Long-Term Dependence and Least Squares Regression in Investment Analysis

It is widely assumed that common stock returns approximate a random walk, i.e., the returns are assumed to be serially independent. As a consequence, estimates of systematic risk and efficient portfolios are usually developed using any convenient differencing interval with the implication that they are applicable to any investor regardless of his horizon period. This paper derives the relationships between least-squares estimators and the differencing interval in the presence of long-term dependence. These relationships are then used to show how long-term dependence affects estimates of systematic risk and efficient portfolios selected with the Sharpe index model. The major implication is that, because of long-term dependence, systematic risk estimates and efficient portfolios must be developed using a differencing interval exactly equal to the investor's horizon period.