Conclusions

The fundamental premise of modern portfolio theory is that risk can be measured, targeted, minimized, and otherwise managed. Most challenging in this premise is measurement. The covariance matrices presented in this chapter are outcomes of considerable empirical effort. We have adjusted what would otherwise be considered standard methods for measuring covariances for the smoothing of returns (real estate and private equity), and short return histories, as well as overlapping observations. These adjustments remove potential biases and improve efficiency by maximizing the information content of our estimates. Finally, we explicitly address the shortcomings associated with covariance estimation using smoothed and truncated series. Specifically, we examine the risk and allocative consequences from a Monte Carlo experiment and conclude that the naïve covariance estimates generate significant weight bias, undesirable allocative tilts, and higher portfolio risk.

Further research might be directed at improved unsmoothing algorithms, especially for non–real estate classes such as private equity and hedge funds (hedge funds are not examined in this paper). Moreover, that research should examine more closely competing theories of smoothing. Attention, too, to the time-invariance property may also be productive. For example, covariance relationships among short and long series may be more efficiently estimated using recursive methods that update each period (for example, Kalman filtering). Nevertheless, the applications presented in this chapter clearly improve allocative efficiency while illuminating some of the deficiencies associated with conventional covariance estimates.