Portfolio Management, Alpha, and Beta
Two of the most central issues of this book are return, as represented by alpha, and risk, as represented by the concept of beta. This chapter provides concluding discussions regarding the portfolio allocation and management of alternative investments within the context of alpha and beta.
31.1 THE ESTIMATION OF ALPHA AND BETA
This chapter and the previous one discuss portfolio management with the explicit or implicit assumption that risk and abnormal return can be estimated with sufficient reliability to facilitate meaningful investment decisions. This section discusses errors in estimating alpha and/or beta.
Alpha and beta are generally unobservable and usually need to be estimated based on historical data. Using past data to measure alpha and beta causes estimation risk. That is, the estimated values of alpha and beta could be very different from their actual or true values. These errors in estimation could be substantial, especially if substantial historical data are not available regarding performance, and if the manager is active.
31.1.1 Example of Errors in Estimating Ex Ante Alpha
To illustrate the challenges, consider a simplified scenario in which a hedge fund's strategy is solely writing out-of-the-money options each month. For simplicity, assume that in every month there is an 11 out of 12 chance that the options expire worthless and the strategy earns 2% for that month, and a 1 out of 12 chance that the options will ...