Question

You have researched information on 3 mutual funds. If the risk-free rate is currently 5.5%, which one of these funds has the best risk-adjusted performance?

Fund Q:

Average annual return: 8.21%

Standard deviation: 7.00%

Beta coefficient: 0.921

Fund R:

Average annual return: 11.55%

Standard deviation: 13.52%

Beta coefficient: 1.100

Fund S:

Average annual return: 12.00%

Standard deviation: 16.05%

Beta coefficient: 1.825

A. Fund S, because it has the highest Treynor ratio

B. Fund R, because it has the highest Sharpe ratio

C. Fund S, because it has the highest rate of return

D. Fund Q, because it has the lowest standard deviation

Answer 1

Risk adjusted performance measurement ways are first

Sharpe ratio

Sharpe ratio formula = (Average Annual return - risk free rate of return) / standard deviation

Sharpe ratio of fund Q = (8.21% - 5.5%)/7%

=0.38714285714285

Sharpe ratio of fund R = (11.55% - 5.5%)/13.52%

0.44748520710059

Sharpe ratio of fund S = (12% - 5.5%)/16.05%

0.40498442367601

Trenyor ratio formula = (Average Annual return - risk free rate of return)/ beta of stock

Trenyor of fund Q = (8.21%-5.5%)/0.921

2.94245385450597

Trenyor of fund R = (11.55% - 5.5%)/1.1

= 5.5

Trenyor of fund S = (12% - 5.5%)/1.825

=3.56164383561643

Sharpe ratio of fund R is highest 0.44748520710059.

Trenyor ratio of fund R is highest 5.5

So, fund R will be chosen because of highest Sharpe ratio. Answer is B.