AIM 2: Distinguish between basic and advanced return-based performance assessment models.

1、How many of the following statements, regarding the cross-sectional analysis of fund managers’ performance, are CORRECT? Cross-sectional analysis:

I.           focuses only on surviving firms.

II.         does not make adjustment for the size of a portfolio.

III.        does not make adjustment for the riskiness of a portfolio.

IV.      offers only a snapshot of performance.

A) None of these.

B) Three of these.

C) All of these. 

D) Two of these.

The correct answer is C

All of these statements are correct.

2、All of the following statements regarding performance analysis are correct EXCEPT:

A) return-based performance analysis is a method of assessing risk and returns of an investment.

B) hedge funds use only return-based performance analysis to evaluate managers’ performance and skill.

C) return-based advanced performance analysis adds statistical and theoretical refinement to the basic model.

D) the term performance analysis refers to return-based performance analysis and portfolio-based performance analysis.

The correct answer is B

Hedge funds use both return-based and portfolio-based performance analysis to evaluate managerial performance and skill.

AIM 3: Describe how basic performance assessment models account for performance and risk.

1、Based on monthly returns for an actively managed portfolio during the last five years, a benchmark timing regression equation produces an estimate of MTCP (market timing coefficient) equal to 2.3 and a standard error of the estimate equal to 1.8. Based on the estimated t-statistics of _______, we _____________ the null hypothesis that true MTCP = 0 (absence of market timing skills) at 99% confidence level.

A) 2.67; fail to reject.

B) 1.27; fail to reject.

C) 1.27; reject.

D) 3.67; reject.

The correct answer is B

In order to reject the null hypothesis of H0: true MTCP = 0 versus H1 = true MTCP ≠ 0, at 99% confidence level, we need an estimated t-statistics of 2.67 or larger. Since the t-statistic equals 1.27, we fail to reject the null hypothesis and conclude that there is no evidence of market timing skills.

2、Nazik, a portfolio manager, claims to have consistently produced excessive returns (over and above the benchmark returns) 95% of the time due to her skill and not luck. To support her claim, she presents regression results based on 72 monthly observations as follows:

alpha = 0.58%.

standard error of alpha = 0.232%

Would you reject the null hypothesis of true α = 0 and accept her claim of superior performance 95% of the time due to her skill?

A) t = 2.50; reject the null hypothesis; reject her claim.

B) t = 2.39; fail to reject the null hypothesis; accept her claim.

C) t = 2.50; reject the null hypothesis; accept her claim.

D) t = 2.39; reject the null hypothesis; accept her claim.

The correct answer is C

t = alpha / standard error of alpha

t = 0.0058 / 0.00232 = 2.5

Since t is greater than 2, we reject the null hypothesis at 95% confidence level and accept her claim of producing skill-based superior performance.

3、Benchmark Timing regression (below) is used to evaluate market timing skills of a portfolio manager. A successful market timer will correctly foresee the future directions of the market and will load the portfolio with high beta stocks (low beta stocks) for pending up market (down market).

RP(t) = αP + BP × RB(t) + MTCP(Dt × RB(t)) + εP(t)

RP(t) = realized returns on a portfolio p during time t

αP = intercept of the regression equation

BP = portfolio beta

MTCP = market timing estimated coefficient

εP(t) = regression error terms during time period t

Dt = a dummy variable that is assigned a value of zero for down market and a value of 1 for up market

Regression on twelve years of portfolio returns produces an estimate of MTCP = 4.3 with a standard error of 1.4. These results offer an evidence of a market timing strategy:

I.           which is successful.

II.         which produces a t-statistic of 3.07.

III.        which prohibits us from rejecting the null hypothesis of H0: true, MTCP = 0.

IV.      which enables us to give due credit to the portfolio manager for implementing a successful market timing strategy.

Which of the above statements are CORRECT?

A) I, II, and IV.

B) I, II, and III.

C) II, III, and IV.

D) I, II, III, and IV.

The correct answer is A

t = 4.3 / 1.4 = 3.07. We rejected the H0: true, MTCP = 0 in favor of H1: true, MTCP ≠ 0, at least at 95% confidence level (α = .05). So statement III is incorrect.

4、Which of the following statements regarding performance analysis are NOT correct?

I.           Information ratio (IR) is the ratio of risk to annual return.

II.         CAPM assumes the alpha (regression intercept) is positive.

III.        Significant t-statistic requires a smaller alpha (αP) relative to its standard deviation, as well as fewer observations.

IV.      Superior performance as shown by Sharpe ratio implies negative Jensen alpha.

A) I, II, and III only.

B) I, II, III, and IV.

C) I and II only.

D) I only.

The correct answer is B

Information ratio is the ratio of annual return to risk. As per the CAPM model, alpha should be zero. Significant t statistic requires a higher alpha relative to its standard deviation and many observations. Superior performance, as per the Sharpe ratio, implies positive Jensen alpha. So, all statements are incorrect.

5、During the last fifteen years, Norma, a portfolio manager, earned excess returns (over risk-free rate) of 16% with a standard deviation of 12%. During the same time period, excess returns (over risk-free rate) and standard deviation of a benchmark portfolio were 11% and 14% respectively. Norma claims to have beaten the benchmark portfolio at 95% confidence level. Based on our estimation:

I. we reject her claim.

II. we fail to reject her claim.

Which of the above statements is (are) CORRECT given that the t-statistic for the Sharpe ratio is 1.5?

A) I only.

B) II only.

C) Both I and II.

D) Neither I nor II.

The correct answer is A

t = 1.5 < 2 (critical t at 95%), so we fail to reject the null hypothesis: H0: difference in Sharpe ratios is zero. Thus, we can reject her claim to have beaten the benchmark portfolio at 95% confidence level.

6、Which of the following statements regarding performance analysis is NOT correct?

A) Return regression model assumes that the error terms are uncorrelated over time.

B) CAPM is based on a single factor, the market portfolio, which explains the variations in realized portfolio returns.

C) Performance of two portfolio managers cannot be compared based on estimates of IR (information ratio)—excess returns per unit of risk.

D) Sharpe ratio of an actively managed portfolio (statistically) significantly greater than the benchmark Sharpe ratio is taken as evidence of superior performance.

The correct answer is C

A higher information ratio will indicate a better performance. Thus, the performance of two portfolio managers can be compared using information ratio.

AIM 4: List and describe the effects various refinements to the basic return-based performance assessment models achieve.

1、Refinements to the basic return-based performance assessment models include:

I.           Bayesian correction.

II.         benchmark timing.

III.        a priori beta estimates.

IV.      correction for serial correlation.

A) I, II, and III only.

B) I, II, and IV only.

C) I, II, III, and IV.

D) I, III, and IV only.

The correct answer is C

All of the above are refinements introduced to the basic return-based performance assessment models.

2、Which of the following statements are CORRECT? Various refinements to the basic return-based performance assessment models include:

I.           using prior knowledge for making ex-post adjustments in regression coefficients.

II.         correcting for serially or auto correlated error terms to draw valid t-test inferences.

III.        assessing market timing skills of portfolio managers by incorporating up and down market betas into a dummy regression.

IV.      estimating variations in realized portfolio excess returns as a result of variations in the benchmark portfolio returns after controlling for dividend yield and interest rates.

A) II, III and IV.

B) I, II and III.

C) I and II.

D) I, II, III and IV.

The correct answer is D

Statement I refers to Bayesian correction; statement II refers to correction for serial correlation; statement III refers to benchmark timing; and finally, the statement IV refers to controlling for public information.

AIM 5: Describe the portfolio-based performance analysis, including the use of performance attribution and performance analysis.

1、The fundamental goal of investment performance analysis is:

A) to develop non-parametric estimates. 

B) to compare past performance with future performance.

C) to estimate residual variance.

D) to distinguish skill from luck.

The correct answer is D

The remaining statements are not the goals of investment performance analysis.

2、Which of the following statements regarding portfolio attribution and portfolio performance analysis are CORRECT?

I.           Performance analysis is used to determine the statistical significance of information ratios (IR).

II.         Performance attribution analysis focuses on portfolio returns over a single period.

III.        Returns-based performance analysis is based on a top-down approach.

IV.      Portfolio-based analysis involves a three step process: cross-sectional analysis, portfolio attribution, and performance analysis.

A) I, II, III, and IV.

B) I, II, and IV only.

C) I, II, and III only.

D) II, III, and IV only.

The correct answer is C

Portfolio-based analysis involves a two-step process: portfolio attribution and portfolio performance analysis.

3、Which of the following statements is (are) CORRECT? Investment returns can be defined as:

I.           compound returns.

II.         geometric returns.

III.        arithmetic returns.

IV.      logarithmic returns.

A) III only.

B) I, II, III, and IV.

C) I, II, and III only.

D) I and III only.

The correct answer is B

All the stated returns are examples of investment returns.

AIM 6: Define, describe, and calculate active systematic returns, expected active beta returns, active beta surprise, and active benchmark timing return.

1、How many of the following statements regarding active systematic returns are NOT correct?

I.           Active returns are defined as the difference between the manager’s portfolio returns and the benchmark returns.

II.         Expected active beta return is the return that results from the product of average active beta and the long-run expected benchmark excess return, where excess return is defined as the realized return minus the risk-free rate.

III.        Active beta surprise is the product of active beta and the deviation of the benchmark returns from its long-term expected return.

IV.      Active benchmark timing return is a product of the deviation from the average beta and the deviation from the benchmark return.

A) Four of these.

B) Two of these.

C) One of these.

D) None of these.

The correct answer is D

All of these statements are correct.