Portfolio Selection in a Dynamic and Uncertain World

Abstract

This article examines the kind of performance obtainable from a portfolio when the Sharpe diagonal model is used to make the selection decisions over a period of time.' The word dynamic in the title means that we are looking at stocks whose prospects and returns are continually changing through time, causing us to make changes in the portfolio. The article is based on a simulation study. We have assumed a plausible (if somewhat simplified) structure for a population of stocks, and random numbers are used to generate typical returns that might result from this structure. For each set of returns we also use random numbers to produce a set of forecasts of these returns. The forecasts are subject to considerable forecasting errors, hence the reference to the uncertain world referred to in our title. The Sharpe diagonal model is used to make changes in the portfolio on the basis of these forecasts. Our simulations make annual forecasts of the stocks and annual changes in a portfolio which is held over an eight-year period, starting from an all cash position and thereafter being fully invested in stock. We assume that there arel transaction costs amounting to five per cent. Each of these eight-year simulations is repeated 100 times, using different random numbers. We calculate the average value and the standard deviation of the portfolio's eight-year wealth ratio as measures of its performance. Many topics can be studied using this type of simulation model. The chief ones we considered here are the following: 1. The relationship of portfolio performance to forecasting ability.