1.	(25 points)

You are given the following data on three securities, A, B, and the market, M:

Security	Expected
Standard Deviation
Covariance with “M”

A	10%	15%	225
B	10%	15%	180
M	10%	15%	225
Note:  The risk-free rate is  .

a.	Compute the correlation between A and the market, and B and the market.  (6 points)

b.	Based on your answer to part (a), which of the two securities, A or B, is better to be combined into a portfolio with M?  Explain briefly.  (5 points)

c.	Compute the expected return and standard deviation for a portfolio formed between M and your choice in part (b).  Then compute the weighted-average standard deviation of this portfolio and explain why the portfolio’s actual standard deviation is less than just holding any of the three securities, all of which have a standard deviation of 15% and an expected return of 10%.  (10 points)

d.	Compute the systematic risk  CAPM expected return for your choice in part (b).  Why is it less than 10%?  Explain in the context of systematic and total risk.  (4 points)

2.	(25 points)

You are given the following data for options on a common stock;

a.	Use the Black-Scholes Option Pricing Model to find the price of the options.

(i)	Find   and    (6 points)

(ii)	Use your answers from a(i) to find   and  .  Note:  Round your answers to 2 decimal places before looking the values up in the tables. (4 points)

(iii)	Use the Black-Scholes OPM to find C.  (5 points)

(iv)	Use the put-call parity relationship to find the value of  .  (4 points)

b.  	State the intrinsic value and the speculative premium for the call and put options. Why is the speculative premium so small for each option? (5 points)

3.	(25 points)

A call option has a value of   and a put has a value of  .  Both options have an exercise price of  .  The options are to expire today.

a.	Compute the payoff schedule for the call option using the following stock prices,  , and draw a graph of the payoff schedule. (7 points)

S	10	15	20	25	30
Intrinsic Value

b.	Compute the payoff schedule for the put option using the following stock prices,  , and draw a graph of the payoff schedule. (7 points)

S	10	15	20	25	30

Intrinsic Value

c.	Suppose that you buy the share for $20, but you would like to hedge your downside risk.  Choose either the call or put option to eliminate some of the potential loss, and complete the table below.  State what the resulting payoff schedule looks like.  (11 points)

S	10	15	20	25	30
Gain/loss on share
Intrinsic Value (Call or Put)


4.  	Provide a description of the three forms of the Efficient Market Hypothesis using the picture below.  Do you think the markets are efficient?

Look at the graph below.  It depicts the price adjustment at the time of the announcement of Martha’s Stewart’s conviction on Friday, March 5, 2004.

Bonus question:  (5 points)

Revalue the call option using   so that there is no volatility.  All other input values for the option remain the same as in question 2.

5.  (25 points)

A firm has issued a bond with the following characteristics:

 , coupon rate = 5% (paid annually), and time to maturity of

a.	Find the market value of the bond if the market rate of interest is  .  (7 points)

b.	Find the duration of the bond if the market rate of interest is  .  (8 points)

c.	Provide an estimate of the change in the price of the bond if the market rate of interest changes to  .  (6 points)

d.	To protect against loss of wealth, what should be the duration of the asset that was purchased with this bond?  Explain briefly.  (4 points)

6.  (25 points)

The following data is obtained from the Wall Street Journal regarding Treasury securities:

Time to Maturity	Coupon Rate	YTM	Price
0.5 yrs	4.0%	5.0%	99.512
1.0 yrs	5.0%	5.5%	99.520

The face value is assumed to be $100, and interest is paid semi-annually.

a.	Find the zero coupon rates for the first two periods  .  (10 points)

b.	Use the zero coupon rates to find the forward rates   and  .  (10 points)

c.	What is the market’s expectation of interest rates?  Does part (b) describe a no-arbitrage equilibrium?  (5 points)

7.  (25 points)

a.	Currently, the cash market price of an asset is  .  The cost of borrowing is   and the rate of return on the asset is  .  If the price of a futures contract with a settlement date 6 months from now has a price of  , is there an arbitrage opportunity available, and how would you take advantage of it?  (20 points)

b.	How can futures contracts be used to hedge against long and short positions in an asset?  Explain using graphs.  (5 points)

8.  (25 points)

Suppose that a futures price for 5,000 ounces of silver is $5.10 per ounce.  The spot price today is also $5.10.

a.	Show the “marking to market” calculations for short and long positions in the futures contract in the Table below. (20 points)

Day	Spot
Price	Long
Futures	Short
Futures	Long
Forward	Short
0	$5.10
1	$5.20
2	$5.25
3	$5.18
4	$5.18
5	$5.21

b.	How would a long position help a “user” of silver and a short position help a “producer” of silver?  Explain briefly.  (5 points)

For question 1c just make up values for w_B and w_M...say .5 and .5.  Compute the expected return, which should be 10% because both have the same return, but the standard deviation should be about 14 point something, less than the weighted average standard deviation of 15.  The question is why is it less...