03-PS2-FI - MIT Sloan School of Management J. Wang 15.407...

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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. Explain the terminology and the differences between (i) spot interest rate (ii) forward rate and (iii) yield to maturity. 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) Compute the price of the t-bond? (b) Calculate the YTM of the t-bond. (c) Calculate the 2- and 3-year spot interest rates. (d) We do not know for sure that the interest rate in one year will be 4%. Explain, in details, why the forward rates provide sufficient information for us to compute the price of the bond. (e) Explain why the answer in part (d) applies to t-bond but not corporate bonds. 3. (Deriving the yield curve from treasury bonds)From the Wall Street Journal, September 15 issue, the following treasury bonds trade at the prices below: Coupon Maturity Ask Price 4.75 Feb 2004 101.53125 2.125 Aug 2004 100.96875 7.5 Feb 2005 108.71875 6.5 Aug 2005 109.28125 5.625 Feb 2006 108.90625 2.375 Aug 2006 100.625 6.25 Feb 2007 112.5 3.25 Aug 2007 102.125 3 Feb 2008 100.375 3.25 Aug 2008 100.625 We will try to re-create the yield curve by looking at the prices of some t-bonds. We will still make some simplifying assumptions: There are 30 days for each month, and each bond in the table makes semi-annual payments on the 15th of February and August. (notice the coupon rate above are annualized; you only receive half of that each time a coupon is paid) 1 (a) The quoted price of the bond is often called the Clean Price (or quoted price)....
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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 - MIT Sloan School of Management J. Wang 15.407...

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