Estimation and control of security risk are subjects of major theoretical and practical importance. Much of the literature in this area has focused on the risk associated with returns over a single holding period. Within this context, a great deal of attention has been devoted to estimation of security betas, which relate to coveriance with “the market,” since the well-known Capital Asset Pricing Model implies that expected returns will, in equilibrium, be related to such values. However, a number of papers [3, 7, 14] have considered “extra-market covariances,” i.e., covariances among security returns not due to common correlations with the market as a whole. Accurate estimates of such covariances are necessary for tailoring portfolios to account for differences in investors' circumstances (e.g., tax brackets) and, a fortiori, for active portfolio management designed to exploit any security mispricing.