Increased Correlation in Bear Markets

Abstract

A number of studies have provided evidence of increased correlations in global financial market returns during bear markets. Other studies, however, have shown that some of this evidence may be biased. We derive an alternative to previous estimators for implied correlation that is based on measures of portfolio downside risk and that does not suffer from bias. The unbiased quantile correlation estimates are directly applicable to portfolio optimization and to risk management techniques in general. This simple and practical method captures the increasing correlation in extreme market conditions while providing a pragmatic approach to understanding correlation structure in multivariate return distributions. Based on data for international equity markets, we found evidence of significant increased correlation in international equity returns in bear markets. This finding proves the importance of providing a tail-adjusted mean–variance covariance matrix. A generally accepted concept today is that, over time, returns when the markets are experiencing large negative movements are more highly correlated than returns during more normal times. If true, this phenomenon has serious implications for portfolio and risk management because it means that the benefits of diversification are curtailed precisely when investors most need them. The correlation, however, depends on how the returns are conditioned on the size of the returns. Previous studies have provided alternative correlation structures with which to compare conditional empirical correlations, but these estimates have upward or downward biases that need to be corrected. In this article, we provide a quantile correlation approach that is not biased by the size of the return distribution. The result is a simple and pragmatic approach to estimating correlations conditional on the size of the returns. Based on empirical data, we show how the correlation estimates can be used directly in portfolio and risk management. We derive a conditional correlation structure based on the quantile of the joint return distribution; that is, correlation is conditioned on the size of the return distribution. In a bivariate framework, the correlation is estimated by using those observations that fall below the portfolio return of the two assets. The approach is thus in line with current correlation measures used in Markowitz-style portfolio analysis and in current risk management techniques. The quantile correlation structure is determined by the weights of the assets in the portfolio and the quantile estimates of the distribution of returns on the two assets and of the portfolio return. When the distribution is normal, the conditional correlation structure is constant; hence, the conditional quantile correlation will equal the unconditional correlation. Therefore, because the correlation structure is constant over the distribution for normality, one can easily compare empirical estimates of conditional correlation with their theoretical values under conditions of normal distribution. We examine a variety of daily returns from international stock market indexes for the period May 1990 through December 1999 to establish, first, their unconditional correlations. For example, this procedure produced a correlation between the U.S. market (S&P 500 Index) and the U.K. market (the FTSE 100 Index) of 0.349. Assuming bivariate normality for the whole distribution, we would expect the quantile conditional correlation also to be 0.349. For quantiles up to the 95 percent level, we found that the assumption of normality cannot be rejected at the 95 percent confidence level for all the series. For higher quantiles, however—that is, large negative returns in the bivariate return distribution—the conditional correlation structure increased the correlations; in the case of the U.S. and U.K. markets, the correlation increased to 0.457. The effect on mean–variance portfolio optimization is a reduction in the recommended weight of the risky assets held in the portfolio. These results imply that the gains from diversification are not reaped in periods when diversification benefits are most crucial from a mean–variance perspective—in bear markets. Practitioners, therefore, need to know what sort of model is generating the correlations they are relying on. If the underlying model assumed normality, then the correlation estimates used in the model need to be adjusted to incorporate the bear market's higher-than-normal correlation structure.