Problem 1 Indexes (33 points)

Consider the three stocks in
the following table. P
t 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

$
125.00

150.00

$
112.00

150.00

$ 117.00

150.00

B

$
63.00

400.00

$
73.00

400.00

$ 78.00

400.00

C

$
34.00

200.00

$
39.00

200.00

$ 19.00

600.00

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 returns for the periods ending in 1 and 2 (7 points).




Problem
2 Margin (34 Points)




2.A.
The current market price for XYZ is $46 per share. Initial margin is 50%,
maintenance margin is 35% and margin interest is 1.25% 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 $59 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 $72 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 $60 per share at the end of the
year. What is your percentage return on equity for this trade (4 points)?

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

Normal

Bull

Market

Market

Market

Probability

35.00%

50.00%

15.00%

Stock X

-15.00%

9.00%

21.00%

Stock Y

-22.00%

14.00%

48.00%

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 riskā€“free rate of return is 1.50%, 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 $60,000
in stock X and the remainder in stock Y. What is the expected return for this
portfolio (8 points)?