Final 1 solution - MGCR 341: Finance 1 Summer 2010 Vadim di...

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MGCR 341: Finance 1 Summer 2010 Vadim di Pietro Sample Final Student Name:____________________________________ Student Number:__________________________________ Time: Do not turn past this page until the exam has begun. The exam will be 175 minutes in length, from 6:05pm to 9:00pm . Show your work: In order to receive credit for your answers, you must show your work. Correct answers with no work shown will not receive any credit. Incorrect answers with partial correct work may receive partial credit. The exception to this rule is the True or False section, where no explanations are required. Answer questions directly on the exam sheet. If you need more space, use the back side of the pages. Formula sheet: The exam is closed book, and you may not bring any notes into class. A formula sheet is provided on the last 2 pages of this exam. You may detach the formula sheets if you like. You do not need to hand in the formula sheets at the end of the exam. Calculator: You are allowed a non-programmable calculator with nothing stored in memory. This exam has a total of 10 pages, including the cover page and formula sheets. The exam is worth a total of 100 points. GOOD LUCK!
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1) (10 points, 15 mins) You are given the following information about several coupon paying bonds. Bond A Face value = 100 Maturity = 2 years Coupon rate = 10% YTM = 8% Bond B Face value = 500 Maturity = 1 year Coupon rate = 5% Price today = 470 Bond C Face value = 800 Maturity = 3 years Coupon rate = 0% YTM = 9% Based on the above information, what is the price of a 3-year , 2% coupon bond, with face value $100 ? The price of the bond is given by P = 2/(1+r 1 ) + 2/(1+r 2 ) 2 + 102/(1+r 3 ) 3 So we need to use the above info to get r 1 , r 2 , and r 3 From bond B we know that 470 = (500 + 500(5%))/(1+ r 1 ) r 1 = 11.70%
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From bond A we know that P A = 10/1.08 + 110/1.08 2 = 103.57 But this is also equal to 103.57 = 10/(1+ r 1 ) + 110/(1+ r 2 ) 2 Since we already know r 1 , the above has only one unknown and thus r 2 = 7.82% Finally, since Bond C is a 3-yr zero coupon bond, its YTM is equal to r 3 . r 3 = 9% And thus P = 2/(1+r 1 ) + 2/(1+r 2 ) 2 + 102/(1+r 3 ) 3 = 82.27 2) (5 points, 5 mins) Suppose the yield curve is flat at 3% . You expect the curve to steepen but have no view on the level of rates. You have $1,600 , and can go long or short either a 2-yr coupon paying bond, which has a duration of 1.5 years, or an 8-yr coupon paying bond, which has a duration of 7.5 years. Set up a position that will profit if the curve steepens, and lose money if the curve flattens (i.e., becomes inverted). Base your calculations on the modified duration approximation. If you believe the curve will steepen, then you need to go long the 2-yr bond, and short the 8- yr bond. The ratio of the bond price sensitivities to changes in interest rates is given by the ratio of the bonds’ modified durations. Thus, you need to go long 5 times more of the 2-yr than you go short of the 8-yr.
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Let X equal how much you short of the 8-yr. With the proceeds, X, of this short sale, you
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This note was uploaded on 08/31/2010 for the course MANAGEMENT MGCR 341 taught by Professor Jassim during the Summer '09 term at McGill.

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Final 1 solution - MGCR 341: Finance 1 Summer 2010 Vadim di...

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