FBE459_Spring06_Midterm_SOLUTIONS

FBE459_Spring06_Midterm_SOLUTIONS - FBE459: Financial...

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FBE459: Financial Derivatives Solutions to Spring 2006 Midterm Exam 1. (20 points) Suppose you are a dealer in S&R stock index forwards. The S&R index spot price is standing at 400, the riskfree interest rate is 10% per year (with continuous compounding) and the dividend yield on this stock index is 4% per year. 1.a. (5 points) What should be the forward price for a contract deliverable in four months? Do you think this market is an example of contango or backwardation? SOLUTION: The arbitrage-free forward price is: F 0,4M = S 0 .e (r-q).T = 400.e (0.10-0.04).4/12 =408.0805 At current market conditions, you would conclude that Forward Prices (F 0,T ) > Spot (S 0 ) for all maturities (T). Thus this market is in CONTANGO. 1.b. (5 points) Another market participant quotes you the 4-month S&R forward at 410. What arbitrage opportunities exist? SOLUTION: The actual futures price is above the arbitrage-free value of 408.08, thus the index forward is too high relative to the underlying index. The correct arbitrage strategy is: - “Buy low”: Buy the shares underlying the index by borrowing money - “Sell high”: Sell the forward contract Outlining the arbitrage strategy would be enough for your answer, but here are the arbitrage profits you can make: Today In 4 months, Forward is settled Buy S Borrow PV(F) Borrow PV(D) -400 +410e -0.10.4/12 = +396.56 +400[e q.4/12 -1] e -0.10.4/12 = +5.193 S T +Div = S T +400[e q.4/12 -1] = S T +5.369 -410 - Div = -400[e q.4/12 -1] = -5.369 Short F 0 410 – S T Profit +1.752 0
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FBE 459 Midterm Exam: Spring 2006 [SOLUTIONS] Page 2 1.c. (5 points) Suppose a customer wishes to enter a long index forward contract. If you sell him the contract, outline how you would hedge your resulting short forward position by using the S&R index and any borrowing or lending? SOLUTION: To hedge a short forwards position you would take the same position when shorting the forwards in an arbitrage strategy [as in question 1.b)]. The hedge strategy when you sell sell the forward contract is: - Buy the shares underlying the index + Borrowing money 1.d. (5 points) Suppose you enter a short position in the forward contract at the “fair” price you determined in part a. above. Two months later, the S&R stock index spot price is at 405 and the risk-free interest rate is still 10%. What should be the S&R forward price prevailing at that time? What would be the value of your short forward position? SOLUTION: The new arbitrage-free forward price is: F 2M,4M = S 2M .e (r-q).T = 405.e (0.10-0.04).2/12 =409.0703 Since the forward price has gone up, we expect to be loosing money on a short forward position. The rationale is that we agreed to sell the asset in 4M at F 0,4M = 408.08 when now the “fair” would have been F 2M,4M =409.07. To calculate the value (now in 2M) of the old
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FBE459_Spring06_Midterm_SOLUTIONS - FBE459: Financial...

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