Another name for the reward-to-variability ratio is the Sharpe ratio, and the Sharpe ratio measures the excess return per unit of risk. So, the question is asking us to identify which investment has the highest Sharpe ratio. The formula is:

The Sharpe Ratio measures the excess return per unit of risk.

For the apartment building:

• The standard deviation of apartment building returns is 3.97%.
• The mean expected return of the apartment building = (10 − 1 + 8 + 8 + 9) / 5 = 6.8%
• Thus, the Sharpe Ratio_Apt = (6.80% - 5.00%) / 3.97% = 0.45.

For the REIT:

• The standard deviation of the REIT returns is 2.65%.
• The mean expected return of the REIT = (15 + 8 + 13 + 9 + 13) / 5 = 11.6%
• Thus, the Sharpe Ratio_REIT = (11.60% − 5.00%) / 2.65% = 2.49.

Thus, the REIT has a higher Sharpe ratio and thus a higher excess return per unit of risk than the apartment building has per unit of risk. Investors prefer a large Sharpe ratio because it is assumed that they prefer return to risk.

The other statements are false. Remember that the partner asked about the reward-to-variability ratio. The safety-first ratio is very similar to the Sharpe ratio, except that the safety-first ratio replaces the risk-free rate term with the threshold rate. Thus, the safety-first ratio for the REIT = [(11.6% − 5.7%) / 2.65%] = 2.23. If the partner had asked about the safety-first ratio, he would have been asking Bellow to select the investment with the minimal probability that the return falls below 5.70%. As shown in the calculation of the REIT Sharpe Ratio, the REIT’s excess return over the risk free rate = 11.6% − 5.0% = 6.60%.