ikoreaii

The ratio of return to systematic risk for an investment portfolio is 0.70, while the market is 0.50. This information suggests that the portfolio:

A) exhibits inferior performance because it has more risk than the market.

B) exhibits superior performance because the return per unit of risk is above that of the market.

C) is not diversified enough, and more securities should be purchased to bring the portfolio in line with the market.

---

Risk-averse investors prefer a portfolio with a higher ratio of return to systematic risk to a portfolio with a lower ratio. In this case, we can also say that the portfolio would plot above the SML since the portfolio's ratio is above that of the market. Since portfolios that plot above the SML are undervalued, they are likely to provide an above average return. Note: The ratio (Treynor's Measure) implicitly assumes a diversified portfolio, hence the use of beta (or systematic risk) in the denominator.

ikoreaii

The Sharpe ratio, Treynor measure, the M2 measure and Jensen’s Alpha techniques all measure the risk/return performance of portfolios. Which of the following statements about these measurement techniques is least accurate?

A) The Sharpe ratio measures the slope of the capital allocation line (CAL), with the lowest slope having the most desirable risk/return combination.

B) Using the capital market line the M2 compares the account's return to the market return and is a comparative measure.

C) While the Treynor measure computes excess return per unit of risk, Jensen's Alpha measures differential return for a given level of risk.

---

Although it is true that the Sharpe ratio measures the slope of the CAL, the higher the slope the more desirable the portfolio. Your goal is to select the portfolio that has the highest Sharpe measure, which will also have the steepest slope. At any given risk level, the higher the slope the greater the return.

ikoreaii

An analyst has gathered the following information about the performance of an equity fund and the S&P 500 index over the same time period.   

                                                         Equity Fund            S&P 500

                           Return                             21%                  24%            

                           Standard Deviation            19%                  17%

                           Beta                              1.05                    1.00

                           Risk-free rate is 4.50%

The Sharpe ratio for the equity fund is:

A) 0.87.

B) 0.76.

C) 0.84.

---

(0.21 – 0.045)/0.19 = 0.87.

ikoreaii

An analyst has gathered the following information about the performance of an equity fund and the S&P 500 index over the same time period.   

                                                               Equity Fund                 S&P 500

               Return                                            13%                          10.5%               

               Standard Deviation                           22%                          20%

               Beta                                             1.21                          1.00

               Risk-free rate is 5.25%

The Treynor measure for the equity fund is:

A) 0.570.

B) 0.064.

C) 0.048.

---

(0.13 – 0.0525)/1.21 = 0.064.

ikoreaii

Which of the following measures used to evaluate the performance of a portfolio manager is (are) NOT subject to the assumptions of the capital asset pricing model (CAPM)?

A) Jensen's alpha.

B) Jensen's alpha and the Treynor measure.

C) Sharpe measure.

---

Both the Treynor measure and the Jensen's alpha assume that the CAPM is the underlying risk-adjustment model. The Sharpe measure on the other hand does not make this assumption. It uses total risk of a portfolio, unlike the Treynor measure and Jensen's alpha, which use the systematic (undiversifiable) risk as measured by beta to compute the risk-adjusted return of a portfolio.

ikoreaii

The following information is available for the Trumark Fund:

• The Trumark Fund has an average annual return of 12% over the last five years.
• Trumark has a beta value of 1.35.
• Trumark has a standard deviation of returns of 16.80%.
• During the same time period, the average annual T-bill rate was 4.5%.
• During the same time period, the average annual return on the S&P 500 portfolio was 18%.

What is the Sharpe ratio for the Trumark Fund?

A) 0.80.

B) 0.45.

C) 5.56.

---

Sharpe Ratio = Sj = (Rj – RF) / σj = (12 − 4.50) / 16.80 = 0.45

---

What is the Treynor measure for Trumark Fund?

A) 0.45.

B) -0.04.

C) 0.06.

---

Treynor measure = Tj = (Rj – RF) / βj = (0.12 − .0450) / 1.35 = 0.0556

ikoreaii

Which of the following risk measures is NOT dependent on capital asset pricing model (CAPM)?

A) Sharpe measure.

B) Neither of these.

C) Jensen measure.

---

The Sharpe measure uses standard deviation as its risk measure. The Jensen measure uses beta.

ikoreaii

If a portfolio had an alpha of −10 bps, then the portfolio:

A) earned 10 bps less than the market.

B) had less risk than the market.

C) earned 10 bps less than the market on a risk-adjusted basis.

---

Recall that Jensen’s alpha measures excess return for a given level of risk. It is a “risk-adjusted” measure of return.

ikoreaii

Which of the following statements about fund performance is CORRECT?

A) A fund had total excess return of 1.82%. Of the total, 1.60% was due to the style of the fund that was specified by the sponsor, and 0.22% was due to security selection. The amount of the excess return that should be credited to the fund manager is 1.82%.

B) When analyzing the performance of a bond portfolio the manager should be evaluated relative to a style universe. Focusing on maturity ranges or a particular market segment is not one of the accepted style universes.

C) An equity fund had a return over the past year of 17% and a standard deviation of returns of 12%. During this period the risk-free return was 3%. The Sharpe ratio for the fund was 1.17.

---

The Sharpe ratio = (0.17 – 0.03)0.12 = 1.17.
Note that focusing on maturity ranges or a particular market segment are definitions of style for a bond portfolio manager. Also, managers whose styles are specified for them should only get credit for the excess return that is due to security selection.

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.

---

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.