Complete Problem 22 in the Questions and Problems section of Chapter 13 (shown b
ID: 2726371 • Letter: C
Question
Complete Problem 22 in the Questions and Problems section of Chapter 13 (shown below). When you pick the best choice for your portfolio, defend your decision in a one-page essay following APA guidelines. You have been given the following return information for two mutual funds (Papa and Mama),
Year Papa Fund Mama Fund Market Risk-free
2008 -12.6% -22.6 -24.5% 1%
2009 25.4 18.5 19.5 3
2010 8.5 9.2 9.4 2
2011 15.5 8.5 7.6 4
2012 2.6 -1.2 -2.2 2
Calculate the Sharpe ratio, Treynor ratio, Jensen’s alpha, information ratio, and R-squared for both funds and determine which is the best choice for your portfolio.
Explanation / Answer
Calculate the Sharpe ratio, Treynor ratio, Jensen’s alpha, information ratio, and R-squared for both funds and determine which is the best choice for your portfolio.
Given Information:
Year
Papa Fund
Mama Fund
Market
Risk-Free Rate
2008
-12.60%
-22.60%
-24.50%
1.00%
2009
25.40%
18.50%
19.50%
3.00%
2010
8.50%
9.20%
9.40%
2.00%
2011
15.50%
8.50%
7.60%
4.00%
2012
2.60%
-1.20%
-2.20%
2.00%
Averages
7.88%
2.48%
1.96%
2.40%
Standard Deviation
14.25%
15.66%
16.68%
Year
Papa Fund Excess
Mama Fund Excess
Market Excess
Papa Fund Excess Diff
Mama Fund Excess Diff
2008
-13.60%
-23.60%
-25.50%
11.90%
1.90%
2009
22.40%
15.50%
16.50%
5.90%
-1.00%
2010
6.50%
7.20%
7.40%
-0.90%
-0.20%
2011
11.50%
4.50%
3.60%
7.90%
0.90%
2012
0.60%
-3.20%
-4.20%
4.80%
1.00%
Sharpe Ratio
(7.8-2.4)/14.25 = 0.3845
(2.48-2.4) / 15.66 = 0.0051
Treynor Ratio
(7.88-2.40) / 80.99 (Beta) = 0.0677
(2.48-2.4) / 93.42 (Beta) = 0.0009
Jensen's Ratio
(Jensen's Alpha, or just "Alpha", is used to measure the risk-adjusted performance of a security )
5.84%
0.49%
Tracking Error
4.68%
1.13%
Coefficients (Alpha)
5.84%
0.49%
Coefficients (Beta)
0.8099
0.9342
Information Ratio
1.2482
0.4345
Correlation
0.9635
0.9996
R-squared
92.83%
99.91%
R-squared
92.83%
99.91%
I think the best option for my portfolio would be Papa Fund. It has a Sharpe ratio of 0.3845 which means that the risk involved is 0.3845 as opposed to the Sharpe ratio of 0.0051 of Mama Fund. The more the value of a portfolio’s Sharpe ratio, the more risk-adjusted it is.
Furthermore, the Treynor ratio of Papa Fund is 0.0677 whereas 0.0009 of Mama Fund. The Treynor ratio represents the return centered on methodical and calculated risk. Papa Fund’s ratio is higher than Mama Fund’s; nevertheless I believe that a risk should be taken for the return.
In closing, Papa Fund is a better option compared to Mama Fund. The Jensen’s ratio of the former is 5.84% whereas 0.49% of the latter. This indicates that Papa fund has hit the market with a positive Alpha. Mama fund on the other hand shows underperformance. Therefore, Papa fund is a great investment option to increase your portfolio.
Given Information:
Year
Papa Fund
Mama Fund
Market
Risk-Free Rate
2008
-12.60%
-22.60%
-24.50%
1.00%
2009
25.40%
18.50%
19.50%
3.00%
2010
8.50%
9.20%
9.40%
2.00%
2011
15.50%
8.50%
7.60%
4.00%
2012
2.60%
-1.20%
-2.20%
2.00%
Averages
7.88%
2.48%
1.96%
2.40%
Standard Deviation
14.25%
15.66%
16.68%
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