Multiple Choice Questions
1. In the Treynor-Black model
A) portfolio weight are sensitive to large alpha values which can lead to
infeasible long or short position for many portfolio managers.
B) portfolio weight are not sensitive to large alpha values which can lead to
infeasible long or short position for many portfolio managers.
C) portfolio weight are sensitive to large alpha values which can lead to the
optimal portfolio for most portfolio managers.
D) portfolio weight are not sensitive to large alpha values which can lead to the
optimal portfolio for most portfolio managers.
E) none of the above.
Answer: A Difficulty: Moderate
2. Benchmark portfolio risk is defined as
A) the return difference between the portfolio and the benchmark
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B)
the variance of the return of the benchmark portfolio
C) the variance of the return difference between the portfolio and the
benchmark
D) the variance of the return of the actively-managed portfolio
E) none of the above.
Answer: C Difficulty: Moderate
3. Benchmark portfolio risk
A) is inevitable and is never a significant issue in practice.
B) is inevitable and is always a significant issue in practice.
C) weights.
cannot be constrained to keep a Treynor-Black portfolio within reasonable
D) weights.
can be constrained to keep a Treynor-Black portfolio within reasonable
E) none of the above.
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Answer: D Difficulty: Moderate
4. ____________ can be used to measure forecast quality and guide in the proper
adjustment of forecasts.
A) regression analysis
B) exponential smoothing
C) ARIMA
D) moving average models
E) GAUSS
Answer: A Difficulty: Moderate
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5. Even low-quality forecasts have proven to be valuable because R-squares of
only ____________ in regressions of analysts' forecasts can be used to substantially improve portfolio performance.
A) 0.656
B) 0.452
C) 0.258
D) 0.153
E) 0.001
Answer: E Difficulty: Moderate
6. The ____________ model allows the private views of the portfolio manager to
be incorporated with market data in the optimization procedure.
A) Black-Litterman
B) Treynor-Black
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C)
Treynor-Mazuy
D) Black-Scholes
E) none of the above.
Answer: A Difficulty: Moderate
7. The Black-Litterman model and Treynor-Black model are
A) nice in theory but practically useless in modern portfolio management.
B) complementary tools that should be used in portfolio management.
C) contradictory models can not be use together; therefore, portfolio managers
must choose which one suits their needs.
D) not useful due to their complexity.
E) none of the above.
Answer: B Difficulty: Moderate
8. The Black-Litterman model is geared toward ____________ while the
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Treynor-Black model is geared toward ____________.
A) security analysis; security analysis
B) asset allocation; asset allocation
C) security analysis; asset allocation
D) asset allocation; security analysis
E) none of the above
Answer: D Difficulty: Moderate
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9. Alpha forecasts must be ____________ to account for less-than-perfect
forecasting quality. When alpha forecasts are ____________ to account for forecast imprecision, the resulting portfolio position becomes ____________.
A) shrunk, shrunk, far less moderate
B) shrunk, shrunk, far more moderate
C) grossed up, grossed up, far less moderate
D) grossed up, grossed up, far more moderate
E) none of the above
Answer: B Difficulty: Moderate
10. Tracking error is defined as
A) the difference between the returns on the overall risky portfolio versus the
benchmark return.
B) the variance of the return of the benchmark portfolio
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C)
the variance of the return difference between the portfolio and the
benchmark
D) the variance of the return of the actively-managed portfolio
E) none of the above.
Answer: A Difficulty: Moderate
11. The tracking error of an optimized portfolio can be expressed in terms of the
____________ of the portfolio and thus reveal ____________.
A) return; portfolio performance
B) total risk; portfolio performance
C) beta; portfolio performance
D) beta; benchmark risk
E) relative return; benchmark risk
Answer: D Difficulty: Moderate
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12.
The Treynor-Black model is a model that shows how an investment manager
can use security analysis and statistics to construct __________.
A) a market portfolio
B) a passive portfolio
C) an active portfolio
D) an index portfolio
E) a balanced portfolio
Answer: C Difficulty: Easy
Rationale: The Treynor-Black model utilizes the statistics of diversification to select securities for an actively managed portfolio.
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13. If a portfolio manager consistently obtains a high Sharpe measure, the
manager's forecasting ability __________.
A) is above average
B) is average
C) is below average
D) does not exist.
E) cannot be determined based on the Sharpe measure
Answer: A Difficulty: Easy
Rationale: The manager with the highest Sharpe measure presumably has true forecasting abilities.
14. Active portfolio management consists of __________.
A) market timing
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B)
security analysis
C) indexing
D) A and B
E) none of the above
Answer: D Difficulty: Easy
Rationale: Although one can engage in various degrees of active portfolio management (security selection without market timing and vice versa), the most active portfolio management strategy consists of engaging in both pursuits.
15. The critical variable in the determination of the success of the active portfolio
is ________.
A) alpha/systematic risk
B) alpha/nonsystematic risk
C) gamma/systematic risk
D) gamma/nonsystematic risk
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E)
none of the above
Answer: B Difficulty: Moderate
Rationale: A portfolio with a positive alpha is outperforming the market. If this portfolio also has a low degree of nonsystematic risk, the portfolio is adequately diversified.
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16. In the Treynor-Black model, the weight of each security in the portfolio
should be proportional to its __________.
A) alpha/beta
B) alpha/beta/residual variance
C) beta/residual variance
D) alpha/residual variance
E) none of the above
Answer: B Difficulty: Moderate
Rationale: Use the estimates of alpha, beta, and residual risk to determine the optimal weight of each security in the portfolio.
17. Active portfolio managers try to construct a risky portfolio with __________.
A) a higher Sharpe measure than a passive strategy
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B)
a lower Sharpe measure than a passive strategy
C) the same Sharpe measure as a passive strategy
D) very few securities
E) none of the above
Answer: A Difficulty: Moderate
Rationale: A higher Sharpe measure than a passive strategy is indicative of the benefits of active management.
18. The beta of an active portfolio is 1.20. The standard deviation of the returns
on the market index is 20%. The nonsystematic variance of the active portfolio is 1%. The standard deviation of the returns on the active portfolio is __________.
A) 3.84%
B) 5.84%
C) 19.60%
D) 24.17%
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E)
26.0%
Answer: E Difficulty: Difficult
Rationale: s = [(1.2)2(0.2)2 + 0.01]1/2 = [0.0676]1/2 = 26.0%.
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19. Consider the Treynor-Black model. The alpha of an active portfolio is 2%.
The expected return on the market index is 16%. The variance of return on the market portfolio is 4%. The nonsystematic variance of the active portfolio is 1%. The risk-free rate of return is 8%. The beta of the active portfolio is 1. The optimal proportion to invest in the active portfolio is __________.
A) 0%
B) 25%
C) 50%
D) 100%
E) none of the above
Answer: D Difficulty: Difficult
Rationale: wO = [2%/1%]/[(16% - 8%)/4%] = 1, or 100%; w* = 1/[1 + (1-1)1] = 1.
20. Consider the Treynor-Black model. The alpha of an active portfolio is 1%.
The expected return on the market index is 16%. The variance of the return on the
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market portfolio is 4%. The nonsystematic variance of the active portfolio is 1%. The risk-free rate of return is 8%. The beta of the active portfolio is 1.05. The optimal proportion to invest in the active portfolio is __________.
A) 48.7%
B) 50.0%
C) 51.3%
D) 100.0%
E) none of the above
Answer: C Difficulty: Difficult
Rationale: wO = [1%/1%]/[(16% - 8%)/4%] = 0.5; w* = 0.5/[1 + (1 - 1.05)0.5] = 0.513, or 51.3%.
21. because
There appears to be a role for a theory of active portfolio management
A) some portfolio managers have produced sequences of abnormal returns that
are difficult to label as lucky outcomes.
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B)
the \"noise\" in the realized returns is enough to prevent the rejection of the
hypothesis that some money managers have outperformed a passive strategy by a statistically small, yet economic, margin.
C) some anomalies in realized returns have been persistent enough to suggest
that portfolio managers who identified these anomalies in a timely fashion could have outperformed a passive strategy over prolonged periods.
D) A and B.
E) A, B, and C.
Answer: E Difficulty: Easy
Rationale: Statements A, B, and C are true.
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22. The Treynor-Black model
A) considers both macroeconomic and microeconomic risks.
B) considers security selection only.
C) is relatively easy to implement.
D) A and C.
E) B and C.
Answer: D Difficulty: Easy
Rationale: A and C are true for the model.
23. To improve future analyst forecasts using the statistical properties of past
forecasts, a regression model can be fitted to past forecasts. The intercept of the regression is a __________ coefficient, and the regression beta represents a __________ coefficient.
A) bias, precision
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B)
bias, bias
C) precision, precision
D) precision, bias
E) none of the above
Answer: A Difficulty: Moderate
Rationale: The estimated equation adjusts future forecasts for direction and magnitude of bias and degree of imprecision in past forecasts.
24. A purely passive strategy is defined as
A) one that uses only index funds.
B) one that allocates assets in fixed proportions that do not vary with market
conditions.
C) one that is mean-variance efficient.
D) both A and B.
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E)
all of the above.
Answer: D Difficulty: Easy
Rationale: A purely passive strategy is one that calls for no market analysis.
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25. Consider these two investment strategies:
Strategy ___ is the dominant strategy because __________.
A) 1, it is riskless
B) 1, it has the highest reward/risk ratio
C) 2, its return is at least equal to Strategy 1 and sometimes greater
D) 2, it has the highest reward/risk ratio
E) both strategies are equally preferred.
Answer: C Difficulty: Moderate
Rationale: Strategy 2 dominates Strategy 1, even though it is riskier, because it always returns at least as much as Strategy 1 and sometimes more.
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26.
The Treynor-Black model assumes that
A) the objective of security analysis is to form an active portfolio of a limited
number of mispriced securities.
B) the cost of less than full diversification comes from the nonsystematic risk of
the mispriced stock.
C) the optimal weight of a mispriced security in the active portfolio is a function
of the degree of mispricing, the market sensitivity of the security, and its degree of nonsystematic risk.
D) all of the above are true.
E) none of the above is true.
Answer: D Difficulty: Moderate
Rationale: All of the statements correctly describe assumptions of the Treynor-Black model.
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27. Consider the Treynor-Black model. The alpha of an active portfolio is 3%.
The expected return on the market index is 18%. The standard deviation of the return on the market portfolio is 25%. The nonsystematic standard deviation of the active portfolio is 15%. The risk-free rate of return is 6%. The beta of the active portfolio is 1.2. The optimal proportion to invest in the active portfolio is __________.
A) 50.0%
B) 69.4%
C) 72.3%
D) 80.6%
E) 100.0%
Answer: D Difficulty: Difficult
Rationale: wO = [3%/2.25%]/[(18% - 6%)/6.25%] = 0.6944; w* = 0.6944/[1 + (1 - 1.2)0.6944] = 0.80, or 80.6%.
28. According to the Treynor-Black model, the weight of a security in the active
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portfolio depends on the ratio of __________ to __________.
A) the degree of mispricing; the nonsystematic risk of the security
B) the degree of mispricing; the systematic risk of the security
C) the market sensitivity of the security; the nonsystematic risk of the security
D) the nonsystematic risk of the security; the systematic risk of the security
E) the total return on the security; the nonsystematic risk of the security
Answer: A Difficulty: Moderate
Rationale: The weight of the mispriced security in the active portfolio depends on the degree of mispricing (alpha) in proportion to the nonsystematic risk added by holding the security.
29. One property of a risky portfolio that combines an active portfolio of
mispriced securities with a market portfolio is that, when optimized, its squared Sharpe measure increases by the square of the active portfolio's
A) Sharpe ratio.
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B)
information ratio.
C) alpha.
D) Treynor measure.
E) none of the above.
Answer: B Difficulty: Moderate
Rationale: When optimized, a property of the overall risky portfolio is that its squared Sharpe measure increases by the square of the active portfolio's information ratio.
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30. A purely passive strategy
A) uses only index funds.
B) uses weights that change in response to market conditions.
C) uses only risk-free assets.
D) is best if there is “noise” in realized returns.
E) is useless if abnormal returns are available.
Answer: A Difficulty: Moderate
Rationale: A purely passive strategy uses only index funds and keeps the proportions constant when there are changes in perceived market conditions.
31. A manager who uses the mean-variance theory to construct an optimal
portfolio will satisfy
A) investors with low risk-aversion coefficients.
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B)
investors with high risk-aversion coefficients.
C) investors with moderate risk-aversion coefficients.
D) all investors, regardless of their level of risk aversion.
E) only clients with whom she has established long-term relationships, because
she knows their personal preferences.
Answer: D Difficulty: Easy
Rationale: The optimal portfolio will be the one with the highest reward-to-variability ratio. Investors can choose for themselves how they want to combine this portfolio with the risk-free asset to take on more or less risk.
32. Ideally, clients would like to invest with the portfolio manager who has
A) a moderate personal risk-aversion coefficient.
B) a low personal risk-aversion coefficient.
C) the highest Sharpe measure.
D) the highest record of realized returns.
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E)
the lowest record of standard deviations.
Answer: C Difficulty: Easy
Rationale: The Sharpe measure is commonly used to measure the performance of professional managers. A good manager has a steeper CAL than the one from following a passive strategy.
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33. An active portfolio manager faces a tradeoff between
I)using the Sharpe measure.
II) using mean-variance analysis.
III) exploiting perceived security mispricings.
IV) holding too much of the risk-free asset.
V) letting a few stocks dominate the portfolio.
A) I and II
B) II and V
C) III and V
D) III and IV
E) II and III
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Answer: C Difficulty: Difficult
Rationale: The active manager can use both the Sharpe measure and mean-variance analysis. The risk-free asset can be included as called for by market conditions. The active manager is seeking out mispricings and will want to exploit them. If there are a few very attractive securities the manager might have a concentration of these in the portfolio, which could lead to poor diversification.
34. To determine the optimal risky portfolio in the Treynor-Black Model,
macroeconomic forecasts are used for the _________ and composite forecasts are used for the __________.
A) passive index portfolio; active portfolio
B) active portfolio, passive index portfolio
C) expected return; standard deviation
D) expected return ; beta coefficient
E) alpha coefficient; beta coefficient
Answer: A Difficulty: Moderate
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Rationale: The two factors combine to determine the optimal risky portfolio.
35. The beta of an active portfolio is 1.45. The standard deviation of the returns
on the market index is 22%. The nonsystematic variance of the active portfolio is 3%. The standard deviation of the returns on the active portfolio is __________.
A) 36.30%
B) 5.84%
C) 19.60%
D) 24.17%
E) 26.0%
Answer: A Difficulty: Difficult
Rationale: s = [(1.45)2(0.22)2 + 0.03]1/2 = [0.13176]1/2 = 36.3%.
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36. Consider the Treynor-Black model. The alpha of an active portfolio is 1%.
The expected return on the market index is 11%. The variance of return on the market portfolio is 6%. The nonsystematic variance of the active portfolio is 2%. The risk-free rate of return is 4%. The beta of the active portfolio is 1.1. The optimal proportion to invest in the active portfolio is __________.
A) 45%
B) 25%
C) 50%
D) 100%
E) none of the above
Answer: A Difficulty: Difficult
Rationale: wO = [1%/2%]/[(11% - 4%)/6%] = .4286, or 42.86%; w* = .4286/[1 + (1-1.1).4286] = 0.4478.
37. Consider the Treynor-Black model. The alpha of an active portfolio is 3%.
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The expected return on the market index is 10%. The variance of the return on the market portfolio is 4%. The nonsystematic variance of the active portfolio is 2%. The risk-free rate of return is 3%. The beta of the active portfolio is 1.15. The optimal proportion to invest in the active portfolio is __________.
A) 48.7%
B) 98.3%
C) 51.3%
D) 100.0%
E) none of the above
Answer: B Difficulty: Difficult
Rationale: wO = [3%/2%]/[(10% - 3%)/4%] = 0.857; w* = 0.857/[1 + (1 - 1.15)0.857] = .983., or 98.3%.
38. Consider the Treynor-Black model. The alpha of an active portfolio is 2%.
The expected return on the market index is 12%. The variance of the return on the market portfolio is 4%. The nonsystematic variance of the active portfolio is 2%. The risk-free rate of return is 3%. The beta of the active portfolio is 1.15. The optimal
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proportion to invest in the active portfolio is __________.
A) 48.7%
B) 98.3%
C) 47.6%
D) 100.0%
E) none of the above
Answer: C Difficulty: Difficult
Rationale: wO = [2%/2%]/[(12% - 3%)/4%] = 0.444; w* = 0.444/[1 + (1 - 1.15) 0.444] = .476., or 47.6%.
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39. portfolio.
Perfect timing ability is equivalent to having __________ on the market
A) a call option
B) a futures contract
C) a put option
D) a commodities contract
E) none of the above
Answer: A Difficulty: Easy
Rationale: Perfect foresight is equivalent to holding a call option on the equity portfolio.
40. Kane, Marcus, and Trippi (1999) show that the annualized fee that investor
should be willing to pay for active management, over and above the fee charged by a passive index fund, depends on
I)the investor's coefficient of risk aversion
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II)
the value of at-the-money call option on the market portfolio
III) the value of out-of-the-money call option on the market portfolio
IV) the precision of the security analyst
V) the distribution of the squared information securities
A) I, II, IV
B) I, III, V
C) II, IV, V
D) I, IV, V
E) II, IV, V
Answer: D Difficulty: Moderate
Essay Questions
41. Discuss the Treynor-Black model.
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Difficulty: Moderate
Answer:
The Treynor-Black estimates the alpha, beta, and residual risk of securities under consideration for a portfolio. The model uses these estimates to determine the optimal weights of each of these securities in the portfolio. These composite estimates for the active portfolio and the macroeconomic forecasts for the passive index portfolio are used to determine the optimal risky portfolio, which will be a combination of the passive and active portfolios.
The purpose of this question is to ascertain if the student understands the basic concepts behind this model, which allows the portfolio manager to utilize both active and passive components of portfolio building to obtain an optimal portfolio.
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42. You have a record of an analyst's past forecasts of alpha. Describe how you
would use this information within the context of the Treynor-Black model to determine the forecasting ability of the analyst.
Difficulty: Difficult
Answer:
You can use the index model and valid estimates of beta, you can estimate the ex-post alphas from the average realized return and the return on the market index. The equation is RRM .
Then you would estimate a regression of the forecasted alphas on the realized
falphas as in the equation a0a1 . The coefficients a0 and a1 reflect the bias in
the forecasts. If there is no bias a0=0 and a1=1. The forecast errors are uncorrelated with the true alpha, so the variance of the forecast is
222f .
To measure the value of the forecast, you would use the squared correlation coefficient between the forecasts and the realizations. This can also be determined by
222the formula . If the analyst has perfect forecasting ability the correlation
2coefficient will be 1. If the analyst has no ability then the correlation coefficient will be 0.
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For values in between 0 and 1 you can adjust the forecasts by multiplying by the correlation.
The value of active management depends on the analyst's ability to forecast accurately. The best way to exploit analysts' forecasts is with the Treynor-Black model.
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