ESSENTIALS OF INVESTMENTS>LL<+CONNECT
ESSENTIALS OF INVESTMENTS>LL<+CONNECT
11th Edition
ISBN: 9781264001026
Author: Bodie
Publisher: MCG
Question
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Chapter 18, Problem 21PS
Summary Introduction

(a)

To calculate:

The sharpe ratios for the fund and index i.e. Miranda fund and S&P 500 .

Introduction:

Sharpe ratio is a ratio which helps in computing the reward-to-volatility ratio. This ratio gives an understanding of the incremental return which an investor will expect to earn on every 1% increase in the value of standard deviation.

Expert Solution
Check Mark

Answer to Problem 21PS

The sharpe ratio for Miranda fund is 0.2216 and for the S&P 500 is 0.556 .

Explanation of Solution

Given:

Risk free rate of Return or T-bill Rate, rf¯=2%

    One- Year Trailing Returns
    Miranda Fund S&P 500
    Return 10.2% -22.5%
    Standard Deviation 37% 44%
    Beta 1.10 1.00

The sharpe ratio is calculated by the following formula:

  Sharpe Ratio=Expected returnRisk free returnStandard deviation

The sharpe ratio for Portfolio Miranda is:

  Sharpe Ratio=Expected returnRisk free returnStandard deviation= 10.2237=0.2216

The sharpe ratio for S&P 500 is:

  Sharpe Ratio=Expected returnRisk free returnStandard deviation= 22.5244=0.556

Summary Introduction

(b)

To calculate:

The M2 measure for the fund and index i.e. Miranda fund and S&P 500

Introduction:

  M2 is a measure which helps in ascertaining the adjusted return in regard to the associated risk with the portfolio.

Expert Solution
Check Mark

Answer to Problem 21PS

The M2 measure is 34.25% .

Explanation of Solution

Given:

Risk free rate of Return or T-bill Rate, rf¯=2%

    One- Year Trailing Returns
    Miranda Fund S&P 500
    Return 10.2% -22.5%
    Standard Deviation 37% 44%
    Beta 1.10 1.00

The M2 is calculated by the following formula:

  M2=rPrM

For computing M2 , first adjusted portfolio should be calculated:

  Adjusted Portfolio=Standard deviation of S&P 500Standard deviation of M fund=44%37%=1.1892

Now, the position of T-bills:

  Portfolio in T-bills=1Adjusted portfolio=11.1892=0.1892

  M2 for Portfolio Miranda is:

  M2=rPrM= 1.1892×10.2%+ 0.1892×2%22.50%=34.25%`

Thus, the M2 measure is 34.25% .

Summary Introduction

(c)

To calculate:

The treynor ratios for the fund and index i.e. Miranda fund and S&P 500 .

Introduction:

Treynor ratio is a ratio which helps in computing the reward-to-volatility ratio. This ratio provides excess return over expected in regard to systematic risk i.e. beta.

Expert Solution
Check Mark

Answer to Problem 21PS

The treynor ratio for Miranda fund is 7.45% and for the S&P 500 is 24.50% .

Explanation of Solution

Given:

Risk free rate of Return or T-bill Rate, rf¯=2%

    One- Year Trailing Returns
    Miranda Fund S&P 500
    Return 10.2% -22.5%
    Standard Deviation 37% 44%
    Beta 1.10 1.00

The treynor ratio is calculated by the following formula:

  Treynor Ratio=Expected returnRisk free returnBeta

The treynor ratio for Portfolio Miranda is:

  Treynor Ratio=Expected returnRisk free returnBeta= 10.2%2%1.10=7.45%

The treynor ratio for S&P 500 is:

  Treynor Ratio=Expected returnRisk free returnBeta= 22.5%2%1.00=24.50%

Summary Introduction

(d)

To calculate:

The Jensen measure i.e. alpha for the fund i.e. Miranda fund.

Introduction:

The alpha shows the performance of portfolio in relation to benchmark.

Expert Solution
Check Mark

Answer to Problem 21PS

The Jensen measure for Miranda fund is 35.15% .

Explanation of Solution

Given:

Risk free rate of Return or T-bill Rate, rf=2%

    One- Year Trailing Returns
    Miranda Fund S&P 500
    Return 10.2% -22.5%
    Standard Deviation 37% 44%
    Beta 1.10 1.00

The Jensen measure i.e. alpha is calculated by the following formula:

  α=rprf+βprMrf

The Jensen measure i.e. alpha for Portfolio Miranda is:

  α=rprf+βp r M r f =10.2%2%+1.10 22.5%2%=35.15%

Thus, the Jensen alpha of the fund id 35.15%

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