Calculate the 95 prediction intervals for the four different

Calculate the? 95% prediction intervals for the four different investments included in the following table.

Small Stocks

?S&P 500

Corporate Bonds

?T-Bills

Average Return

19.45?%

11.18?%

6.83?%

4.41?%

Standard Deviation of returns

38.74?%

20.62?%

7.42?%

3.21?%

Solution

The Z value corresponding to 95% confidence interval is -1.96 to +1.96

Confidence interval will be mean-1.96 *standard deviation to mean+1.96*standard deviation

For Small stocks: Confidence interval is 19.45%-1.96*38.74% to 19.45%+1.96*38.74% that is -56.48% to +95.3804%

For S&P500: Confidence interval is 11.18%-1.96*20.62% to 11.18%+1.96*20.62% that is -29.235% to +51.5952%

For Corporate Bonds: Confidence interval is 6.83%-1.96*7.42% to 6.83%+1.96*7.42% that is -7.713% to 21.3732%