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MC9901C03 Lecture Notes - Lecture 1: Treynor Ratio, Sharpe Ratio, Systematic Risk

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anujacob091
2 Mar 2022
School
Mahatma Gandhi University - Kerala
Department
Finance
Course
MC9901C03
Professor

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Document Summary

Jack l. treynor based his model on the concept of characteristics line. This line is the least squares regression lines relating the return to the risk and beta is the slope of the line. Treynor also pointed out that investment risk in a diversified portfolio is the sum of the responses to general market fluctuations and fluctuations peculiar to the particular securities held in the portfolio. Treynor"s measures is the measures of the portfolio"s excess return per unit of portfolio"s beta coefficient (b). The sharpe measures relates a portfolio"s excess return to total risk while treynor measure relates to non-diversifiable or systematic risk as measured by the portfolio"s volatility. Treynor"s index has ranked portfolio a as the better performer because value is higher (2. 4 >2. 0) despite the fact that b has higher return (24%>20%) . It is due to the difference of two portfolios. In essence, the treynor ratio is a risk-adjusted measurement of return based on systematic risk.

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Related Questions

1. Congratulations! Your portfolio returned 9.4% last year, 1.9% better than the market return of 7.5%. Your portfolio had a standard deviation of earnings equal to 19%, and the risk free rate is equal to 3.5%. Calculate the Sharpe's measure for your portfolio. If the market's Sharpe's measure is .23, did your do better or worse than the market from a risk return perspective? Explain why? 2. Niki Malone's portfolio earned a return of 11.9% during the year just ended. The portfolio's standard deviation of return was 14.4%. The risk free rate is currently 6.2%. During the year, the return on the market portfolio was 9.5% and its standard deviation was 10.5%. a. Calculate Sharpe's measure for Niki Malone's portfolio for the year just ended. b. Compare the performance of Niki's portfolio found in part A to that of Hector Smith's portfolio, which has a Sharpe's measure of .343. Which portfolio performed better? Why? c. Calculate Sharpe's measure for the market portfolio for the year just ended. d. Use your findings in part A and C to discuss the performance of Niki's portfolio relative to the market during the year just ended. 3. Your portfolio has a beta equal to 1.5. It returned 10.1% last year. The market returned 7.9%; the risk-free rate is 5.1%. Calculate Treynor's measure for your portfolio and the market. Did you earn a better return than the market given the risk you took? 4. Your portfolio returned 14.2% last year, with a beta equal to 1.3. The market return was 11.7%, and the risk-free rate is 4.3%. If you use the Jensen's measure, did you earn more or less than the required rate of return on your portfolio?

For a particular sample period, the risk free rate was 6% and: Portfolio P: Average return=35%; Beta=1.20; Standard Deviation=40%; Tracking Error (nonsystematic risk)=20% Market M: Average return=30%; Beta=1.00; Standard Deviation=30%; Tracking error=0

A) For both the portfolio and the market calculate the Sharpe ratio, the Treynor ratio and the information ratio.

B) Why should the Sharpe measure only be used to judge the performance of a well-diversified portfolio?

Suppose that the return on a risk-free security is 5 percent. The expected return on the market portfolio is 16 percent and the volatility of the market portfolio is 22 percent

(a) Write down the equation for CML.

(b) Consider a portfolio on CML such that the expected return on the portfolio is 14 percent. What is the volatility of this portfolio? What percentages of your portfolio you need to invest on the risk-free security and the market portfolio in order to create this portfolio (i.e., the portfolio on the CML with expected return equal to 14 percent).

c) What is the volatility of the risk-free security? What is the correlation of the return on the risk-free security and the market portfolio? Show that the beta of the risk-free security is zero.