Correlation Risk C . N . V . KRISHNAN

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 correlation would be a systematic risk factor, and investors would pay a premium for securities that offer higher payouts in regimes in which the correlation is high. We empirically test this hypothesis and find that correlation carries a statistically and economically significant negative price of risk, after controlling for the volatility of the assets and other risk factors that have been found to affect stock returns. (Time-varying Correlation; Price of Correlation Risk) Diversification benefits depend on the correlation structure among asset returns. There is now considerable evidence that correlations among asset returns change over time, that they generally increase during financial crises, and, more generally, they increase in bear markets.1 Li (2002) finds that macroeconomic variables can account for a small but statistically significant portion of the time varying correlation between asset returns. In particular, this correlation is positively related to inflation risk. When inflation risk is high, asset returns tend to be more volatile, and in such regimes investors have a stronger incentive to diversify. However, in these very regimes, Li’s result implies that correlations are high and diversification opportunities are low, thus leading him to Murphy’s Law of Diversification:“diversification opportunities are least available when they are most needed.” If diversification opportunities diminish in regimes when they are most needed, investors could pay a premium to insure against such states. In other words, if correlation between assets is a systematic risk factor, all things being equal, investors would pay a premium for securities that offer higher payouts in states where asset correlations are high. This paper empirically tests this hypothesis. Specifically, we investigate whether time varying correlation between individual assets carries a significant price of risk in the cross-section of stock returns. However, before we examine whether there exists a significant price of correlation risk in the cross-section of stock returns, we are faced with the following important issues. First, we need to determine an aggregate measure of correlation, or more specifically, correlation innovation. Clearly, this measure is influenced by pair-wise correlations among securities, and there are many asset classes to choose. Second, we need to be careful in relating increasing correlation to reduced diversification benefits. An alternative explanation could be that correlation is just a business cycle indicator. For example, correlations may be related to unanticipated inflation, as Li’s result implies, to the market return, to T-bill rates and to industrial production, all of which are business cycle variables that define the investment opportunity set. Any analysis would clearly have to carefully control for or remove these business cycle effects, before assessing whether correlation risk is priced. Third, increasing correlation, per se, does not necessarily mean lower diversification benefits. Diversification opportunities increase when the correlations among assets decrease, conditional on the volatility of assets remaining the same or increasing. Indeed, Campbell, Lettau, Malkiel and Xu (2001) examine the 1962-1997 period and show that the benefits of diversification among U.S. stocks changed because of two effects: changing average standard deviation of the returns of individual stocks and changing average correlation of returns between any two stocks. Thus, in any analysis for determining the price of correlation risk, we need to control for volatility of assets. Several strands of literature have examined correlation between asset returns. The first strand, already alluded to, focuses on understanding the time varying nature of aggregate stockSee, for example, Bollerslev, Chou and Kroner (1992).