Investments
Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
Question
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Chapter 24, Problem 21PS

a.

Summary Introduction

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.

Expert Solution
Check Mark

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 FundS&P 500
    Return10.20%-22.50%
    Standard deviation37.00%44.00%
    Beta1.101.00

Let us calculate the Sharpe ratio using the formula:

  Sharpe ratio=RPRfStandard deviation

Let us now substitute the given values in the formula.

    Mirinda FundS&P 500
    Sharpe Ratio=10.20%2%37.00% =8.20%37.00%0.2216=22.50%2%44.00% =24.50%44.00%0.5568

Therefore, the Sharpe ratio for Mirinda Fund is 0.2216 and S&P 500 is -0.5568.

b.

Summary Introduction

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.

Expert Solution
Check Mark

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 FundS&P 500
    Return10.20%-22.50%
    Standard deviation37.00%44.00%
    Beta1.101.00

The formula to calculate the M2is as follows:-

  M2=RP¯RM¯

Where,

  RP¯=Return on adjusted portfolio

  RM¯=market return

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.

  Adjusted portfolio=Standard deviation of S&P 500Standard deviation of Mirinda Fund=44.00%37.00%1.1892

Now, we have to calculate the position in T-Bills:

  Position in TBills=1 Adjusted portfolio=11.18920.1892

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:

  M2=RP¯RM¯

  =(1.1892×10.20%)+(0.1892×2%)(22.50%)=0.12120.0037+0.225=0.3425

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.

Summary Introduction

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.

Expert Solution
Check Mark

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 FundS&P 500
    Return10.20%-22.50%
    Standard deviation37.00%44.00%
    Beta1.101.00

The formula to be used to calculate the Treynor’s measure is as follows:

  Treynors ratio=RPRfβ

Where

RP=Return on portfolio

RF= Risk free rate of return

ß = Systematic risk

    Mirinda FundS&P 500
    Treynor’s measure=10.20%2%1.10 =8.20%1.107.45%=22.50%2%1.00 =24.50%1.0024.50%

Therefore, the Sharpe ratio for Mirinda Fund is 7.45% and S&P 500 is -24.50%.

d.

Summary Introduction

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.

Expert Solution
Check Mark

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 FundS&P 500
    Return10.20%-22.50%
    Standard deviation37.00%44.00%
    Beta1.101.00

The formula is as follows:

  Jenson measure=RP[rf+β×(rmrf)]=10.20%[2%+1.10×(22.502%)]=10.20%+24.95%=35.15%

Therefore, the Jenson measure of Mirinda fund is 35.15%.

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