03-PS2-FI_sol

03-PS2-FI_sol - MIT Sloan School of Management J. Wang...

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Unformatted text preview: MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2003 Problem Set 2: Fixed-Income Securities Due: September 30, 2003 1. (i) Spot rate is the interest rate you get if you make a deposit today. (ii) Forward rate is the interest rate of a specified term, that starts at a specified time in the future. Spot rate can be thought as an average of the forward rate. (iii) Yield to maturity is a constant rate that if you use it to discount the bond, it will give you the cost. YTM does not give you the whole term structure, and it is different for different bonds, but it is an easy-to-quote number for a rough comparison between bonds. 2. A 3-year treasury bond has a face value of $1000 and annual coupon of 8%. The 1-year spot rate is r 1 = 2%, and the 1-year forward rates for the next two years are r 2 = 4% and r 3 = 5% (a) P = sumofPV s = 78 . 43 + 75 . 41 + 969 . 62 = $1 , 123 . 46 (b) YTM = 3.586% (c) 2-year spot rate = q (1 + 2%)(1 + 4%)- 1 = 2 . 995% 3-year spot rate = [(1 + 2%)(1 + 4%)] 1 3- 1 = 3 . 659% (d) This is due to no-arbitrage. To lock in the payment of the second year, deposit $75.41 into the 1-year spot rate and also enter into a (1-year) forward agreement of the amount $75 . 41 * 1 . 02 = $76 . 92. Then you receive $80 for sure at year 2. You can do the same to replicate the other two cashflows. Since we can use the spot rate and forward rates to replicate all cashflows of the T-bond, it provides sufficient information to price the bond....
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This note was uploaded on 01/19/2011 for the course 15 15.407 taught by Professor Wang during the Fall '03 term at MIT.

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03-PS2-FI_sol - MIT Sloan School of Management J. Wang...

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