ikoreaii

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) Treynor measure.

B) Sharpe ratio.

C) Information ratio.

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The equations for the 3 measures are as follows:Treynor measure = (RP − RF) / βP
Sharpe ratio = (RP − RF) / σPInformation 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.

ikoreaii

Which of the following measures would be the most appropriate one to use when comparing the results of two portfolios in which each portfolio contains only a few number of stocks representing a limited number of industries?

A) Treynor measure.

B) Information ratio.

C) Sharpe ratio.

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The equations for the 3 measures are as follows:Sharpe ratio = (RP − RF) / σP
Treynor measure = (RP − RF) / βPInformation ratio = (RP − RB) / (σP − B)
Since both portfolios are not well diversified most of their risk comes from unsystematic (company specific) risk and is not tied to the overall level of risk in the market thus in this case standard deviation is the best measure of risk to use. The Sharpe ratio is the best measure to use to compare the two portfolios which are undiversified since the Sharpe ratio uses standard deviation or total risk in the denominator of the equation as its measure of risk. The Treynor measure uses beta or systematic market risk as the measure of risk in the denominator and the information ratio is best to use when comparing a portfolio to a benchmark.

ikoreaii

Which of the following measures would be the most appropriate one to use when comparing the results of two portfolios in which each portfolio contains many stocks from a broad selection of different industries?

A) Sharpe ratio.

B) Treynor measure.

C) Information ratio.

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The equations for the 3 measures are as follows:Treynor measure = (RP − RF) / βP
Sharpe ratio = (RP − RF) / σPInformation ratio = (RP − RB) / (σP − B)
Since both portfolios are well diversified most of their risk comes from systematic risk or beta and is tied to the general level of overall risk in the market. In this case the best measure to use would be the Treynor measure since this uses beta or systematic risk as the measure of risk. The Sharpe ratio uses standard deviation as the measure of risk in the denominator and the information ratio is best to use when comparing a portfolio to a benchmark.

ikoreaii

The Information ratio is also referred to as the benefit-cost ratio. What is cost defined as?

A) The standard deviation of surplus returns.

B) The standard deviation of benchmark returns.

C) The standard deviation of portfolio returns.

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The information ratio is calculated as the surplus return divided by the standard deviation of surplus returns. The cost in the information ratio is the standard deviation of surplus returns.

ikoreaii

Jack Gallon is a portfolio manager whose fund sponsor would like to evaluate his performance. It is very important to the fund sponsor to minimize tracking risk. Which of the following would be most appropriate for evaluating his performance?

A) The Treynor ratio.

B) The information ratio.

C) Jensen’s alpha.

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The information ratio is the manager’s excess return (relative to a benchmark return) divided by the standard deviation of excess returns. Because it measures risk and return relative to a benchmark, it would be the most appropriate measure when the minimization of tracking risk is important.

ikoreaii

Jim Kyle has been the manager of the Superior Asset Portfolio for the past ten years. During this time, Superior’s average return was 14.50%. For the purpose of performance evaluation, the Superior Asset Portfolio is compared to the S&P 500. During the same time period, the S&P 500 had an average annual return of 18%. The standard deviation of surplus return is 23%. What is Superior’s information ratio?

A) 0.16.

B) -0.56.

C) –0.15.

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Information ratio = IRj = SRj / σSR = (14.50 - 18) / 23 = -0.15

ikoreaii

Which of the following statements regarding the Sharpe ratio is most accurate?

A) Beta is not a component of the Sharpe ratio.

B) The denominator of the Sharpe ratio is standard deviation which is comprised partly of systematic risk called beta.

C) The measure of risk used in the denominator of the Sharpe ratio is standard deviation also known as unsystematic risk.

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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.

ikoreaii

Which of the following best describes the use of quality control charts in portfolio management? Quality control charts are used to determine if a manager has:

A) strayed from their stated style.

B) statistically significant excess returns.

C) substantial excess returns.

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In portfolio management, quality control charts are used to determine if a manager has statistically significant excess returns. The manager’s returns versus a benchmark are plotted on a graph where time is on the x-axis and value-added (excess) return is plotted on the y-axis. A confidence interval is formed around the x-axis of zero. If the manager’s returns plot outside the confidence interval, we conclude that the manager has generated statistically significant excess returns.

ikoreaii

When constructing a quality control chart which of the following is an important assumption that is made about the distribution of the manager’s value added returns?

A) The investment process is consistent thus ensuring that a high degree of the error term in one period can be explained by the error term in the previous period.

B) The null hypothesis states that the expected value-added return is the risk free rate of return.

C) Value-added returns are independent and normally distributed.

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The null hypothesis states that the expected value-added return is zero. We are testing the manager’s ability to generate positive expected value added returns. We want a consistent process to ensure that the distribution of value added returns about their mean is constant. We do indeed assume that value-added returns are independent and normally distributed.

ikoreaii

Which of the following is NOT a conclusion that could be derived from plotting a manager's value-added returns relative to the benchmark on a quality control chart?

A) The chart can be used to determine whether or not the potential superior performance is statistically significant.

B) If returns are consistently above the horizontal axis this would indicate superior performance on the part of the manager under review.

C) If value added returns are distributed randomly around the horizontal axis then manager’s added value returns are more or less random.

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In order to determine statistical significance or otherwise, confidence intervals need to be constructed using the standard deviation of the returns. Simply looking at the manager's value added returns above horizontal line alone does not tell you if the returns are significant or random.