Lee_Sample_Midterm_2013

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Georgia Institute Of Technology *

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3076

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Apr 3, 2024

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Student Name: Student ID Number: Section Number: Professor Suzanne S. Lee Sample Midterm Exam Investments Spring 2013 DO NOT GO BEYOND THIS PAGE UNTIL YOU ARE TOLD TO DO SO. Honor Code Pledge: You must adhere to the standards of the Georgia Tech Honor Code. You must sign the following statement to receive credit for this exam. I pledge my honor that I have not violated the honor Code during this examination. In addition to the usual violations of the code, additional violations of the code for this exam would include obtaining information from other students about the exam, or informing other students (in other sections of those taking it at other times) about the exam. Signed: 1. You have 1 hour and 20 minutes to complete this examination. 2. This is a closed book exam. A formula sheet (same as the one posted in T-square) is provided. 3. You are to answer questions without consulting anyone . 4. Be neat and show your work. Answers without work receive no credit. Wrong answers with partially correct work may receive partial credit. 5. The exam consists of 3 questions and sub problems. You are to answer each in the space provided. 1

1. Multiple Choice Concept Problem. (a) (5 points) If the market prices of each of the 30 stocks in the Dow Jones Industrial Average (DJIA) all change by the same percentage amount during a given day, which stock will have the greatest impact on the DJIA? A) The stock trading at the highest dollar price per share. B) The stock with total equity has the higher market value. C) The stock having the greatest amount of equity in its capital structure. D) The stock having the lowest volatility. E) None of the above. Answer: (b) (5 points) Assume you purchased 200 shares of XYZ common stock on margin at $70 per share from your broker. If the initial margin is 55%, how much did you borrow from the broker? A) $6,000 B) $4,000 C) $7,700 D) $7,000 E) $6,300 Answer: (c) (5 points) You sold short 200 shares of common stock at $60 per share. The initial margin is 60%. Your initial investment was A) $4,800. B) $12,000. C) $5,600. D) $7,200. E) none of the above. Answer: 2

(d) (5 points) Suppose you are interested in investments using two individual stocks A and B. We are allowed to borrow and lend at the risk free rate at 5%. After your empirical analysis, you found out that the correlation between A and B stock returns is - 1. The expected returns on A and B stocks are E ( r A ) = 20% and E ( r B ) = 7 . 5%. You learn that if you invest 80% of your money in B and 20% in A , your portfolio variance becomes zero. How much would be your arbitrage profit? A) 12.5% B) 17.5% C) 5% D) 22.5% E) none of the above. Answer: 3

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2. Consider the following information about the return on two stocks 1 and 2: E ( r 1 ) = 8% , σ 1 = 14% E ( r 2 ) = 10% , σ 2 = 18% ρ 1 , 2 = 0 where σ 1 and σ 2 are standard deviation of stock 1 and 2 returns respectively, and ρ 1 , 2 is the correlation between the two stock returns. This risk-free rate r f is 4%. (a) Suppose that you currently invest 20% in the risk-free security, 10% in stock 1 and 70% in stock 2. (a.1) (5 points) What is the standard deviation of the return? (a.2) (5 points) What is the Sharpe ratio of your portfolio? 4

(b) Now, your optimization software indicates that the optimal (tangency) portfolio weights for stock 1 and 2 are and ω 1 = 0 . 52 and ω 2 = 0 . 48. Your client wants to invest in a combination of this tangency portfolio and T-bills with the same standard deviation as that of your portfolio p in (a) but with a higher expected return. (b.1) (10 points) Construct this new portfolio (i.e. give portfolio weights) (b.2) (10 points) What is the expected return of the new portfolio for your client? 5

3. Consider the following properties of the return of stock 1, of stock 2 and of the market (M): σ 1 = 0 . 20 , ρ 1 ,M = 0 . 4 σ 2 = 0 . 30 , ρ 2 ,M = 0 . 7 σ M = 0 . 15 , E ( r M ) = 0 . 10 Suppose further that the risk-free rate r f is 5%. (a) (5 points) According to the Capital Asset Pricing Model, what should be the expected return of stock 1 ? (b) (5 points) Please graph a Security Market Line (SML). 6

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(c) Suppose you found a stock 3 whose beta is 1 and expected return 14%. (c.1) (5 points) If CAPM is correct, is this stock correctly priced? (c.2) (5 points) What is the alpha of this stock 3? (d) Suppose that the correlation between the return of stock 1 and the return of stock 2 is 0.5. Your current portfolio X has 40% investment in stock 1 and 60% investment in stock 2. Assume that the Capital Asset Pricing Model is valid. (d.1) (10 points) Construct a new portfolio using the market portfolio and the risk free asset that has the same expected return as the portfolio X . (d.2) (10 points) What is the standard deviation of the return of this new portfolio? 7

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