The Effects of Sampling Fluctuations on the Required Inputs of Security Analysis

This project was intended to test the usefulness of the Markowitz-based allocation model of which sampling fluctuations are clearly a possible weakness. Realistic conditions were formulated and a data set was simulated to insure a stable, independent, and normally distributed data set. The methodology was constructed such that the only difference in the portfolio performance results was the number of historical observations to estimate the inputs.It was found that a minimum of 30 historical observations was required to yield efficient portfolio performance characteristics. It may be argued that this represents a large number of observations, although it is clearly not as large as those of other statistical procedures such as factor analysis or discriminant analysis.This article addressed only the issue of the number of observations and not the appropriate length, i.e., monthly or quarterly. Dickinson demonstrated that the ratio of variances of two securities influenced the accuracy of the estimates of wi, the proportion of total capital invested in each of the two assets. Changing the length of the observation will change these variance ratios for many assets. A study is currently in progress to trace this effect on subsequent portfolio performance. It is hoped that these results, and those yet to come, will ease the burden of many of the arbitrary assumptions that we are presently forced to make in empirical investigations of efficient portfolio performance.