Chapter 22

Data Problems¹

There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery.

—Enrico Fermi

When historical returns series vary in length, covariances are typically estimated using a shorter common subset of returns, thereby discarding some information contained in the longer series. Problems associated with returns truncation are particularly troublesome for allocations across broad asset classes; there are typically only a small number of classes, and because many of these are relatively new (for example, TIPS), they contribute little information to covariance estimates. Covariance precision will necessarily suffer for more severely truncated returns, and the information loss from truncation will generally produce inefficient and, in some cases, biased covariance estimates (Stambaugh 1997). Perhaps more important are the obvious adverse implications for plan-wide risk management—at a minimum, it is likely that exposures will be miscalculated as will the investor's overall exposure to risk. I present Monte Carlo evidence further on that supports this assertion.

It is also well known that the reported returns to some asset classes (for example, real estate, private equity) are smoothed estimates of the underlying true returns. Smoothing will cause these returns to have artificially lower volatilities and covariations with the remaining asset classes, which, if uncorrected, will bias allocations toward the smoothed asset classes. Smoothing is a data problem whose origins lie in the way the returns are computed and reported, for example, as moving averages of previously observed prices (real estate appraisals) or as a timing issue in which returns are reported at irregular intervals (private equity valuations). In any case, smoothing alters the time series relationships that, when combined with truncation, may produce seriously misleading covariance estimates and exacerbate exposure to unwanted risk.

In this chapter, I draw primarily from Stambaugh (1997) and Fisher and Geltner (2000) to resolve problems associated with returns truncation and smoothing, using return streams from seven asset classes commonly analyzed by institutional investors. I also present results from a Monte Carlo experiment that generates mean-variance optimal portfolios for both cases, that is, when returns are smoothed and truncated against mean returns and covariances drawn from identical series with the effects of smoothing and truncation removed. The following section develops the covariance model as a response to the aforementioned considerations. A discussion of the data I use for my analysis follows in the third section followed by general findings and results from the Monte Carlo experiment and some concluding remarks.