Question

Problem 2

Risk-free rate is 4%. Expected return on actively managed fund P is 16%, expected return on the market index is 12%. Standard deviation of the fund is 20%, and standard deviation of the index is 17%. Beta of the fund is 0.73.

1. Calculate Sharpe ratio of the market index and of fund P. Does the fund beat the market?

2. Calculate Treynor measure of the market index and of fund P. Does the fund beat the market?

3. Calculate the –M² measure. Explain what it means.

Answer 1

a. Sharpe Ratio of market index fund =(Expected Return -Risk free Rate)/Standard Deviation =(12%-4%)/17%=0.47
Sharpe Ratio of fund =(Expected Return -Risk free Rate)/Standard Deviation =(16%-4%)/20%=0.8
The fund's sharpe ratio is higher than market index, hence it's beat the market index

b. Treynor measure of market index fund =(Expected Return -Risk free Rate)/Beta =(12%-4%)/1 =8%
Treynor measure of fund P fund =(Expected Return -Risk free Rate)/Beta =(16%-4%)/0.73 =16.44%
The fund beats the market index

c. M-2 measure =(Standard Deviation of Market/Standard Deviation of Portfolio)*(Expected Return of P -Risk Free Rate)+Risk Free Rate =(17%/20%)*(16%-4%)+4%=14.20%

It is the risk adjusted return of the portfolio .It is less than expected Return.