Investment Analysis Exam Paper
In the standard deviation and expected return space, the mean-variance combination line is convex while the indifference curve is concave. (c). The variance of portfolio with equal proportions of n assets tends to zero as n > ?. (d). For portfolios of many assets, it is not possible to reduce the risk to zero. (e). None of the above. 3. Consider a portfolio of one risky asset and one risk-free asset. Which of the following statements is correct? (a). the correlation between the two assets is not zero. (b). the combination line will be a straight line only if the correlation coef? cient equals -1 or +1. (c). he combination line will be a straight line. (d). the combination line will not be a straight line. (e). none of the above. 4.
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In the Single Factor Model, you can best measure the contribution that an individual stock makes to the variance of a well diversi? ed portfolio by the stock’s: (a). Variance (b). Correlation coef? cient. (c). Residual variance. (d). Systematic risk. (e). None of the above. 2 E(rP ) A ? X Y ? C ? (rP ) Z B? F IGURE 1. The MVS for assets X, Y and Z, where B is the global minimum variance portfolio. Refer to Figure 1 for questions 5-7 5. Which of the following statements is correct? (a).
Without short-selling, you can select portfolio A. (b). All the weights of portfolio C are always positive. (c). All the weights of portfolio A must be positive. (d). It must be the case that some short selling is being permitted. (e). None of the above. 6. Rational investors would prefer (a). Portfolio A. (b). Portfolio B. (c). The portfolios represented along the curve starting at B and passing through A. (d). Portfolio located anywhere on the MVS. 7. With short-selling is allowed, (a). Both A and X are ef? cient (b). Both A and C are inef? cient (c). Both A and X are ef? cient (d). Both C and X are inef? ient 8.
Which of the following statements is correct? (a). With short-selling, portfolios made up of the minimum variance portfolios will always be on the MVS. (b). The MVS of many assets is bounded. (c). With short-selling, some of the assets must be located on their MVS. (d). Without short-selling, all assets are always located on their MVS. (e). None of the above. 3 9. The following table lists the expected returns and standard deviation of returns for ? ve assets. Assume an investor must invest all of his/her money in one of the assets. µi ? i Asset 1 0. 05 0. 25 Asset 2 0. 10 0. 25 Asset 3 0. 5 0. 30 Asset 4 0. 16 0. 45 Asset 5 0. 17 0. 32 Which of the following statements is true? (a). Asset 3 is inef? cient; (b). Asset 1 is ef? cient; (c).
A non-satiated, risk-averse investor could possibly choose Asset 4 depending on the parameters of his/her utility function; (d). A non-satiated, risk-averse investor could possibly choose Asset 2 depending on the parameters of his/her utility function; (e). None of the above 10. Under the standard assumptions of the Single Factor Model ri = ? i +? i rm +oi , how many parameters do you need to estimate in order to construct the MVS of 20 risky assets?
Assume the expected return and the variance of the market return rm are given. (a). 420. (b). 200. (c). 61. (d). 60. (e). None of the above. 4 PART II Question 1 The following table gives the expected returns and standard deviations of returns for two securities: µi ? i Security 1 0. 10 0. 08 Security 2 0. 20 0. 3 Assume correlation ? 1,2 = ? 0. 5. (1). Calculate the expected return and standard deviation of the global MVP, G. (2). Draw the combination line for these two securities and indicate the portfolio G, the ef? cient portfolios and the inef? cient portfolios. (3).
Find the weights and standard deviation of the portfolio with an expected return of 25%. Do you need to sell-short? Question 2 Consider a market containing three risky securities. Suppose the vector of expected returns E(r) and the variance-covariance matrix ? and its inverse variance-covariance matrix ?? 1 are given by ? ? ? ? ? ? 100 0 0 0. 01 0 0 0. 1 0. 04 ? 0. 02? , ?? 1 = ? 0 31. 25 12. 5? . E(r) = ? 0. 15? , ? = ? 0 0 12. 5 25 0 ? 0. 02 0. 05 0. 2 (1). Formulate the Markowitz problem for a portfolio of the three risky securities with a target return of 16% and obtain the ? rst order conditions.
Note: you are not required to solve the problem. (2). Compute the values of the scalars A, B, C and ?. (3). Find the expected return and standard deviation of the MVP. Find the standard deviations of the two minimum variance portfolios P1 and P2 with E(rP1 ) = 10% and E(rP2 ) = 25%. (4). Draw a rough sketch of the MVS and the asymptotes in the mean-standard deviation space. Your diagram should indicate the positions of P1 , P2 and the MVP. Without short-selling, is it possible to construct an optimal portfolio with an expected return of 25%? Explain why? 5 Question 3 Note: You may use your answers from Question 2 to answer this question.
Consider portfolios containing the three risky securities in the previous question (Question 2) together with a risk-free security paying rF = 0. 05. (1) Verify that ??? 1 = I. (2) Find the standard deviations of the two minimum variance portfolios P3 and P4 with E(rP3 ) = 10% and E(rP4 ) = 25%. Find the mean and standard deviation of the tangency portfolio T . (3) Draw a rough sketch to indicate the tangency relation between the MVS with and without the risk-free asset and locate P3 and P4 on the MVS. Are they ef? cient or inef? cient? (4) For the minimum variance portfolios with the expected returns of 10% and 25%, do you bene? from investing in both the risky assets and the risk-free asset in compare with investing in the risky assets only?
If so, what are the bene? ts? Question 4 Suppose a single-factor model (SFM) has been ? t to the returns of Stocks A and B as follows: rA = 0. 02 + rM + oA rB = 0. 01 + 0. 8rM + oB . Suppose further that the expected return and standard deviation of the market return is 2 µM = 0. 1, ? M = 0. 20, and that the R-square statistics for the two stocks are RA = 0. 8 2 and RB = 0. 9, respectively. Now answer the following questions: (a) What are the total risks and unsystematic risks for the two stocks? b) What is the correlation between the returns of the two stocks?