Asset Allocation Models and Market Volatility

Asset allocation and risk management models assume at least short–term stability of the covariance structure of asset returns, but actual covariance and correlation relationships fluctuate dramatically. Moreover, correlations tend to increase in volatile periods, which reduces the power of diversification when it might most be desired. We propose a framework to both explain these phenomena and to predict changes in correlation structure. We model correlations between assets as resulting from the common dependence of returns on a marketwide factor. Through this link, an increase in market volatility increases the relative importance of systematic risk compared with the unsystematic component of returns. The increase in the importance of systematic risk results, in turn, in an increase in asset correlations. We report that a large portion of the variation in correlation structures can be attributed to variation in market volatility. Moreover, market volatility contains enough predictability to construct useful forecasts of covariance. Asset allocation and risk management models assume at least short–term stability of the covariance structure of asset returns, but actual covariance and correlation relationships fluctuate wildly, even over short horizons. Moreover, correlations increase in volatile periods, which reduces the power of diversification when it might most be desired. This phenomenon, often called “correlation breakdown,” has been widely recognized in the international context, but the pattern is even more characteristic of cross-industry correlations in a domestic context.We attempt to explain correlation breakdown and to present a framework for predicting short–horizon changes in correlation structure. We modeled correlations between assets as resulting from the common dependence of returns on a systematic, marketwide factor. Through this link, an increase in factor volatility increases the importance of systematic risk relative to the unsystematic component of returns. The result is an increase in asset correlations.We found that a simple index model with only one systematic factor can explain a surprisingly large portion of the short–horizon time variation in correlation structure. This finding suggests that univariate models of time variation in volatility, such as the ARCH (autoregressive conditional heteroscedasticity) model and its variants, which are already widely and successfully applied, can be integrated with the index model to form useful short–horizon forecasts of cross-sector correlations.We examined the source of correlation breakdown in the domestic context using returns on 12 industry groups and treating the value–weighted NYSE Index as the systematic factor; in the international context, we used returns on 10 major country indexes and treated the MSCI World Index as the systematic factor. We document that variation in cross-sector correlation is highly associated with market volatility (where “sector” means industry in the U.S. context and country in the international context). Using daily data within quarters to calculate both cross-sector correlations and the volatility of the market index, we measured the tendency for time variation in correlation (across quarters) to track time variation in market volatility. In both the domestic and international contexts, we found that correlation clearly fluctuates in line with market volatility.We found that short–term variation across time in the volatility of the market index can be used to forecast most of the time variation in correlation structure and thus guide managers in updating portfolio positions. The results are qualitatively the same in the international and domestic settings. We found considerably more country-specific volatility, however, than industry-specific volatility, which implies that, although the proposed methodology can be quite effective in the domestic setting, it will be less useful in the international setting.Having established that predictions of market volatility are useful in predicting correlation structure, we next examined the extent to which this methodology can be used in risk management applications. Can predictions of market volatility in conjunction with the index model be used to efficiently diversify portfolio risk? We compared the predictive accuracy of several forecasts of covariance and found that a constrained correlation using a simple autoregressive relationship to forecast next-quarter market variance from current-quarter market variance is highly accurate. In fact, the predictive accuracy of this model is equal to a model of “full-sample constant covariance” (i.e., a covariance estimate obtained by pooling all daily returns and calculating the single full-sample covariance matrix). This latter forecast obviously is not feasible for actual investors because it requires knowledge of returns over the full sample period. It turned out to be the best unconditional covariance estimator, but our constrained index model estimator conditioned on a forecast of market volatility was equally accurate.We conclude that portfolios constructed from covariance matrixes based on an index model and predicted market volatilities will perform substantially better than portfolios that do not account for the impact of time-varying volatility on correlation and covariance structure. The ability of market volatility to explain correlation structure suggests that univariate models of time variation in that volatility can be integrated with the index model to make useful short–horizon forecasts of cross-sector correlations.