Returns Volatility and Correlation in Asset Pricing: A Review

In this paper we provide a survey of the role of equity returns volatility and correlation within the asset pricing literature. In general, the literature of the second moments of stock returns can be classified in three main “phases”. In the first one, which started with the pioneering work of Markowitz (1952, 1959) and (building on this) culminated in what has come to be known as the Capital Asset Pricing Model (CAPM), variances and covariances were assumed to be constant over time. Only at the beginning of the '80s, and in particular with the leading contribution of Engle (1982), a new generation of approaches appeared. This literature abandoned the hypothesis of constant volatility and modeled the variance of the current error term to be a function of the variances of the previous time-period's error terms. However, in this “phase”, multivariate ARCH (GARCH) models were either assuming that equity correlations are constant over time or specifying the covariance term as a unique unknown, without differentiating the several components of the covariance matrix. Only in more recent years (the third “phase”), the asset pricing literature, recognizing that stock returns correlations are not stable over time but fluctuate dramatically, started separating volatility shocks from correlation shocks.