HML return is also countercyclical-a positive, one-standard-deviation shock to real consumption growth rate lowers this premium by about 0.45%. Unlike the equity premium, there is only mixed evidence suggesting that the value premium has declined over time.

## Do the Fama-French factors proxy for innovations in predictive variables?, 2006

The Fama-French factors HML and SMB are correlated with innovations in variables that describe investment opportunities. A model that includes shocks to the aggregate dividend yield and term spread, default spread, and one-month Treasury-bill yield explains the cross section of average returns better than the Fama-French model. When loadings on the innovations in the predictive variables are present in the model, loadings on HML and SMB lose their explanatory power for the cross section of returns. The results are consistent with an ICAPM explanation for the empirical success of the Fama-French portfolios.

## Is value riskier than growth? (with Lu Zhang), 2005

We study the relative risk of value and growth stocks. We find that time-varying risk goes in the right direction in explaining the value premium. Value betas tend to covary positively, and growth betas tend to covary negatively with the expected market risk premium. Our inference differs from that of previous studies because we sort betas on the expected market risk premium, instead of on the realized market excess return. However, we also find that this beta premium covariance is too small to explain the observed magnitude of the value premium within the conditional capital asset pricing model.

## Working Papers

## Absolute Strength: Exploring momentum in stock returns (with Huseyin Gulen), 2016

Revision requested by *Journal of Financial Economics*

We document a new pattern in stock returns that we call absolute strength momentum. Stocks that have significantly increased in value in the recent past (absolute strength winners) continue to gain, and stocks that have significantly decreased in value (absolute strength losers) continue to lose in the near future. Absolute strength winner and loser portfolio breakpoints are recursively determined by the historical distribution of realized cumulative returns across time and across stocks. The historical distribution yields stable breakpoints that are always positive (negative) for the winner (loser) portfolios. As a result, winners are those that have experienced a significant upward trend, losers are those that have experienced a significant downward trend, and stocks with no momentum have cumulative returns that are not significantly different from zero. The absolute strength momentum strategy is related to, but different from, the relative strength strategy of Jegadeesh and Titman (1993). Time-series regressions show that the returns to the absolute strength momentum strategy completely explain the returns to the relative strength strategy, but not vice versa. Absolute strength momentum does not expose investors to severe crashes during crisis periods, and its profits are remarkably consistent over time. For example, an 11-1-1 strategy that buys absolute strength winners and sells absolute strength losers delivers a risk-adjusted return of 2.42% per month from 1965-2014 and 1.55% per month from 2000-2014.

## Idiosyncratic volatility of liquidity and expected stock returns (with Ferhat Akbas and Will Armstrong), 2013

We show that idiosyncratic liquidity risk is positively priced in the cross-section of stock returns. Our measure of idiosyncratic liquidity volatility is based on a "market" model for stock liquidity. Idiosyncratic volatility of liquidity is priced in the presence of systematic liquidity risk: the covariance of stock returns with aggregate liquidity, the covariance of stock liquidity with aggregate liquidity, and the covariance of stock liquidity with the market return. Our results are puzzling in light of Acharya and Pedersen (2005) who develop a model in which only systematic liquidity risk affects returns.

## The time-varying liquidity risk of value and growth stocks (with Ferhat Akbas, Ekkehart Boehmer, and Egemen Genc), 2012

We study the liquidity exposures of value and growth stocks over business cycles. In worst times, value stocks have higher liquidity betas than in best times, while the opposite holds for growth stocks. Small value stocks have higher liquidity exposures than small growth stocks in worst times. Small growth stocks have higher liquidity exposures than small value stocks in best times. Our results are consistent with a flight-to-quality explanation for the countercyclical nature of the value premium. Exposure to time-varying liquidity risk captures 35% of the small-stock value premium and 100% of the large-stock value premium.