Large declines in stock prices are not rare events. Investors assuming that the distribution of asset price changes conforms to the well-known “normal distribution” [Gaussian distribution], however, may be startled by the frequency and magnitude of asset price declines.
This essay compares the historical behavior of stock price movements to the behavior that the normal distribution predicts. It then substitutes a more dynamic and credible stochastic risk model , and compares its outputs to the static, pre-parameterized outputs obtained under the assumption of distributional normality.
After demonstrating that the outputs can differ widely, the essay returns to the topic of risk by examining the nature of the return process. It presents four price change processes and cautions the investor not to confuse them. If a trustee does not understand the nature of the return generating process governing the trust asset portfolio, it may be difficult to elect prudent asset management decisions.
Finally, the essay departs from the conventional world of discrete time finance to explore briefly the asset management implications of the mathematics of continuous time finance. Academic research in this area often completely belies traditional asset management maxims; and, therefore, can provide valuable insight for trustees.