Reference no: EM131153734

Answer problems 1 to 3 based on the following information.

You are the owner of Sweet Juice Farm in Florda. On January 1, you sold 15 March FCOJ futures contracts at $1.5115 per pound. At the contract maturity date, the spot price of orange juice is $1.6115 per pound. Contract Size is 15,000 pounds of orange juice solids (hint: you can consider this as "multiplier."

1. What is the futures price at the contract maturity date?
a. 1.5115
b. 1.6115
c. 0
d. Need more information.

2. What is the basis at the contract maturity date?
a. 1.5115
b. 1.6115
c. 0
d. 'Need more information.

3. What is your profit (loss) if your close your position by buying 15 futures contracts on maturity date? (Hint: you are in a short position)
a. Gain of $1.5
b. Loss of $1.5
c. Gain of $22,500
d. Loss of $22,500

4. You are managing a $5 million portfolio. You want to reduce the beta from the current value of 1.8 to 0. The beta on the future contract you are going to use is 1.05, and the total future price is $240,000. The correct statement includes:
a. You want to reduce portfolio beta to zero because you are expecting the stock market to go down.
b. You want to reduce portfolio beta to zero because you are expecting the stock market to go up.
c. You want to reduce portfolio beta to zero because you are expecting the stock market to flatten.
d. You want to reduce portfolio beta to zero because you are not certain about the stock market movement in the future.

5. Go back to the above question. Estimate the required number of future contracts that will reduce your portfolio to zero beta.
a. Buy 36 futures contracts
b. Short 36 futures contracts
c. Short 35 futures contracts
d. None of the above

6. You are managing a large pension fund, which has $150 million large cap position, with a beta of one. You want to create a synthetic cash position approximately equal to the value of $150 million. Three-month large- cap futures are currently at $1,250 with a multiplier of 250 and beta of one. The 3-month Treasury has a yield of 1.5%. Assume cash has a beta of zero. Determine the appropriate strategy for creating a synthetic cash position.
a. Short 480 futures contracts
b. Long 480 futures contracts

c. Short 482 futures contract
d. Long 482 futures contracts

7. You are the CIO (chief investment officer) of Flyers Endowment with $100 million of large-cap stocks (for example, S&P500 index stocks). You are becoming concerned about the relatively large exposure of the large-cap stocks. You decide to diversify your portfolio by shifting 18% of the large-cap stocks to mid-cap equities. Rather than to determine which stocks to sell and also try to avoid transaction costs, you decide to use futures contracts to achieve the diversification. Your research department has collected the following information for you:
- The current beta of the large-cap stocks is 0.85.
- The beta of mid-cap stocks on average is 1.26,
- The beta of the large-cap futures contracts is 0.78.
- The beta of the mid-cap futures contracts is 1.28.
- The large- and mid-cap futures prices are $395 and $260, respectively.
- , The multiples for the both large- and mid-cap futures contracts are 250.
- Cash beta is 0.
Determine the appropriate strategy to achieve your portfolio balance
a. Short 199 large-cap futures contracts and long 273 mid-cap futures contracts
b. Short 199 mid-cap futures contracts and long 273 large-cap futures contracts
c. Short 199 large-cap futures contracts and short 273 mid-cap futures contracts
d. None of the above

8. You have $200 million in T-bills with a yield of 1.5% and a beta of zero. For the next six months, you wish to have a synthetic large equity position approximately equal to this value and a beta of one. You choose S$P500 index futures, and the index has a dividend yield of 3% one year later. The future price is $1,000 and the multiple is $250, with a beta of one. Calculate the required number of contracts.
a. Short 804 contracts.
b. Short 805 contracts.
c. Long 806 contracts.
d. None of the above.

9. You are managing a bond portfolio with a value of $10 million and a holding period of one year. The 1-year total bond futures price is $102,510. The modified duration of the bond portfolio and futures contract are 1.793 and 1.62, respectively. The yield beta is 1.2. You want to increase your portfolio duration to 3. The correct statement is:
a. You want to increase your portfolio duration to 3 because most likely, you are expecting the stock market will go up.
b. You want to increase your portfolio duration to 3 because most likely, you are expecting the stock market will go down.
c. You want to increase your portfolio duration to 3 because most likely, you are expecting the interest rate will go up.
d. You want to increase your portfolio duration to 3 because most likely, you are expecting the interest rate will go down.

10. Go back to the above question. Calculate the number of bond futures contracts needed to increase the portfolio duration to 3.
a. Long 87 bond futures contracts.
b. Short 87 bond futures contracts.

c. Short 73 bond futures contracts.
d. None of the above.

11. The correct statement is
a. Based on the BSM formula, if So increases, other things being constant, the call price will increase and the put price will increase.
b. Based on the BSM formula, if X increases, other things being constant, the call price will increase and the put price will increase.
c. Based on the BSM formula, if r increases, other things being constant, the call price will increase and the put price will decrease.
d. Based on the BSM formula, if a increases, other things being constant, the call price will increase and the put price will increase.

12. On September 26 the spot price of wheat was $3.5225 per bushel. The interest forgone on money tied up in bushel until expiration is $0.04, and the cost of storing the whet is $0.0875 per bushel. What is the future price?
a. '3.64
b. 3.56
c. 3.61
d. 3.65

13. On a particular day, the September S&P 500 stock index futures was priced at 960. The S&P 500 index was at 956.49. The contract expires 73 days later. Assume the simple interest rate (not compounding interest rate) and the risk free rate is 5.96%, and the dividend yield on the index is 2.75% during the 73 days. What is the true/intrinsic value of this futures contract?
a. 966.09
b. 962.55
c. 973.18
d. None of the above

14. You are managing a $1 billion stock portfolio that tracks the S&P 500. You are concerned that the stock market will fall over the next year. A 1-year, quarterly equity swap is available from a dealer with a notional principal equal to the value of the portfolio and a fixed rate of 6.8%. If you enter the swap, then
a. You pay a quarterly return on your own portfolio to the dealer and receive 6.8% return of $1 billion from the dealer.
b. You receive a quarterly return on your own portfolio and also receive 6.8% return of $1 billion from the dealer.
c. You pay a quarterly return on your own portfolio to the dealer and receive 1.7% return of $1 billion from the dealer.
d. You pay a quarterly return on your own portfolio and receive $1 billion.

15. Based on the BSM formula, you estimate a call intrinsic value to be $8.647. The quoted call price is 8.13. The N(dl) = 0.583 and N(d2)=0.540. What are your actions that you can take?
a. Short 1000 calls and buy 583 shares of underlying stocks.
b. Buy 1000 calls and short 583 shares of underlying stocks.
c. Short 1000 calls and buy 540 shares of underlying stocks.
d. Buy 1000 calls and short 540 shares of underlying stocks

Calculation problems:
Problem 1 (8 points): Flyers Inc. is a US based firm and has entered into a contract to import £3 million worth of oilseed from SeedDepot Inc. in United Kingdom, and the spot rate is GBP/USD = 1.5772. Flyers will make the payment upon receipt of products 60 days later. Management of Flyers wants to hedge the risk associated with foreign currency. The 30-day forward rate is GBP/USD = 1.5558. The 60-day forward rate is GBP/USD = 1.5367. Determine the appropriate strategy to hedge the foreign exchange risk and explain. Discuss your liability when the contract matures.

Problem 2: You are the CFO of Flyers Inc . Your company has a 3-year, $15 million loan outstanding at a variable rate or LIBOR. You forecast that the interest rate in the US will be increasing in the near future and would like to refinance at a fixed rate for the next two years. You contact Goldman Sachs and the investment banker quotes you a 2-year plain vanilla interest rate swap, with the annual swap rate of 9,2%. Meantime, the investment bank has another client
Lakers Corp. enters the same swap contract, which receives 8.8% as a fixed swap rate and pays LIBOR. Lakers Corp. also has a debt outstanding of $15 million with a fixed interest rate of 9%. One year LIBOR is currently 8.1%.
(1) Draw the diagram to show how the swap works.
(2) Estimate your company's net borrowing cost.
(3) Estimate the net borrowing cost of Lakers Corp.
(4) Estimate Goldman Sachs's swap spread.

Problem 3: You are the CIO (chief investment officer) of UD Endowment with total $500 million assets under management. The asset mix of the endowment currently is 45% large-cap equities, 20% small-cap equities, and 35% bonds. UD Endowment expects a large donation of $80 million in two months from one of its generous alumni. The donor has specified that the asset allocation of his donation should be the same of UD Endowment - that is, 45% of $80 should be invested into large-cap equities, 20% into small-cap equities, and the reset into bonds.

You would like to use futures to make a pre-investing. Pre-investing is widely used to gain market exposure in anticipation of a certain amount of cash inflow. You will close out your futures positions when the anticipated donation is finally received. The donation will then be directly invested into the market according to the desired asset allocation. The following information has been provided to you.

	Large-cap equities	Small-cap equities	Large-cap futures	Small-cap futures	Cash
Beta     ,	0.95	1.58	1.10	1.45	0.10
Price	NA	NA	1,500	1,100	NA
Multiplier	NA	NA	250	250	NA
	Bond	Bond/Treasury futures (yield beta = 1.1)	NA	NA	Cash
Duration	5.9	5.4	NA	NA	0.15
Total price	NA	100,000	NA	NA	NA

Determine the appropriate strategy for pre-investing the $80 million of donation.

Problem 4: BSM option pricing model

C = S_oN(d₁) - Xe^-tN(d₂)

P = Xe^-r_cT[1- N(d₂)] - S₀[1 - N(d1)]

where

d₁ = ln (S₀/X) + (r_c + σ²/2)T/σ√T

d₂ = d₁ - σ√T

Textbook, Page 178, Problem 8 DCRB Option quote, 7/6.

		Calls			Puts
X	July	Aug	Oct	July	Aug	Oct
155	10.50	11.75	14.00	0.19	1.25	2.75
160	6.00	8.13	11.13	0.75	2.75	4.50
165	2.69	5.25	8.13	2.38	4.75	6.75
current stock price: 165.13
expirations: 7/17, 8/21, 10/16; the continuously compounded risk free rate with the expiration of 10/16 is 0.0571.

Hint: (1) from today 7/6 to 10/16 there are 102 days.

Assume the standard deviation of the continuously compounded return on the stock be 0.21. Use the BSM formula to estimate the true value for the October 165 PUT option (follow steps we have done on the class).

Determine the put is overpriced or underpriced. Estimate hedge ratio (a hedge ratio for a put = 1 - N(d1)). NO Need to discuss your actions.