Given the performance of 4 mutual funds and S&P500 over the past 15 years in tab
ID: 2647895 • Letter: G
Question
Given the performance of 4 mutual funds and S&P500 over the past 15 years in table below:
Return and Risk data for 4 equity mutual funds and the market over the past 15 years
Mutual Fund
Average R eturn %
Standard Deviation %
Beta
R2
1
15.86
22.85
1.46
.64
2
18.10
13.44
0.96
.79
3
22.09
17.27
1.24
.79
4
18.39
11.82
0.60
.39
S&P 500
16.35
12.44
1.0
1.0
And assuming that current and average of past 15 years risk free rate is 7.96 %, and using a market risk premium of 8.39% (16.35 -7.96) for the 15 year period, estimate:
Sharpe ratios of all 4 funds and S&P 500. Which fund has the highest risk adjusted performance according to Sharpe measure? Which of the above funds have beaten the market?
Treynor of all 4 funds and S&P 500. Which fund has the highest risk adjusted performance according to Treynor measure? Which of the above funds have beaten the market according to Treynor measure?
Estimate Jensen
Return and Risk data for 4 equity mutual funds and the market over the past 15 years
Explanation / Answer
Sharpe ratio = (Mean portfolio return ? Risk-free rate)/Standard deviation of portfolio return
Mutual fund 4 has the highest risk adjusted performance according to Sharpe measure.
The Treynor ratio is calculated as:
(Average Return of the Portfolio - Average Return of the Risk-Free Rate) / Beta of the Portfolio
In other words, the Treynor ratio is a risk-adjusted measure of return based on systematic risk. It is similar to the Sharpe ratio, with the difference being that the Treynor ratio uses beta as the measurement of volatility.
Only fund 4 has beaten the market because the rate of return is more than the market rate of return.
Unsystematic risk, also known as
Mutual fund Average return Standard deviation 1 15.86% 22.85% 2 18.10% 13.44% 3 22.09% 17.27% 4 18.39% 11.82% Risk free 7.96% Sharpe ratio 1 34.57% Sharpe ratio 2 75.45% Sharpe ratio 3 81.82% Sharpe ratio 4 88.24%Related Questions
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