Equity Valuation and Portfolio Management

ROBUST PARAMETER ESTIMATION

The most commonly used approach for estimating security expected returns, covariances, and other parameters that are inputs to portfolio optimization models is to calculate the sample analogues from historical data. These are sample estimates for the parameters we need. It is important to remember that when we rely on historical data for estimation purposes, we in fact assume that the past provides a good representation of the future.

It is well-known, however, that expected returns exhibit significant time variation (referred to as nonstationarity). They are impacted by changes in markets and economic conditions, such as interest rates the political environment, consumer confidence, and the business cycles of different industry sectors and geographical regions. Consequently, extrapolated historical returns are often poor forecasts of future returns.

Similarly, the covariance matrix is unstable over time. Moreover, sample estimates of covariances for portfolios with thousands stocks are notoriously unreliable, because we need large data sets to estimate them, and such large data sets of relevant data are difficult to procure. Estimates of the covariance matrix based on factor models are often used to reduce the number of statistical estimates needed from a limited set of data.

In practice, portfolio managers often alter historical estimates of different parameters subjectively or objectively, based on their expectations and forecasting models for future ...