Asset Allocation

CHAPTER 13Forecasting

THE CHALLENGE

Mean-variance analysis requires investors to specify views for expected returns, standard deviations, and correlations. These properties of assets vary over time. Long-run averages are poor forecasts because they fail to capture this time variation. On the other hand, extrapolating from a short sample of recent history is ineffective because it introduces noise and assumes a level of persistence that does not occur reliably (see Chapter 19 on estimation error, and Chapter 9 on the fallacy of 1/N). As an alternative, investors may use additional data such as economic variables to project expected returns from the current values of those variables and their historical relationships to asset returns. However, this approach does not guarantee success because additional variables contribute noise along with information. The investor's challenge is to maximize the information content and minimize the noise, thereby generating the most effective predictions. In this chapter, we reinterpret linear regression to reveal the predictive information that comes from each historical observation in our sample, and we extend it to focus on a subset of the most relevant historical observations, which can significantly improve the quality of the forecasts. This procedure, which was introduced by Czasonis, Kritzman, and Turkington (2020), is called partial sample regression.

CONVENTIONAL LINEAR REGRESSION

Financial analysts face the challenge of mapping predictive ...