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Risk ModelingThe deadline is Sunday,December 11th, 20111. Consider a futures contract to purchase a coupon-bearing bond whose current price is $875. The futures contract matures in 15 months and the bond matures in 4 years. The bond holder receives an annual coupon of $60 paid semiannually and the next coupon will be paid in 3 months. Thus, if we want to take a long position in the futures on this bond we will have to take into account three coupons until the maturity of the futures (the last coupon will be paid immediately prior to the delivery date). We can borrow and lend money at the following continuously compounded interest rates:•R3 = 7% per annum for 3 months•R9 = 9% per annum for 9 months•R10 = 10% per annum for 10 months•R15 = 11% per annum for 15 months Assume that the futures price and the spot price follow the futures-spot parity condition.a)If the futures price is $905 will you be able to benefit from these prices? If a profit is possible then present the strategy that you can use to obtain this profit.b)What if the futures price is $910? Can you make any profit? Explain how.2. Consider the following prices of the stock and the futures at the end of the one month. monthspot pricesfutures prices112.00015.000212.02915.021312.04915.056412.00515.010512.01315.011612.03915.055712.02015.026812.01015.000912.00314.9711012.04615.0191112.05715.0131212.02114.9771312.00314.9661412.01214.9851511.98014.9581612.00314.987Compute the optimal number of futures contracts that is needed for the best hedge, considering that you are long on the spot market and you wish to sell your stock in 1 month.What can you say about the hedge effectiveness?Describe how you obtained the hedge ratio. Who is your independent variable?
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