Homework 4 fx

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University of Texas, Dallas *

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6360

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Finance

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Feb 20, 2024

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Homework 4 1. If the spot exchange rate between US dollar and Japanese Yen is 100 Yen per dollar and the three- month forward rate is 110 Yen per dollar, can you tell which country has higher interest rate, U.S. or Japan? Explain your answer. S (0) = 1/100 US equivalent F (0,3) = 1/110 US$ equivalent F (0,3) = S (0) *(1+R)/(1+Rf) 1/110=1/100*(1+R)/(1+Rf) 100/110 = (1+R)/(1+Rf) (1+R)/(1+Rf) <1, therefore, R < Rf Japan has a higher interest rate since we need 100 Yen to exchange to US$1 equivalent at the spot rate, while the three-month forward rate is 110 Yen to exchange to equivalent US$1,which means Japanese Yen is depreciated, also indicating higher interest rate is associated with Japanese Yen. 2. If the spot price is higher than the 3-month futures price in the heating oil market and the cost of carry for the futures is 3%, should the convenience yield be higher than 3%? You can use either simple rate or continuous compounding. S (0)>F (0,3) Cost of carry: 3% Cost of carry = r + u - δ y=convenience yield F (t, T) = [ S (t)+U] ∙ e^(r−y) (T −t) = S (t) e^(r+u−δ−y) (T −t) The convenience yield should be higher than 3%. According to the lecture slides, when the spot price is higher than the forward price, the market is in backwardation. Based on the formula, we can derive that when the S(t) is higher than F(t,T), which means the e ^(r+u−δ−y) should be lower. Specifically, when the convenience yield is greater than cost of carry, we would have lower value of e that makes F(t, T) is smaller than S(t). 3. The spot price of the S&P 500 index is currently at 1200 per share and the 6-month futures price is 1250. The interest rate is 4% per annum and the dividend yield is 5% per annum. You can use either simple rate or continuous compounding. (a) How many shares of index are needed to buy now to generate 100 shares in 6 months? (b) Is there an arbitrage opportunity? If so, provide an arbitrage trading strategy in the cash flow table. $1,200 * (1+4%)/(1+5%)=$1,188.57< actual future price $1,200 Transactions Cash flow at 0 Cash flow at 6-month Short Futures (1.025 shrs) 0 1.025*($1,250- S(t)) Long Spot (1 shrs) -$1,200 1.025*S(t) Money mkt $1,200 -1.02*$1,200 1
Net 0 1.025*$1,250-1.02*$1,200 (=$57.25) 4. The spot Dollar-GBP sterling exchange rate is $1.80 per pound. The U.S. and U.K. 1-year simple interest rates are 4% and 2% respectively. The futures price for delivery in one year is $1.86 per pound. Compute the arbitrage-free futures price and provide an arbitrage trading strategy in the following table. Transactions Payoff at 0 Payoff in 1 year Long GBP Spot (1.04 p) -$1.80 1.02*S(t) Short GBP Futures 0 1.02*($1.86-S(t)) Money mkt $1.80 -1.04*$1.80 Net 0 1.02*$1.86-1.04*$1.80 (=0.0252) 2
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