Sample Mid-Exam Paper Formula Sheet Answers

1

Sample Mid-Exam Paper PART I

2 1. Let µm = 0.01 and σm = 0.002 be the sample mean and variance of monthly 2 returns of a risky asset. Denote µa and σa the annualized sample mean and variance of returns of the risky asset. Then 2 (a). µa = 0.01 and σa = 0.024; 2 (b). µa = 0.12 and σa = 0.024; 2 (c). µa = 0.12 and σa = 0.288; (d). µa = 0.12 and σa = 0.024; (e). None of the above.

2. Which of the following statements is correct? (a). Expected utility of wealth is constant on the MVS. (b). 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 coefﬁcient equals -1 or +1. (c). the combination line will be a straight line. (d). the combination line will not be a straight line. (e). none of the above. 4. In the Single Factor Model, you can best measure the contribution that an individual stock makes to the variance of a well diversiﬁed portfolio by the stock’s: (a). Variance (b). Correlation coefﬁcient. (c). Residual variance. (d). Systematic risk. (e). None of the above.

2

E(rP ) A ⋆ X Y ⋆ C σ(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 efﬁcient (b). Both A and C are inefﬁcient (c). Both A and X are efﬁcient (d). Both C and X are inefﬁcient 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 ﬁve assets. Assume an investor must invest all of his/her money in one of the assets. µi σi Asset 1 0.05 0.25 Asset 2 0.10 0.25 Asset 3 0.15 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 inefﬁcient; (b). Asset 1 is efﬁcient; (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 = αi +βi rm +ǫi , 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 σi Security 1 0.10 0.08 Security 2 0.20 0.3 Assume correlation ρ1,2 = −0.5. (1). Calculate...