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Final 1 solution

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

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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%
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 will add your 1600 and go long X + 1600 of the 2-yr. Thus (X + 1600)/X = 5 X = 400 X + 1600 = 2000 3) (5 points, 5 mins) In general, what are three possible explanations for a market anomaly ? In other words, what are three possible reasons why one might observe that
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Final 1 solution - MGCR 341 Finance 1 Summer 2010 Vadim di...

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