# Fin 5620 quantitative problem set #1 36595

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Question

1.Consider the three stocks in the following table. Pt represents the price at the end of period t and Qt is the number of shares outstanding. Stock C splits 3:1 during period 2.

 P0 Q0 P1 Q1 P2 Q2 A 64 100 70 100 74 100 B 42 300 35 300 32 300 C 10 200 15 200 8 600

1.1 Calculate the price-weighted index of the three stocks for each period (4 points). What is the divisor for each period (4 points)? Does it change in the last period (2 points)? Why or why not (2 points)?

1.2 Calculate the price-weighted index returns for the periods ending in 1 and 2 (7 points).

1.3 Calculate the value-weighted index returns for the periods ending in 1 and 2 (7 points).

1.4 Calculate the equal-weighted index return for the periods ending in 1 and 2 (7 points).

Question 2

1.Problem 2 Margin (34 Points)

2.A. The current market price for XYZ is \$45 per share. Initial margin is 50%, maintenance margin is 35% and margin interest is 1.50% per year.

2.A.1) You believe the stock price will increase over the next year and wish to trade exactly one round lot. What trade should you make (2 points)? How much margin would you have to post to your account (4 points)? At what price would you receive a margin call (7 points)?

2.A.2) Suppose you are correct and the stock rises to \$53 per share at the end of the year. What is your percentage return on equity for this trade (4 points)?

2.B. The current market price for ABC is \$75 per share. Initial margin is 50%, maintenance margin is 35% and there is no margin interest.

2.B.1) You believe the stock price will decrease over the next year and wish to trade exactly one round lot. What trade should you make (2 points)? How much margin would you have to post to your account (4 points)? At what price would you receive a margin call (7 points)?

2.B.2) Suppose you are correct and the stock falls to \$62 per share at the end of the year. What is your percentage return on equity for this trade (4 points)?

Question 3

1.Problem 3 Scenario Analysis (33 points)

Use the following scenario analysis for stocks X and Y to answer the questions. Round to the nearest 1/100 of 1% (i.e., 15.07%).

 Bear Market Normal Market Bull Market Probability 0.2 0.4 0.4 Stock X -24% 8% 33% Stock Y -9% 5% 16%

3.a) What are the expected rates of return for stocks X and Y (9 points)?

3.b) What are the standard deviations for of returns for stocks X and Y (8 points)?

3.c) If the risk–free rate of return is 2.25%, what are the Sharpe Ratios for stocks X and Y (8 points)? (Please assume that the standard deviations of the excess returns are the same as the standard deviations of returns calculated in part b.)

3.d) Assume you have a \$150,000 portfolio and you invest \$45,000 in stock X and the remainder in stock Y. What is the expected return for this portfolio (8 points)?

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