Arizona State University - FIN 421 / FIN421 Practice Midterm - Answers

Shares outstanding (St), stock prices (Pt), and Dividends (Dt+1) for assets A and B are given below. All dividends are paid out at the end of the year, 12/31/2014. Asset B performed a 3:1 stock split at the beginning of the year, 01/01/2014. What is the value weighted portfolio return? Date Asset A Asset B St Pt Dt St Pt Dt 12/31/2013 (t) 12/31/2014 (t+1) * 50 3 Asset B performed a 3:1 stock split on 01/01/2014. A) -18.67% B) 6.33% C) 9.33% D) 24.00% E) None of the above Answer: B Weights are wA = 100 × 20=(100 × 20 + 10 × 100) = 2=3 and wB = 1 − wA = 1=3 Returns are rA = (14 + 2)=20 − 1 = −0:2; rB = 3(50 + 3)=100 − 1 = 0:59: The value weighted return is 2=3 × (−20)% + 1=3 × 59% = 6:33%. 2. You purchased 400 shares of Starbucks common stock on margin at $120 per share. Assume the initial margin is 50% and the maintenance margin is 30%. Following an earnings warning, the price of Starbucks starts declining rapidly. At what price do you get a margin call from your broker? Assume the stock pays no dividends and ignore interest on margin. A) $36:00 B) $78:00 C) $85:71 D) $102:88 E) None of the above Answer: C Assets Liabilities Value of stock $48,000 Loan $24,000 Equity $24,000 (400P − $24; 000)=400P = :3 P − $60 = 0:3P P = $85:71 33. There are two possible scenarios for the future, war and peace. The table below contains the returns of LMT and TIF in each state. Your portfolio has 40% invested in LMT and 60% in TIF. What is the standard deviation of your portfolio return? State of the Economy Probability LMT TIF War 25% 40% -10% Peace 75% -20% 20% A) 0:03074 B) 0:03248 C) 0:00068 D) 0:00095 E) 0:02598 Answer: E The portfolio return equals rP;w = 0:4 · 0:4 + 0:6 · (−0:1) = 0:1 in the war state and rP;p = 0:4 · (−0:2) + 0:6 · 0:2 = 0:04 in the peace state. The expected portfolio return equals µP = 0:25 · 0:1 + 0:75 · 0:04 = 0:055 and the portfolio standard deviation equals σP = p0:25 · (0:1 − 0:055)2 + 0:75 · (0:04 − 0:055)2 = p0: = 0:02598. Alternatively, one can find the answer by first computing means, standard deviations, and the covariance for the two assets, and then use them in conjunction with the formulas for the mean and variance of a portfolio. This will yield the same result, but requires somewhat more algebra in this example. 4. A risk parity portfolio is composed of three stocks, A, B, and C. Stock A has a portfolio weight of 0:5 while stock B’s weight is 0:25. Stock C has a volatility of σC = 0:3. What is the volatility of Stock A? A) 0.0125 B) 0.25 C) 0.60 D) 0.15 E) The answer cannot be determined based on the information provided. Answer: D • Portfolio weights always sum to one ) wC = 0:25 • Risk parity weights only depend on the stocks’ volatilities. Because B and C have identical weights, their volatilities must be equal as well, i.e. wB = wC ) σB = σC = 0:3 • A’s weight is twice as big as B’s weight: wA = 2wB , 1 σA 1 σA + 1 σB + 1 σC = 2 1 σB 1 σA + 1 σB + 1 σC