B 4 You are a financial consultant on trades exploiting movements in the yield curve in...

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B 4 You are a financial consultant on trades exploiting movements in the yield curve in the US. You learn that US zero-coupon government bonds are selling for 95 cents per dollar of face value at a 1-year maturity, 88 cents per dollar at a 2-year maturity, and 85 cents per dollar at a 3-year maturity. (a) Calculate the log yields on zero-coupon bonds at 1-year, 2-year, and 3-year maturities. Calculate the forward rate for the one-year bond. Note: Use natural logarithms, not base-10 logarithms! (b) You find the 2-year bond to be attractive and you propose to your clients to buy $10 million of the 2-year bond and finance the position by shorting $10 million of the 1-year bond. Your client asks you to explain under what circumstances the trade will make money over the next year if you sell the 2-year bond next year. Write down the log return on your 2-year bond position in terms of bond yields prevailing now (time t) and a year from now (time t+1). What values for the 1-year interest rate, prevailing one year from now, will give you a profitable trade a year from now? Use the forward rate view of the expectations hypothesis to relate your answer to the forward rate you calculated in part a). (c) You put on the trade, but the next day it is revealed that the US government deficits are finally eroding the credibility that the US will repay all bonds in full and the log yields on government bonds of all maturities rise by 500 basis points. Calculate the new return of your trade (the value of the 2-year bonds you bought less the value of the 1-year bonds you sold). How much money have you made or lost? (d) Assume now that in addition to the zero-coupon bonds mentioned above there is also a 2-year bond available that pays a coupon of 3 cents each year and sells at par. Show that there are arbitrage opportunities. In this case, how much would you invest in this arbitrage strategy (assuming zero comissions on the part of the broker handling the short sale)? B 4 You are a financial consultant on trades exploiting movements in the yield curve in the US. You learn that US zero-coupon government bonds are selling for 95 cents per dollar of face value at a 1-year maturity, 88 cents per dollar at a 2-year maturity, and 85 cents per dollar at a 3-year maturity. (a) Calculate the log yields on zero-coupon bonds at 1-year, 2-year, and 3-year maturities. Calculate the forward rate for the one-year bond. Note: Use natural logarithms, not base-10 logarithms! (b) You find the 2-year bond to be attractive and you propose to your clients to buy $10 million of the 2-year bond and finance the position by shorting $10 million of the 1-year bond. Your client asks you to explain under what circumstances the trade will make money over the next year if you sell the 2-year bond next year. Write down the log return on your 2-year bond position in terms of bond yields prevailing now (time t) and a year from now (time t+1). What values for the 1-year interest rate, prevailing one year from now, will give you a profitable trade a year from now? Use the forward rate view of the expectations hypothesis to relate your answer to the forward rate you calculated in part a). (c) You put on the trade, but the next day it is revealed that the US government deficits are finally eroding the credibility that the US will repay all bonds in full and the log yields on government bonds of all maturities rise by 500 basis points. Calculate the new return of your trade (the value of the 2-year bonds you bought less the value of the 1-year bonds you sold). How much money have you made or lost? (d) Assume now that in addition to the zero-coupon bonds mentioned above there is also a 2-year bond available that pays a coupon of 3 cents each year and sells at par. Show that there are arbitrage opportunities. In this case, how much would you invest in this arbitrage strategy (assuming zero comissions on the part of the broker handling the short sale)?