3 Estimating expected returns and covariances

 

This chapter covers

  • Computing means, standard deviations, and correlations from historical data
  • Adjusting historical returns for changes in valuation
  • Estimating expected returns using the capital asset pricing model
  • Using a GARCH model to estimate volatilities
  • Testing for valid correlation matrices

With the Markowitz approach to portfolio construction, investors evaluate alternative portfolios based on their expected returns and volatilities. In chapter 2, we left open the question of how to form these estimates. The two types of inputs needed are

  1. The expected returns of the individual assets
  2. The variances of the individual assets and the pairwise correlations between assets

Together, these are sometimes referred to as capital market assumptions. We will tackle expected returns in the first section and variances and correlations in the following section.

3.1 Estimating expected returns

Expected returns are probably the most important input for portfolio construction and also the input that is the most difficult to estimate. Statistically, simply sampling historical returns more frequently can provide more accurate estimates of variances and correlations, but that doesn’t help for means. Indeed, to estimate historical average returns, you only need the first and last prices, so accuracy can be obtained only with a longer time series. In this section, we consider several ways to estimate expected returns.

3.1.1 Historical averages

3.1.2 CAPM

3.1.3 Adjusting historical returns for changes in valuation

3.1.4 Capital market assumptions from asset managers

3.2 Estimating variances and covariances

3.2.1 Using historical returns

3.2.2 GARCH models

3.2.3 Other approaches

3.2.4 Subjective estimates

Summary