11.1 Assumptions About Returns and Investor Risk Preferences

To develop a quantitative methodology for investment analysis, we make the following assumptions regarding the probability distribution of asset returns and the behavior of investors:

  1. Returns are covariance stationary and ergodic, and jointly normally distributed over the investment horizon. This implies that means, variances and covariances of returns are constant over the investment horizon and completely characterize the joint distribution of returns.
  2. Investors know the values of asset return means, variances and covariances.
  3. Investors only care about portfolio expected return and portfolio variance. Investors like portfolios with high expected return but dislike portfolios with high return variance.

The first assumption is supported by the stylized facts of asset returns for investment horizons of at least a month as discussed in Chapter 5. The second assumption can be thought of as assuming that investors have access to high quality information that they can use to determine expected returns, variances, and covariances. For example, investors can download asset price data from finance.yahoo.com and compute estimates of expected returns, variances, and covariances using sample statistics. Two points are relevant for the third assumption. First, if the distribution of assets returns is jointly normal then the probability distribution of returns is completely characterized by means, variances, and covariances. Second, the third assumption describes the mean-variance trade-off investors face. All else equal, investors prefer assets that have the highest expected return. However, as we have seen, assets with high expected returns tend to also have high variances. High variance represents more uncertainty about future return and it is assumed that investors do not like uncertainty about future return. That is, we assume that investors are risk averse.