1_FF_example.pdf

# 6 plot the total payoffs to b and p as a function of

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6. Plot the total payoffs to B and P as a function of S 1 with and without entering into the futures contract. Is hedging perfect? 7. What is the payoff to a speculator , who takes a short position on the futures contract in t=0 at the price F 0 with the contract size of 1,000 engines, and then settles it in cash in t=1 ? Fin330 29

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Hedging: Example (solution) 1. Without the futures, what is the payoff to P and B in t=1 ? P: ( S 1 -100)*1,000; B: (1,000- S 1 )*1,000. 2. What are the payoffs to P and B per engine from entering into a futures contract, which is settled in cash in t=1 ? P: F 0 - S 1 =400- S 1 ; B: S 1 - F 0 = S 1 -400. Total payoffs: P: (400- S 1 )*1,000; B: ( S 1 -400)*1,000. Observe that the total payoff (P+B) sums up to 0 because entering into a futures contract is a zero-sum game. Fin330 34
Hedging: Example (solution) 3. Would payoffs in (2) be different if each party would offset the futures position instead of settling it in cash? P: F 0 -F 1 =F 0 - S 1 =400- S 1 ; B: S 1 - F 0 = S 1 -400 l Payoffs are the same! l Because at maturity the spot price, S 1 , must equal to the futures price, F 1 , in order to avoid arbitrage.

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• Spring '16
• Chang
• Hedging, producer, \$100, \$400, 1 \$

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