Midterm_2023_solutions

.pdf

School

Syracuse University *

*We aren’t endorsed by this school

Course

346

Subject

Finance

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by ProfessorWorld12429

Professor John Heaton Midterm Exam Solutions Investments, Winter 2023 1. (15 points total) Short answer and true/false questions. Provide discussion or justi- fication in each case. You are graded on the basis of the quality of your discussion. (a) (5 points) True or False and explain why. You are currently holding a well-diversified portfolio. Call this portfolio “P.” You are approached by an investment manager offering an investment strategy (call it “A”). As part of your evaluation you look at historical performance and run a regression of the form: r A,t − r f,t = α A + β A ( r P,t − r f,t ) + ϵ A,t You find that the value of α A is 5% annually. Based on this result you should switch your investments from “P” to “A.” Solution: You should switch “some” of your investment in P to A. Alpha needs to be balanced against the idiosyncratic risk in the term ϵ A,t (b) (5 points) Short answer You are considering a strategy that invests in stocks with positive news about earnings announcements (announced earnings that beat analyst forecasts). You find that this strategy consistently generates a positive CAPM alpha. Is this evidence against a “semi-strong” form of market efficiency. Explain. Solution: Potentially since the extra return comes from public news other than past price movements. If the CAPM properly corrects for the risk of the position then this is evidence of semi-strong market efficiency. However, the alpha could be due to a correct for risk that we are missing and therefore would reflect that risk and not market inefficiency. (c) (5 points) Short Answer You are looking at the historical performance of the endowment of the Art Institute. Several of the trustees of the Art Institute are pushing to have the endowment invest substantially more in investment classes that have historically performed very well. What advice might you give the trustees as they consider how to use this historical evidence to inform their investment allocation? Solution: Issues advice: 1

In using past data we must consider that we are estimating parameters governing performance. Even if the investment world is stable over time we will be chancing performance that was good randomly. The world may not stay the same over time. We should be therefore be careful of using past performance of an indicating of the future. Look at what other similar institutions are using. Carefully consider the purpose of the endowment. 2

2. (45 points) Consider the following information about two risky securities: E ( r A ) = 8% σ A = 0 . 25 ρ A,B = 0 . 2 E ( r B ) = 12% σ B = 0 . 25 (a) (7 points) Suppose you currently hold a portfolio that invests 50% in security B and 50% in security C . What is the expected return to this portfolio? What is the standard deviation of the return to the portfolio? Solution E ( r p ) = 50% × 8% + 50 × 12% = 10% σ 2 p = 0 . 5 2 × 0 . 25 2 + 0 . 5 2 × 0 . 25 2 + 2 × 0 . 5 × 0 . 5 × 0 . 2 × 0 . 25 × 0 . 25 = 0 . 0375. σ p = √ 0 . 0375 = 19 . 36%. (b) (8 points) i. Calculate the covariance of the portfolio in part (2a) with each of the secu- rities. Compare the two covariances. ii. What does this result imply about the portfolio from part (2a) compared to all other portfolios that combine securities A and B together? In a world without a risk-free security, why might an investor choose this portfolio? Solution The covariance between security A and the portfolio is given by: cov ( r A , r p ) = 0 . 5 × cov ( r A , r A ) + 0 . 5 × cov ( r A , r B ) = 0 . 5 × 0 . 25 2 + 0 . 5 × 0 . 2 × 0 . 25 × 0 . 25 = 0 . 0375 The covariance between security B and the portfolio is given by: cov ( r B , r p ) = 0 . 5 × cov ( r B , r A ) + 0 . 5 × cov ( r B , r B ) = 0 . 5 × 0 . 2 × 0 . 25 × 0 . 25 + 0 . 5 × 0 . 25 2 = 0 . 0375 Since this are equal, this must be the minimum variance portfolio . The investor does not like risk and would like the minimum volatility possible. 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version