Question 1. Multiple Choice Concept Problem: Please write down your answer clearly.
(a) 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.
(b) 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
(c) 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.
(d) 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(rA) = 20% and E(rB) = 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 prot?
A) 12.5%
B) 17.5%
C) 5% D) 22.5%
E) none of the above.
Question 2. Consider the following information about the return on two stocks 1 and 2:
E(r1) = 8%, σ1 = 14%
E(r2) = 10%, σ2 = 18%
ρ1,2 = 0
where σ1 and σ2 are standard deviations of stock 1 and 2 returns respectively, and ρ1,2 is the correlation between the two stock returns. This risk-free rate rf is 4%.
Suppose that you currently invest 20% in the risk-free security, 10% in stock 1 and 70% in stock 2.
(a) What is the expected return on your portfolio?
(b) What is the standard deviation of the return?
(c) What is the Sharpe ratio of your portfolio?
(b) Now, your optimization software indicates that the optimal (tangency) port- folio weights for stock A and B are and ω1 = 0.52 and ω2 = 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 (b) but with a higher expected return. Is it possible? If yes, construct this new portfolio
(e) What is the expected return of the new portfolio for your client?
Question 2. Consider the following properties of the return of stock 1, of stock 2 and of the market (M):
σ1 = 0.20, ρ1,M = 0.4
σ2 = 0.30, ρ2,M = 0.7
σM = 0.15, E(rM ) = 0.10
Suppose further that the risk-free rate rf is 5%.
(a) According to the Capital Asset Pricing Model, what should be the expected return of stock 1?
(b) According to the Capital Asset Pricing Model, what should be the expected return of stock 2?
(c) Please graph a Security Market Line (SML) based on your answers in (a) and (b) and other information.
(d) Suppose you found a stock 3 whose beta is 1 and expected return 14%. If CAPM is correct, is this stock correctly priced?
(e) What is the alpha of this stock 4?
(f) 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. Construct a new portfolio using the market portfolio and the risk free asset that has the same expected return as the portfolio X but has the lowest standard deviation?
(g) What is the standard deviation of the return of the portfolio you constructed in (f)?