a.
To compute: The Sharpe ratios for the Miranda fund and the S&P 500.
Introduction:
Sharpe ratio: It is one of risk measurement ratios. When a performance of an investment has to be done and that too in comparison with a risk-free asset, Sharpe ratio is utilized.
a.
Answer to Problem 21PS
The Sharpe ratio for Mirinda Fund is 0.2216 and S&P 500 is -0.5568.
Explanation of Solution
Given information:
Risk-free interest rate=2%
One- year Trailing Returns | ||
Miranda Fund | S&P 500 | |
Return | 10.20% | -22.50% |
Standard deviation | 37.00% | 44.00% |
Beta | 1.10 | 1.00 |
Let us calculate the Sharpe ratio using the formula:
Let us now substitute the given values in the formula.
Mirinda Fund | S&P 500 | |
Sharpe Ratio |
Therefore, the Sharpe ratio for Mirinda Fund is 0.2216 and S&P 500 is -0.5568.
b.
To compute: The M2 measures for Miranda and S&P 500.
Introduction:
M2 measure: It is also termed as M-square measure. It is used to calculate the return which has to be adjusted for the risk associated with a portfolio along with benchmark.
b.
Answer to Problem 21PS
The M2 of Mirinda Fund (portfolio P) would be 34.25%.
Explanation of Solution
Giveninformation:
Risk-free interest rate=2%
One- year Trailing Returns | ||
Miranda Fund | S&P 500 | |
Return | 10.20% | -22.50% |
Standard deviation | 37.00% | 44.00% |
Beta | 1.10 | 1.00 |
The formula to calculate the M2is as follows:-
Where,
One point to be kept in mind is that to get the position of volatility which is similar to the market, the funds have to be combined with the T-Bills.
Let us now calculate the adjusted portfolio.
Now, we have to calculate the position in T-Bills:
Therefore, when we check for the weight of Mirinda fund in adjusted portfolio, it will be 1.1892 and when amount is borrowed at a rate which is equal to 0.1892 will result in risk-free rate.
Therefore, the end result would be as follows:
Volatility of return of portfolio=Volatility in return on market index.
Now, let us calculate the M2of Mirinda Fund:
This value has to be converted into percentage by multiplying it with 100.
Therefore, the M2 of Mirinda Fund (portfolio P) would be 34.25%
c.
To compute: The Treynor’s measure ratios for the Miranda fund and the S&P 500.
Introduction:
Treynor’s ratio: It is also termed as Treynor’s measure in some instances. It is one of the measures used to calculate the risk adjusted return. It calculates the returns on the basis of systematic risk which differentiates this ratio with other related ratios.
c.
Answer to Problem 21PS
The Sharpe ratio for Mirinda Fund is 7.45% and S&P 500 is -24.50%.
Explanation of Solution
Given information:
Risk-free interest rate=2%
One- year Trailing Returns | ||
Miranda Fund | S&P 500 | |
Return | 10.20% | -22.50% |
Standard deviation | 37.00% | 44.00% |
Beta | 1.10 | 1.00 |
The formula to be used to calculate the Treynor’s measure is as follows:
Where
RP=Return on portfolio
RF= Risk free
ß = Systematic risk
Mirinda Fund | S&P 500 | |
Treynor’s measure |
Therefore, the Sharpe ratio for Mirinda Fund is 7.45% and S&P 500 is -24.50%.
d.
To compute: The Jenson measure for the Miranda Fund.
Introduction:
Jenson Measure: This measure is used to calculate the average rate of return. The return calculated is on the investment made in a portfolio.
d.
Answer to Problem 21PS
The Jenson measure of Mirinda fund is 35.15%.
Explanation of Solution
Given information:
Risk-free interest rate=2%
One- year Trailing Returns | ||
Miranda Fund | S&P 500 | |
Return | 10.20% | -22.50% |
Standard deviation | 37.00% | 44.00% |
Beta | 1.10 | 1.00 |
The formula is as follows:
Therefore, the Jenson measure of Mirinda fund is 35.15%.
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Chapter 24 Solutions
INVESTMENTS (LL)
- The returns on the Bledsoe Small-Cap Fund are the most volatile of all the mutual funds offered in the 401(k) plan. Why would you ever want to invest in this fund? When you examine the expenses of the mutual funds, you will notice that this fund also has the highest expenses. Does this affect your decision to invest in this fund? A measure of risk-adjusted performance that is often used is the Sharpe ratio. The Sharpe ratio is calculated as the risk premium of an asset divided by its standard deviation. The standard deviation and return of the funds over the past 10 years are listed below. Calculate the Sharpe ratio for each of these funds. Assume that the expected return and standard deviation of the company stock will be 15 percent and 65 percent, respectively. Calculate the Sharpe ratio for the company stock. How appropriate is the Sharpe ratio for these assets? When would you use the Sharpe ratio? Assume the risk-free rate was 2.76 percent. 10-YEAR ANNUAL RETURN…arrow_forwardBart Campbell, CFA, is a portfolio manager who has recently met with a prospective client, Jane Black. After conducting a survey market line (SML) performance analysis using the Dow Jones Industrial Average as her market proxy, Black claims that her portfolio has experienced superior performance. Campbell uses the capital asset pricing model as an investment performance measure and finds that Black’s portfolio plots below the SML. Campbell concludes that Black’s apparent superior performance is a function of an incorrectly specified market proxy, not superior investment management. Justify Campbell’s conclusion by addressing the likely effects of an incorrectly specified market proxy on both beta and the slope of the SML.arrow_forwardA local mutual fund says it has expertise in identifying stocks that are undervalued because they are under researched or unpopular. To prove its point, the fund produces evidence that it returns over the past four years was 3% above the return on the market index. a) What does efficient market hypothesis (EMH) say about undervalued stock? b) Does the fund’s evidence contradict the EMH?arrow_forward
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