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Asset Management Lecture 11.

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Presentation on theme: "Asset Management Lecture 11."— Presentation transcript:

1 Asset Management Lecture 11

2 Quiz 1 Consider the following probability distribution for stocks A and B:    1. The expected rates of return of stocks A and B are E(RA) = 0.1(10%) + 0.2(13%) + 0.2(12%) + 0.3(14%) + 0.2(15%) = 13.2%; E(RB) = 0.1(8%) + 0.2(7%) + 0.2(6%) + 0.3(9%) + 0.2(8%) = 7.7%.

3 Quiz 1 1. Consider the following probability distribution for stocks A and B:    2. The standard deviations of stocks A and B are sA = [0.1(10% %)^ (13% %)^ (12% %)^ (14% %)^ (15% %)^2]^(1/2) = 1.5%; sB = [0.1(8% - 7.7%)^ (7% - 7.7%)^ (6% - 7.7%)^ (9% - 7.7%)^ (8% - 7.7%)^2 ]^(1/2) = 1.1%.

4 Quiz 1 1. Consider the following probability distribution for stocks A and B:    3. The variances of stocks A and B are VAR(A) = 1.5%^2=0.0225%; VAR(B) = 1.1%^2=0.0121%.

5 Quiz 1 1. Consider the following probability distribution for stocks A and B:    4. The coefficient of correlation between A and B is  Cov(A,B) = 0.1(10% %)(8% - 7.7%) + 0.2(13% %)(7% - 7.7%) + 0.2(12% %)(6% - 7.7%) + 0.3(14% %)(9% - 7.7%) + 0.2(15% %)(8% - 7.7%) = 0.76; Corr(A,B) = 0.76/[(1.1)(1.5)] = 0.47.

6 Quiz 1 5. If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and standard deviation?  E(R) = 0.4(13.2%) + 0.6(7.7%) = 9.9%; SD(P) = [(0.4)^2(1.5)^2 + (0.6)^2(1.1)^2 + 2(0.4)(0.6)(1.5)(1.1)(0.46)]^(1/2) = 1.1%.

7 Quiz 1 6. Let G be the global minimum variance portfolio. The weights of A and B in G are   wA = [(1.1)^2 - (1.5)(1.1)(0.46)]/[(1.5)^2 + (1.1)^2 - (2)(1.5)(1.1)(0.46)] = 0.23; wB = = 0.77

8 Quiz 1 7. The expected rate of return and standard deviation of the global minimum variance portfolio, G, are E(RG) = 0.23(13.2%) (7.7%) = 8.97% . 9%; SD(G) = [(0.23)^2(1.5)^2 + (0.77)^2(1.1)^2 + (2)(0.23)(0.77)(1.5)(1.1)(0.46)]^(1/2) = 1.05%.

9 Quiz 1 8. Which of the following portfolio(s) is (are) on the efficient frontier?  A. The portfolio with 20 percent in A and 80 percent in B. B. The portfolio with 15 percent in A and 85 percent in B. C. The portfolio with 26 percent in A and 74 percent in B. D. The portfolio with 10 percent in A and 90 percent in B. E. A and B are both on the efficient frontier. The Portfolio's E(Rp), SD(P), Reward/volatility ratios are 20A/80B: 8.8%, 1.05%, 8.38; 15A/85B: 8.53%, 1.06%, 8.07; 26A/74B: 9.13%, 1.05%, 8.70; 10A/90B: 8.25%, 1.07%, 7.73. The portfolio with 26% in A and 74% in B dominates all of the other portfolios by the mean-variance criterion.

10 Quiz 1 9. Portfolio theory as described by Markowitz is most concerned with:  A. the elimination of systematic risk. B. the effect of diversification on portfolio risk. C. the identification of unsystematic risk. D. active portfolio management to enhance returns. E. none of the above. Markowitz was concerned with reducing portfolio risk by combining risky securities with differing return patterns.

11 Quiz 1 10. The unsystematic risk of a specific security  A. is likely to be higher in an increasing market. B. results from factors unique to the firm. C. depends on market volatility. D. cannot be diversified away. E. none of the above. Unsystematic (or diversifiable or firm-specific) risk refers to factors unique to the firm. Such risk may be diversified away; however, market risk will remain.

12 Quiz 1 11. The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is  A. 0.0 B. 1.0 C. 0.5 D. -1.0 E. negative

13 Quiz 1 12. Security X has expected return of 12% and standard deviation of 20%. Security Y has expected return of 15% and standard deviation of 27%. If the two securities have a correlation coefficient of 0.7, what is their covariance?  A. 0.038 B. 0.070 C. 0.018 D. 0.013 E. 0.054 Cov(rX, rY) = (.7)(.20)(.27) = .0378

14 Quiz 1 13. Given an optimal risky portfolio with expected return of 14% and standard deviation of 22% and a risk free rate of 6%, what is the slope of the best feasible CAL?  A. 0.64 B. 0.14 C. 0.08 D. 0.33 E. 0.36 Slope = (14 - 6)/22 = .3636

15 Quiz 1 14. Security M has expected return of 17% and standard deviation of 32%. Security S has expected return of 13% and standard deviation of 19%. If the two securities have a correlation coefficient of 0.78, what is their covariance?  A. 0.038 B. 0.049 C. 0.047 D. 0.045 E. 0.054 Cov(rX, rY) = (.78)(.32)(.19) = .0474

16 Quiz 1 15. If a firm's beta was calculated as 0.8 in a regression equation, Merrill Lynch would state the adjusted beta at a number  A. less than 0.8 but greater than zero. B. between 1.0 and 1.8. C. between 0.8 and 1.0. D. greater than 1.8. E. zero or less.

17 Quiz 1 16. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 150 stocks in order to construct a mean-variance efficient portfolio constrained by 150 investments. They will need to calculate _____________ expected returns and ___________ variances of returns.  A. 150, 150 B. 150, C. 22500, 150 D. 22500, E. none of the above

18 Quiz 1 17. The index model has been estimated for stocks A and B with the following results: RA = RM + eA RB = RM + eB M = (eA) = (eB) = 0.10 The covariance between the returns on stocks A and B is ___________.  A.  B.  C.  D.  E. 0.4000 Cov(RA,RB) = b(A)b(B)Var(M) = 0.5*1.3*0.25^2 =

19 Quiz 1 18. The index model for stock A has been estimated with the following result: RA = RM + eA If M = 0.30 and R2 = 0.28, the standard deviation of return of stock A is _________.  A.  B.  C.  D.  E. none of the above

20 Quiz 1 19. As a financial analyst, you are tasked with evaluating a capital budgeting project. You were instructed to use the IRR method and you need to determine an appropriate hurdle rate. The risk-free rate is 4 percent and the expected market rate of return is 11 percent. Your company has a beta of 1.4 and the project that you are evaluating is considered to have risk equal to the average project that the company has accepted in the past. According to CAPM, the appropriate hurdle rate would be ______%.  A. 13.8 B. 7 C. 15 D. 4 E. 1.4 The hurdle rate should be the required return from CAPM or (R = 4% + 1.4(11% - 4%) = 13.8%.

21 Quiz 1 20. The expected return-beta relationship  A. is the most familiar expression of the CAPM to practitioners. B. refers to the way in which the covariance between the returns on a stock and returns on the market measures the contribution of the stock to the variance of the market portfolio, which is beta. C. assumes that investors hold well-diversified portfolios. D. all of the above are true. E. none of the above are true.

22 Quiz 1  21. Your opinion is that security C has an expected rate of return of It has a beta of 1.1. The risk-free rate is 0.04 and the market expected rate of return is According to the Capital Asset Pricing Model, this security is  A. underpriced. B. overpriced. C. fairly priced. D. cannot be determined from data provided. E. none of the above. 4% + 1.1(10% - 4%) = 10.6%; therefore, the security is fairly priced.

23 Quiz 1  22. Absent research, you should assume the alpha of a stock  A. zero B. positive C. negative D. not zero E. A or B In efficient markets, alpha should be assumed to be zero.

24 Quiz 1  23. 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. 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 the above. Benchmark portfolio risk can be constrained to keep a Treynor-Black portfolio within reasonable weights.

25 Quiz 1 24. 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 the above. Tracking error is defined as the difference between the returns on the overall risky portfolio versus the benchmark return.

26 Quiz 1 25. The beta of an active portfolio is 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)^ ]^(1/2) = [0.0676]^(1/2) = 26.0%.

27 Quiz 1 26. 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 wO = [2%/1%]/[(16% - 8%)/4%] = 1, or 100%; w* = 1/[1 + (1 - 1)1] = 1.

28 Quiz 1 27. 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


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