Assignment 2 Solutions

Assignment 2 Solutions - MGCR 341: Finance 1 Summer 2010...

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MGCR 341: Finance 1 Summer 2010 Vadim di Pietro Assignment 2: Solutions Due date: Friday July 23 rd , by 9:00pm. You may slide the assignment under my office door (Room 504). If you can’t make it in to school on Friday, you may email your assignment to me, provided that I receive it by 9:00pm on Friday. Of course, you can also hand in your assignment in class on Thursday. Late assignments will not be accepted. Solutions will be posted online on Saturday July 24 th . Groups: You may work in groups of up to 3 students. Grading: You must show your work in order to receive credit for solutions, except where noted otherwise. 1) Topic: Bond Pricing Below are the prices of zero coupon bonds with face value of $1,000. Maturity Price 1-yr $950 2-yr $875 3-yr $820 4-yr $780 5-yr $600 a) Today is t = 0 . You know that you will want to borrow $50,000 at t = 2 , and borrow $20,000 at t = 4 , and pay back both these loans at t = 5 . Using only the above zero coupon bonds, how could you generate the desired cash flows (and zero cash flows at all other dates)? Specify how many units (fractional units are OK) of which of the above bonds will you buy/sell at t = 0 in order to lock in an amount of money you will owe at t = 5 ? (Note: You can only buy/sell bonds at t = 0.) You need to buy 50 2-yr bonds, and 20 4-yr bonds. These will generate cash flows of 50,000 and 20,000 at t = 2 and t = 4, respectively. The cost of buying these bonds is 50*875 + 20 *780 = 59,350. Since you don’t want to have any net cash flow at t = 0, you will fund the purchase of the 2-yr and 4-yr bonds by shorting 5-yr bonds. Each unit you short will raise 600. Thus you need to short 59,350/600 = 98.917 units of the 5-yr bonds in order to raise 59,350.
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b) How much money will you owe at t = 5 ? At t = 5, you will have to cover your short position in the 5-yr bonds. This will cost you 98.917*1000 = 98,917. 2) Topic: Bond Pricing You are given the following information: r 0,3 = 3%; f 3,2 = 5%; the price of a 10-yr zero-coupon bond with face value $1000 is $500. a) What is f 5,5 if there is no arbitrage? There are two ways you can transfer $1 from t = 0 to t = 10. The first strategy is buying $1 worth of the 10-yr zero coupon bond. The cost of the 10-yr bond is $500, for $1000 face value. That means $500 invested in the bond at t = 0 turns into $1000 at t = 10. Thus, $1 invested in the 10-yr bond turns into $2 at t = 10. The second way of transferring $1 from t = 0 to t = 10 is buy investing $1 at r 0,3 = 3% for 3 years, investing that money at f 3,2 = 5% for 2 years, and then investing that amount of money at f 5,5 for 5 years. The amount of money you will have at t = 10 from this strategy is (1+ 0.03) 3 (1+ 0.05) 2 (1 + f 5,5 ) 5 And since both strategies have to give you the same amount at t = 10 if there is no arbitrage we get that 2 = (1+ 0.03) 3 (1+ 0.05) 2 (1 + f 5,5 ) 5 f 5,5 = 10.67% b) If a bank were to quote you a forward interest rate of f 5,5 = 12%, explain how would you construct an arbitrage opportunity using only r
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Assignment 2 Solutions - MGCR 341: Finance 1 Summer 2010...

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