Chapter 24, Problem 6CP

A

Summary Introduction

To calculate: The sharpe measures and treynor ratio for portfolio X and S&P 500. And explain the X portfolio performance using treynor measure and the sharpe ratio.

Introduction: Sharpe ratio tells about the risk premium with respect to the total risk of the market. Treynor ratio is defined as the risk premium and risk premium is difference of risk rate and return.

Answer to Problem 6CP

The value of Sharpe ratio is 0.222 and 0.462 and Treynor ratio is 6.67 and 6.

Explanation of Solution

The Sharpe ratio of the X portfolio and S&P 500 is calculated below,

  $Sharperatio=$$\frac{R_P-I_{RF}}{{\sigma }_P}$ here $R_p$ is portfolio return, $I_{RF}$ is risk free rate, and ${\sigma }_p$ is standard deviation.

  $\begin{array}{l}ForportfolioX,Sharperatio=\left(.10-.06\right)/0.18\hfill \\ =0.222\hfill \\ ForS\&P500,Sharperatio=\left(0.12-.06\right)/.13\hfill \\ =0.462\hfill \end{array}$

Treynor ratio for X portfolio and S&P 500 is calculated below,

  $Treynorratio=$$\frac{R_p-I_{RF}}{{\beta }_P}$ , here $R_p$ is portfolio return, $I_{RF}$ is risk free rate.

  $\begin{array}{l}ForportfolioX,treynorratio=\left(10-6\right)/0.6\hfill \\ =6.67\hfill \\ ForS\&P500,treynorratio=\left(12-6\right)/1.0\hfill \\ =6\hfill \end{array}$

B

Summary Introduction

To explain: The Risk management in both portfolios and the reason for the result when using treynor measure versus the sharpe ratio.

Introduction: The risk taking of any portfolio is decided by the value of beta and standard deviation. For low value of beta means low risk in the market.

Answer to Problem 6CP

Portfolio X has low risk as the low beta value.

Explanation of Solution

The risk of portfolios is decided by the value of beta and standard deviation. As from the value portfolio ‘X’ has low beta value. Hence it has lower risk in market. On the other hand the standard deviation value is high for portfolio ‘X’, this means it has high total risk in the market.