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03rec2_exercise

# 03rec2_exercise - MIT Sloan School of Management J Wang...

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MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2003 Examples Sept 25, 03 1. (20 points) The Wall Street Journal gives the following bond prices: (Each bond has a principle of \$1,000.) Bond Maturity (years) Coupon rate (%) Price (\$) Spot Interest Rate (\$) 1 1 0.00 A 2% 2 2 2.00 1,000 B 3 3 C 1,000 4% (a) Calculate the price of the 1-year bond (A), the 2-year spot interest rate (B) and the appropriate coupon rate for the 3-year bond (C). (b) Calculate the forward rate from year 2 to year 3. Answer: A = 1 , 000 1 . 02 = 980 . 39 30 1 . 02 + 1030 (1+ B ) 2 = 1000 B = 2% 1000 C * ( 1 1 . 02 + 1 (1 . 02) 2 + 1 (1 . 04) 3 ) + 1000 (1 . 04) 3 = 1000 C = 3.92% f 2 = (1 . 04) 3 (1 . 02) 2 - 1 = 8 . 12% 2. (Gibbons) The following table provides some relevant information. For all of the fol- lowing bonds, you may assume that the face or par value is \$100.00. All the following bonds are constant coupon bonds where the next coupon is to be received in one year. The coupon payments are annual. if the coupon yield is 0, then that bond is a zero coupon instrument.

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Yield to Maturity Coupon Maturity Duration Price 1 0 5.00% 5 0 10.00% 10 0 15.00% 20 0 20.00% 30 0 20.00% 5 8.00% 9.65% 4.2868 93.6889 10 10.00% 13.07% 6.4384 83.3879 20 15.00% 14.35% 7.3859 104.2196 30 20.00% 14.42% 7.6859 138.0161 Consider an annuity where the annuity pays \$20 per year for 30 years. What is the
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