Risk Sensitive Asset Management: Two Empirical Examples

Abstract

This paper is concerned with applications of risk sensitive control theory in financial decision making. In earlier work a variation of Merton’s continuous-time intertemporal capital asset pricing model was developed where the infinite horizon objective is to maximize the portfolio’s risk adjusted growth rate. Here the model is illustrated by applying it to two portfolio management problems based upon historical data. In the first there are four assets (a bank account, the Dow Jones Industrials index, the S&P 500 index, and the NASDAQ index) and two stochastic economic factors (the short interest rate for the bank account and a long term interest rate). In the second there are six stochastic economic factors, namely, U.S. Treasury yields of various maturities; in addition to the usual bank account the other assets are rolling horizon bonds corresponding to the factors. These examples demonstrate that the risk sensitive asset management model is tractable and provides economic insight as well as useful results, although the optimal strategies sometimes involve high levels of leverage.