Download Chapter 27 The Theory of Active Portfolio Management

Chapter 27
The Theory of Active Portfolio Management
Multiple Choice Questions
1. In the Treynor-Black model
A. portfolio weights are sensitive to large alpha values which can lead to infeasible long or
short positions for many portfolio managers.
B. portfolio weights are not sensitive to large alpha values which can lead to infeasible long or
short positions for many portfolio managers.
C. portfolio weights are sensitive to large alpha values which can lead to the optimal portfolio
for most portfolio managers.
D. portfolio weights are not sensitive to large alpha values which can lead to the optimal
portfolio for most portfolio managers.
E. None of these is true.
In the Treynor-Black model portfolio weight are sensitive to large alpha values which can
lead to infeasible long or short positions for many portfolio managers.
2. Absent research, you should assume the alpha of a stock is
A. zero
B. positive
C. negative
D. not zero
E. zero or positive
In efficient markets, alpha should be assumed to be zero.
3. If you begin with a ______ and obtain additional data from an experiment you can form a
______.
A. posterior distribution; prior distribution
B. prior distribution; posterior distribution
C. tight posterior; Bayesian analysis
D. tight prior; Bayesian analysis
E. None of these is true.
If you begin with a prior distribution and obtain additional data from an experiment you can
form a posterior distribution.
4. Benchmark risk is defined as
A. the return difference between the portfolio and the benchmark
B. the standard deviation of the return of the benchmark portfolio
C. the standard deviation of the return difference between the portfolio and the benchmark
D. the standard deviation of the return of the actively-managed portfolio
E. None of these is true.
Benchmark portfolio risk is defined as the standard deviation of the return difference between
the portfolio and the benchmark.
5. Benchmark risk
A. is inevitable and is never a significant issue in practice.
B. is inevitable and is always a significant issue in practice.
C. cannot be constrained to keep a Treynor-Black portfolio within reasonable weights.
D. can be constrained to keep a Treynor-Black portfolio within reasonable weights.
E. None of these is true.
Benchmark portfolio risk can be constrained to keep a Treynor-Black portfolio within
reasonable weights.
6. ____________ 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
Regression analysis can be used to measure forecast quality and guide in the proper
adjustment of forecasts.
7. 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
The text provides an example where forecasts improved as r-squared improved from 0.001134
to 0.001536.
8. 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
C. Treynor-Mazuy
D. Black-Scholes
E. None of these is true.
The Black-Litterman model allows the private views of the portfolio manager to be
incorporated with market data in the optimization procedure.
9. 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 that cannot be used together; therefore, portfolio managers must
choose which one suits their needs.
D. not useful due to their complexity.
E. None of these is true.
The Black-Litterman model and Treynor-Black model are complementary tools that should be
used in portfolio management.
10. The Black-Litterman model is geared toward ____________ while the 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 these is true.
The Black-Litterman model is geared toward asset allocation while the Treynor-Black model
is geared toward security analysis.
11. 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 these is true.
Alpha forecasts must be shrunk to account for less-than-perfect forecasting quality. When
alpha forecasts are shrunk to account for forecast imprecision, the resulting portfolio position
becomes far more moderate.
12. 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
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 these is true.
Tracking error is defined as the difference between the returns on the overall risky portfolio
versus the benchmark return.
13. The tracking error of an optimized portfolio can be expressed in terms of the
____________ of the portfolio and thus reveals ____________.
A. return; portfolio performance
B. total risk; portfolio performance
C. beta; portfolio performance
D. beta; benchmark risk
E. relative return; benchmark risk
The tracking error of an optimized portfolio can be expressed in terms of the beta of the
portfolio and thus reveal benchmark risk.
14. 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
The Treynor-Black model is a model that shows how an investment manager can use security
analysis and statistics to construct an active portfolio.
15. 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
The manager with the highest Sharpe measure presumably has true forecasting abilities.
16. Active portfolio management consists of __________.
A. market timing
B. security analysis
C. indexing
D. market timing and security analysis
E. None of these is true.
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.
17. Passive portfolio management consists of __________.
A. market timing
B. security analysis
C. indexing
D. market timing and security analysis
E. None of these is true.
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. Passive management is an indexing strategy.
18. 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
E. None of these is true.
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.
19. The Treynor-Black model requires estimates of ________.
A. alpha/beta
B. alpha/beta/residual variance
C. beta/residual variance
D. alpha/residual variance
E. None of these is true.
Estimates of alpha, beta, and residual risk are required to determine the optimal weight of
each security in the portfolio.
20. Active portfolio managers try to construct a risky portfolio with __________.
A. a higher Sharpe measure than a passive strategy
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 these is true.
A higher Sharpe measure than a passive strategy is indicative of the benefits of active
management.
21. 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%
E. 26.0%
s = [(1.2)2(0.2)2 + 0.01]1/2 = [0.0676]1/2 = 26.0%.
22. The beta of an active portfolio is 1.36. The standard deviation of the returns on the market
index is 22%. The nonsystematic variance of the active portfolio is 1.2%. The standard
deviation of the returns on the active portfolio is __________.
A. 3.19%
B. 31.86%
C. 42.00%
D. 27.57%
E. 2.86%
s = [(1.36)2(0.22)2 + 0.012]1/2 = [0.10152]1/2 = 31.86%.
23. 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 these is true.
24. 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 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 these is true.
wO = [1%/1%]/[(16% − 8%)/4%] = 0.5; w* = 0.5/[1 + (1 − 1.05)0.5] = 0.513, or 51.3%.
25. There appears to be a role for a theory of active portfolio management because
A. some portfolio managers have produced sequences of abnormal returns that are difficult to
label as lucky outcomes.
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. some portfolio managers have produced sequences of abnormal returns that are difficult to
label as lucky outcomes; and 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.
E. some portfolio managers have produced sequences of abnormal returns that are difficult to
label as lucky outcomes; 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; and 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.
There appears to be a role for a theory of active portfolio management because some portfolio
managers have produced sequences of abnormal returns that are difficult to label as lucky
outcomes, 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, and 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.
26. The Treynor-Black model
A. considers both macroeconomic and microeconomic risks.
B. considers security selection only.
C. is nearly impossible to implement.
D. considers both macroeconomic and microeconomic risks and is nearly impossible to
implement.
E. considers security selection only and is nearly impossible to implement.
The Treynor-Black model considers both macroeconomic and microeconomic risks.
27. Which of the following are not true regarding the Treynor-Black model?
A. considers both macroeconomic and microeconomic risks.
B. considers security selection only.
C. is nearly impossible to implement.
D. considers both macroeconomic and microeconomic risks and is nearly impossible to
implement.
E. considers security selection only and is nearly impossible to implement.
The Treynor-Black model considers both macroeconomic and microeconomic risks. Other
answers are false.
28. 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
B. bias, bias
C. precision, precision
D. precision, bias
E. None of these is true.
The estimated equation adjusts future forecasts for direction and magnitude of bias and degree
of imprecision in past forecasts.
29. 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. one that uses only index funds and one that allocates assets in fixed proportions that do not
vary with market conditions.
E. All of these are true.
A purely passive strategy is one that calls for no market analysis.
30. 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.
Strategy 2 dominates Strategy 1, even though it is riskier, because it always returns at least as
much as Strategy 1 and sometimes more.
31. 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.
Strategy 2 dominates Strategy 1, even though it is riskier, because it always returns at least as
much as Strategy 1 and sometimes more.
32. 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 these are true.
E. None of these is true.
All of the statements correctly describe assumptions of the Treynor-Black model.
33. The Treynor-Black model does not assume 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. indexing is always optimal.
E. the objective of security analysis is to form an active portfolio of a limited number of
mispriced securities; the cost of less than full diversification comes from the nonsystematic
risk of the mispriced stock; and 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.
The Treynor-Black model does not assume that the objective of security analysis is to form an
active portfolio of a limited number of mispriced securities, the cost of less than full
diversification comes from the nonsystematic risk of the mispriced stock, and 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.
34. 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%
wO = [3%/2.25%]/[(18% − 6%)/6.25%] = 0.6944; w* = 0.6944/[1 + (1 − 1.2)0.6944] =
0.8064, or 80.6%.
35. According to the Treynor-Black model, the weight of a security in the active 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
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.
36. 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.
B. information ratio.
C. alpha.
D. Treynor measure.
E. None of these is true.
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.
37. 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.
A purely passive strategy uses only index funds and keeps the proportions constant when
there are changes in perceived market conditions.
38. A manager who uses the mean-variance theory to construct an optimal portfolio will
satisfy
A. investors with low risk-aversion coefficients.
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.
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.
39. 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.
E. the lowest record of standard deviations.
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.
40. 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
The active manager can use both the Sharpe measure and mean-variance analysis. The riskfree 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.
41. 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
The two factors combine to determine the optimal risky portfolio.
42. 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%
s = [(1.45)2(0.22)2 + 0.03]1/2 = [0.13176]1/2 = 36.3%.
43. 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 these is true.
wO = [1%/2%]/[(11% − 4%)/6%] = .4286, or 42.86%; w* = .4286/[1 + (1 − 1.1).4286] =
0.4478.
44. Consider the Treynor-Black model. The alpha of an active portfolio is 3%. 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 these is true.
wO = [3%/2%]/[(10% − 3%)/4%] = 0.857; w* = 0.857/[1 + (1 − 1.15)0.857] = .983., or 98.3%.
45. 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 proportion to invest in the active portfolio
is __________.
A. 48.7%
B. 98.3%
C. 47.6%
D. 100.0%
E. None of these is true.
wO = [2%/2%]/[(12% − 3%)/4%] = 0.444; w* = 0.444/[1 + (1 − 1.15) 0.444] = .476., or
47.6%.
46. Perfect timing ability is equivalent to having __________ on the market portfolio.
A. a call option
B. a futures contract
C. a put option
D. a commodities contract
E. None of these is true.
Perfect foresight is equivalent to holding a call option on the equity portfolio.
47. Kane, Marcus, and Trippi (1999) show that the annualized fee that investors 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
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 ratio of in the universe of securities
A. I, II, IV
B. I, III, V
C. II, IV, V
D. I, IV, V
E. II, III, V
Kane, Marcus, and Trippi (1999) show that the annualized fee that investors should be willing
to pay for active management, over and above the fee charged by a passive index fund,
depends on the investor's coefficient of risk aversion, the precision of the security analyst, and
the distribution of the squared information ratio of in the universe of securities.
48. Kane, Marcus, and Trippi (1999) show that the annualized fee that investors should be
willing to pay for active management, over and above the fee charged by a passive index
fund, does not depend on
I) the investor's coefficient of risk aversion
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 ratio of in the universe of securities
A. I, II, IV
B. II, III, V
C. II, III
D. I, IV, V
E. II, IV, V
Kane, Marcus, and Trippi (1999) show that the annualized fee that investors should be willing
to pay for active management, over and above the fee charged by a passive index fund,
depends on the investor's coefficient of risk aversion, the precision of the security analyst, and
the distribution of the squared information ratio of in the universe of securities.
Short Answer Questions
49. Discuss the Treynor-Black model.
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.
Feedback: 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.
50. 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.
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
.
Then you would estimate a regression of the forecasted alphas on the realized alphas as in the
equation
. 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
.
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 the
formula
. If the analyst has perfect forecasting ability the correlation
coefficient will be 1. If the analyst has no ability then the correlation coefficient will be 0. For
values in between 0 and 1 you can adjust the forecasts by multiplying by the correlation.
Feedback: 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.