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Sample Midterm

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									                                 Sample Midterm
Finance 353 Derivatives
Daytime MBA
Fall 2009

Note: Question 8, 9, and 10 in Section I are not required for the midterm.

Section I: Multiple Choice Questions. (4X15=60 points).

1. Assuming frictionless market, which of the following cannot be the profit diagram of
any derivative contract?




2. Suppose you enter into a short futures contract to sell July Silver for $5.20 per ounce
on the New York Commodity Exchange. The size of the contract is 5,000 ounces. The
initial margin is $4,000, and the maintenance margin is $3,000. Which of the following
prices of silver futures will lead to a margin call?

A. $5.45 per ounce.                                  B. $ 5.30 per ounce.
C. $4.89 per ounce.                                  D. $5.10 per ounce.
3. Assuming the risk-free interest rate is 9% per annum with continuous compounding
and that the continuously compounded dividend yield on a stock index varies throughout
the year. In February, May, August, and November, dividends are paid at a rate of 5% per
annum. In other months, dividends are paid at a rate of 2% per annum. Suppose the value
of the index on July 31, 2006 is 300. What is the futures price (per share) for a contract
deliverable on December 31, 2006?

A. $265.41                                           B. $307.34.
C. $305.04                                           D. $317.91

Hint: Use the average dividend yield.

Question 4, 5, and 6 are based on the following information:
A stock is expected to pay a dividend of $1 per share in 2 months and in 5 months. The
current stock price is $50, and the continuous compounding risk free interest rate is 8%
per annum. An investor has just taken a short position in a 6-month forward contract on
the stock.

       4. What is the arbitrage free price of the forward contract?
       A. $52.04                                             B. $50.01
       C. $47.96                                             D. $48.05

       5. Suppose your answer in question 4 is in fact the price specified in the investor’s
       forward contract. What is the value of the forward contract?
       A. $0                                                B. $50.01
       C. $47.96                                            D. $2.00

       6. Suppose your answer in question 4 is in fact the price specified in the investor’s
       forward contract. Three months later, the price of the stock is $48 and the risk free
       rate of interest is still 8% per annum. What is the value of the short position of the
       forward contract?

       A. $0                                                   B. $2.004
       C. $-2.00                                               D. $2.00


7. Suppose the continuously compounded Euro-denominated Libor is 4.5% per annum,
the continuously compounded dollar denominated Libor is 3% per annum, and the
current exchange rate is 0.84 $/€. Which of the following is mostly likely to be the 6-
month forward rate of dollar denominated in Euro traded in Frankfurt?

A. 0.8337 €/$.                                B. 1.1994 €/$.
C. 1.2085 €/$.                                D. 1.1728 €/$
8. Suppose the S&P 500 currently has a level of 900. You wish to hedge a $135,000
thousand portfolio that has a beta of 0.75 (relative to the S&P 500 index). Suppose you
can trade fractions of contracts. How many S&P 500 E-mini futures contracts should you
short to hedge your portfolio?

A. 3.0                                          B. 2.25
C. 2.14                                         D. 2.85

Hint: (One S&P 500 E-mini futures contract is of size $50XS&P500 index.)



Question 9 and 10 are based on the following information:
The contract size of Gold futures traded on CBOT is 100 fine troy ounces (We will use
oz hereafter) per contract. The spot price and futures price on Feb 2, 2007 is as follows:

Spot Price                                       710.00 $/oz
April Futures                                    720.00 $/oz
June Futures                                     735.00 $/oz

A gold producer is expecting to sell 100,000 oz of gold in April and in June, respectively.
Assume interest rate is zero in answering question 9 and question 10.


          9. Suppose the gold producer wants to use a stack hedge strategy to hedge the risk
          of gold price fluctuations. Which of the following is a valid stack hedge strategy?

          A. Purchase 1000 April futures on Feb 2, Accept delivery on the 1000 April
          futures on April 2. Purchase 1000 June futures on April 2, and accept delivery on
          the 1000 June futures on June 2.

          B. Sell 1000 April futures on Feb 2, and deliver the 1000 April futures on April 2.
          Sell 1000 June futures on April 2, and deliver the 1000 June futures on June 2.

          C. Sell 2000 April futures on Feb 2. Deliver 1000 April futures contracts on April
          2 and settle the rest of the 1000 April futures contracts by cash. Sell 1000 June
          futures on April 2, and deliver the 1000 June futures on June 2.

          D. Sell 2000 June futures on Feb 2. Sell 100,000 oz gold on the spot market in
          April. Deliver the 1000 June futures on June 2, and cash settle the rest of the 1000
          June futures on June 2.
        10. Under which of the following circumstances does the stack hedge strategy
        perform as well as a strip hedge strategy?

        A. On April 2, the spread between spot price and June futures price is -15 $/oz
        (meaning Spot price - June futures price =-$15).

        B. On April 2, the spread between spot price and June futures price is -10 $/oz.

        C. The spot price on June 2 is $15 higher than the spot price on April 2.

        D. The spot price on April 2 is $10 higher than the spot price on Feb 2.


11. Suppose in March, you entered into 10 long positions of the September Eurodollar
futures contract when the price index is 92. Suppose also, on the last trading day of the
Sep Eurodollar futures contract 1, the continuously compounded 3-month Libor is 6% per
annum. Which of the following is the gain on your position? (Please ignore marking to
market in answering this question.)

A. -$48869.35                                      B. $49607.92
C. $48869.35                                       D. $488.6935


12. A stock that pays 4% continuously compounded dividend yield per annum currently
sells for $86.00. A 10-month European call option with a strike of $95.00 has a premium
of $5.7405, and a European put option with the same strike price and maturity date is
traded at $14.6371. What is the continuously compounded risk free rate that excludes
arbitrage?

A. 3.5% per annum.                                 B. 3.13% per annum.
C. 3.75% per annum.                                D. 2.95% per annum.


13. Which of the following actions can never be optimal?

A. Exercising before maturity an American put option on a stock that does not pay any
dividend.
B. Exercising before maturity an American call option on a stock that pays continuous
dividend.
C. Exercising an American call option on a stock at maturity just after a large dividend is
paid.
D. Exercising an American put option on a stock at maturity just after a large dividend is
paid.


1
 This is usually the second London bank business day immediately preceding the third Wednesday of the
contract month (September).
14. A stock price is currently $40. It is known that at the end of one month it will be
either $42 or $38, each with 50% probability. The stock does not pay any dividend during
the next month. The risk-free interest rate is 8% per annum with continuous
compounding. What is the value of a 1-month European call option with a strike price of
$39?

A. $1.689                                           B. $1.701
C. $ 1.133                                          D. $1.126


15. The risk free interest rate is 10% per annum, the current price of the stock index ABC
is $50, and volatility of the stock is 30% per annum. The Black-Sholes price of a 3-month
at-the-money European put option on the stock is _____.

A. $3.61                                     B. $2.37
C. $0.047                                    D. $0.072
Section II. Constructing Arbitrage Portfolios (10X2=20 points)

The following scenario creates arbitrage opportunities for investor. Construct an arbitrage
portfolio and complete the Cash Flow Table of the portfolio constructed to verify it is
indeed an arbitrage opportunity.

1. The current exchange rate between Euro and Yen is 0.02 €/¥. The continuously
compounded interest rate of Euro is 4% per annum, and the continuously compounded
interest rate of Yen is 1% per annum. The price of one futures contract with 6-month
maturity is €254,000 (One Yen futures contract contains ¥ 12,500,000).

Portfolio     Cash Flow at Date 0                     Cash Flow at Maturity
Strategy
              In Yen           In euro                In Yen               In Euro




Total



2. The current price of the stock is $100 per share. The continuously compounded interest
rate is 5% per annum. The stock is expected to pay quarterly dividend in the amount of
$2. The price of an at-the-money call option with 6 months to maturity is $3, and the
price of a put with the same strike price and maturity is $2.25. (Assume both the call and
the put expires immediately after the second dividend payment.)

Portfolio Strategy       Cash Flow at Date 0      Cash Flow at Maturity
                                                  ST >=K               ST <K




Total
Section III: Binomial Option Pricing Models. (20 points)
Show your steps. Partial credits will be given even if the final answer is wrong.

Consider a non-dividend paying stock XYZ. Suppose the historical standard deviation of
the log annual return of the stock is   0.30 . Suppose the continuous compounded
interest rate per annum is 8%, and the current price of the stock is S 0  $100 .

1) Construct the following two-step binomial tree of the stock price movement over a
period of 6 months.

                                                             S uu  uuS0
                                                             ( Node uu)
                               S u  uS0
                               ( Node u)
                                                             S du  duS0
S 0  100
                                                             ( Node du)
                               S d  dS 0
                               ( Node d )
                                                             S dd  ddS 0
                                                             ( Node dd )

Compute the appropriate parameters of the model (that is, u , d , and the effective one-
period interest rate R ) using “McDonald’s recipe”.

2) Compute the delta of an at-the-money call option at node u, and d. Which is greater?

3) Compute the price of the call option.

4) Compute the price of a put option with the same strike price and maturity.

								
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