EXAMPLE 7.6 Estimating Difference from a Standard

Following the analysis accepted by the arbitration panel, we are considering the S&P 500 monthly average return as a constant standard. (It is easy to envision scenarios in which we would want to treat this type of quantity as random.) The difference between the mean of the investor’s account and the S&P 500 is . In Example 7.5, we found that the 95% confidence interval for the investor’s account was (−3.04,0.84). To obtain the corresponding interval for the difference, subtract 0.95 from each of the endpoints. The resulting interval is (−3.04−0.95, 0.84−0.95), or (−3.99, −0.11). This interval is presented in the SPSS output of Figure 7.6. We conclude with 95% confidence that the underperformance was between −3.99% and −0.11%. This estimate helps to set the compensation owed to the investor.