Question

The return on stocks in a particular year was 18%. The return on bonds was 8%, and the return on Treasury bills (risk-free rate) was 6%.

The standard deviation of stock returns during the year was 22%, the standard deviation of bond returns during the year was 7%, and the standard deviation of Treasury bill returns was zero.

A 50-50 portfolio combination of stocks and bonds had a return of 13% and a standard deviation of 14%.

1. Which of the three portfolios (stocks only, bonds only, and 50-50 stocks and bonds) is best when judged by the Sharpe (reward to risk) ratio?
2. Should you conclude from the data that bonds are generally inferior to stocks and that your future portfolio should be composed only of stocks and Treasury bills>

Answer 1

A) Sharpe ratio = expected return - risk free rate / standard deviation

Stock only Sharpe ratio = 18% - 6% / 22%

= 12% / 22%

= 0.55

Sharpe ratio of bond only = 8% - 6% / 7%

= 2% / 7%

= 0.29

Sharpe ratio of 50 - 50 bond and stock

= 13% - 6% / 14%

= 7% / 14%

= 0.5

On the basis of Sharpe ratio Stock only portfolio performs the best .

B) Yes, we should conclude that bond is inferior to stock on the basis of above data because the risk to reward ratio from investing in bond is lower than that of the stock. So, when the bond will be combined with t-bill it will provides lower return than that of the combination of stock and t-bill, due to lesser risk taken and lower Sharpe ratio of the combination of bond and t-bill.