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LOS q, (Part 2): Explain how a portfolio's alpha and beta are incorporated into these measures. ffice ffice" />
Q1. Which of the following statements regarding the Sharpe ratio is most accurate?
A) The denominator of the Sharpe ratio is standard deviation which is comprised partly of systematic risk called beta.
B) Beta is not a component of the Sharpe ratio.
C) The measure of risk used in the denominator of the Sharpe ratio is standard deviation also known as unsystematic risk.
Correct answer is A)
The equation for the Sharpe ratio = (RP ? RF) / σP.
The Sharpe ratio contains standard deviation in the denominator of the equation which is total risk and is comprised of both systematic risk called beta and unsystematic risk thus the Sharpe ratio does contain a component of beta.
Q2. A portfolio manager has a well diversified portfolio and they are trying to determine whether or not to add a particular stock to the portfolio to increase the portfolio’s overall risk adjusted return. To decide whether or not to add the stock the manager will back test the portfolio based on historical data of the stock and the portfolio. The relevant measure to use in comparing the results of the back tested model comparing the results of the portfolio before and after the addition of the stock would be the:
A) Sharpe ratio.
B) Information ratio.
C) Treynor measure.
Correct answer is C)
The equations for the 3 measures are as follows:
Treynor measure = (RP ? RF) / βP
Sharpe ratio = (RP ? RF) / σP
Information ratio = (RP ? RB) / (σP ? B)
The goal is to add a greater return to the portfolio without appreciably increasing the level of risk. Since the portfolio is already well diversified most of its risk is related to systematic risk (beta) which is the relevant measure of risk in the denominator of the Treynor measure. Adding one risky stock to an already diversified portfolio will not appreciably change the overall risk of the portfolio thus beta and the Treynor measure remain the relevant measures used to compare the results of the portfolio with and without the addition of the stock. The Sharpe ratio uses standard deviation in the denominator of the equation. Standard deviation is comprised of systematic risk (beta) and unsystematic risk. If the portfolio was not well diversified then most of the risk would be unsystematic or company specific risk. Adding one stock to an undiversified portfolio would most likely still leave a lot of unsystematic risk thus making standard deviation and the Sharpe ratio the relevant measures if the portfolio was undiversified. The information ratio is used to compare the return to a benchmark which is not a concern to the portfolio manager in this question.
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发表于 2009-4-10 14:58
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