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Topic: Forward rates and arbitrage 13) You are given the following information: at t = 0, the price of a 10-year zero coupon bond with FV = $5,000 is $3,500; the price of a 3-year zero coupon bond with FV = $10,000 is X; f3,12 = 6%. A bank is offering the following product: for every $0.60 that you give the bank at t = 10, the bank will give you back $1 at t = 15, or for every $0.60 that you borrow from the bank at t = 10, you will have to pay back $1 at t = 15. a) What should X be if there is no arbitrage? b) Suppose X were $5 less than your answer to part a. Describe how you would construct an arbitrage strategy. Assume that part of your strategy involves buying or selling $1 worth of the 10-year zero coupon bond, and also either buying or selling $1 worth of the 3-year zero coupon bond. Construct the arbitrage in such a way that your profit is realized at t = 15, and the net cash flows at all other points in time are 0. You must specify for f3,12 = 6% whether you are borrowing or lending at that rate, and how much. You must also specify how much you are borrowing or lending using the bank's product. Make sure to also specify for each bond if you are buying or shorting $1 worth of the bond. Finally, make sure to specify for each bond, how many units you are buying or selling. c) What is the magnitude of your arbitrage profit at t = 15? d) Repeat question b, but this time for 2 units of the 3-year bond bought or sold at t = 0. e) What is the magnitude of the arbitrage profit at t = 15 from part d? 14) (This question is from the 2016 Winter Final Exam. As long as you attempt all parts you will receive full credit.) Today is t = 0. The price of a Dollar denominated 10-year zero coupon bond with Face Value = $10,000 is $8,000 r0,5 = 2% (Dollar interest rate); f20,5 = 3% (Dollar forward interest rate) fE20,5 = 4% (Euro forward interest rate) Contract X: for every $1 you give the bank at t = 10 they give you back 2 Euros at t = 20 (or for every $1 you borrow at t = 10 you have to pay back 2 Euros at t = 20) Contract Y: for every $1 you give the bank at t = 0 they give you back K Euros at t = 25 (or for every $1 you borrow at t= 0 you have to pay back K Euros at t = 25) o 8 Note: for a given currency, a forward interest rate in that currency allows you to lock in a lending or borrowing rate for that currency for a certain period of time. a) Assuming there is no arbitrage, write down one equation where the only unknown is K? You do not need to solve or isolate for K. b) Suppose K were 2 less than implied by your answer to part a. Describe how you would construct an arbitrage where you realize the profit (in Euros) at t = 25. Assume that your arbitrage involves buying or shorting 3 units of the 10-year zero coupon bond. Make sure that for each rate you are using you specify if you are borrowing or lending, in what currency, and how much. Make sure that for each contract X, Y, that you use that you specify whether you are using it for lending or borrowing and for how much, and in what currency. You do not need to report the magnitude of the profit. Topic: Forward rates and arbitrage 13) You are given the following information: at t = 0, the price of a 10-year zero coupon bond with FV = $5,000 is $3,500; the price of a 3-year zero coupon bond with FV = $10,000 is X; f3,12 = 6%. A bank is offering the following product: for every $0.60 that you give the bank at t = 10, the bank will give you back $1 at t = 15, or for every $0.60 that you borrow from the bank at t = 10, you will have to pay back $1 at t = 15. a) What should X be if there is no arbitrage? b) Suppose X were $5 less than your answer to part a. Describe how you would construct an arbitrage strategy. Assume that part of your strategy involves buying or selling $1 worth of the 10-year zero coupon bond, and also either buying or selling $1 worth of the 3-year zero coupon bond. Construct the arbitrage in such a way that your profit is realized at t = 15, and the net cash flows at all other points in time are 0. You must specify for f3,12 = 6% whether you are borrowing or lending at that rate, and how much. You must also specify how much you are borrowing or lending using the bank's product. Make sure to also specify for each bond if you are buying or shorting $1 worth of the bond. Finally, make sure to specify for each bond, how many units you are buying or selling. c) What is the magnitude of your arbitrage profit at t = 15? d) Repeat question b, but this time for 2 units of the 3-year bond bought or sold at t = 0. e) What is the magnitude of the arbitrage profit at t = 15 from part d? 14) (This question is from the 2016 Winter Final Exam. As long as you attempt all parts you will receive full credit.) Today is t = 0. The price of a Dollar denominated 10-year zero coupon bond with Face Value = $10,000 is $8,000 r0,5 = 2% (Dollar interest rate); f20,5 = 3% (Dollar forward interest rate) fE20,5 = 4% (Euro forward interest rate) Contract X: for every $1 you give the bank at t = 10 they give you back 2 Euros at t = 20 (or for every $1 you borrow at t = 10 you have to pay back 2 Euros at t = 20) Contract Y: for every $1 you give the bank at t = 0 they give you back K Euros at t = 25 (or for every $1 you borrow at t= 0 you have to pay back K Euros at t = 25) o 8 Note: for a given currency, a forward interest rate in that currency allows you to lock in a lending or borrowing rate for that currency for a certain period of time. a) Assuming there is no arbitrage, write down one equation where the only unknown is K? You do not need to solve or isolate for K. b) Suppose K were 2 less than implied by your answer to part a. Describe how you would construct an arbitrage where you realize the profit (in Euros) at t = 25. Assume that your arbitrage involves buying or shorting 3 units of the 10-year zero coupon bond. Make sure that for each rate you are using you specify if you are borrowing or lending, in what currency, and how much. Make sure that for each contract X, Y, that you use that you specify whether you are using it for lending or borrowing and for how much, and in what currency. You do not need to report the magnitude of the profit