| December 24, 2015

1. Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable for

the investor’s level of risk tolerance. (6 pts)

2.Futures contracts use daily mark to market to calculate the amounts in margin accounts. Explain how mark to market accounting reduces

risk to investors in futures markets. (6pts)
3. Discuss the relationship betweencalloption prices and time to expiration, volatility of the underlying stocks, and the exercise price.

(6 pts)

4. Discuss the major assumptions that are made in formulating the Capital Asset Pricing Model. How realistic are these assumptions in

valuing a real world security? (6 pts)
5. Explain the major similarities and differences between the standard deviation of a securities return and the beta of that security. (6

6. You hold a portfolio of stocks with a value of $1,000,000. You expect that you will be selling the stocks in the portfolio in one year.

You are considering hedging your market risk by using the 1-yr S&P 500 Index Future. The price of the future is currently at 2,000. The

multiplier for the future is 250; the margin requirement is 10% of the total futures position. (10 pts)

a. What side of the futures position will you take? Long or short, and why? How many contracts will you use?

b. What is your initial cash flow?

c. If the price of the futures falls to 1,900, what will happen to your margin account?
d. If, in exactly one year, the futures contract is trading at 1,800 and your stock portfolio has fallen in value by 10%, what will

be your overall profit?
7. The following information is given about options on the stock of a certain company (10 pts)

S0 = 23 X = 20
rf = 0.05 T = 0.5
2 (variance) = 0.24

No dividends are expected.

Use this information to answer questions a through d. Be sure to show your formula’s and calculations.

a. What value does the Black-Scholes-Merton model predict for the call?
b. What is the price of a put on the stock?

8) The current spot price of gold is $1,020 per ounce. The risk free rate is 3% per year. A gold futures contract has a contract size of

100 oz. Assume that anyone can borrow at the risk-free rate. (10 pts)
a. What should the futures price be for a contract with a time period of exactly one year?
b. Say that you observe that the contract for gold with a time period of exactly one year is actually selling for $1,060. Describe a

strategy that you could use to make a profit that would exceed the risk free rate, and what profit you could earn.
9. The following quotes were observed for options on a given stock on November 1 of a given year. These are American calls except where

indicated. Use the information to answer questions (10 pts)

Calls Puts





The stock price was 113.25. The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The

times to expiration were 0.0384 (November), 0.1342 (December), and 0.211 (January). Assume no dividends unless indicated.

A. What is the intrinsic value of the December 115 put?

B. What is the intrinsic value of the January 110 call?

C. What is the time value of the December 105 put?

D. What is the time value of the November 110 call?

E. Suppose you knew that the January 115 options were correctly priced but suspected that the stock was mispriced. Using put-call

parity, what would you expect the stock price to be? For this problem, treat the options as if they were European.
10. You purchased the following futures contract today at the settlement prices. Answer the questions below regarding the contract.

(10 pts)

– What is the total value of the futures contract?
– If there is a 10% margin requirement, how much do you have to deposit?
– Suppose the price of the futures contract changes as shown in the following table.
– Enter the relevant information into the table. Show your calculations.
– Explain why the account is marked to market daily.


11. Consider the following probability distribution for stocks A and B: (10 pts)
a. Calculate the expected return and standard deviation of both Stocks A and B
b. If the correlation coefficient between stocks A and B is .82, calculate the expected return and standard deviation of a portfolio made

up of 75% A and 25% B.

12. A bond has Modified Duration of 5 years, a convexity of 124, and a yield to maturity of 6.5%. The bond is currently trading at $978.

(10 pts)

What will be the bond’s price if the YTM increases to 9.5%? (show your calculations).

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