15b_duration_spread_sheet

15b_duration_spread_sheet - Consider 9% coupon bond at 8%...

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Consider 9% coupon bond at 8% interest then at other interest rates Present values at different interest rates PVs by BI cash pi(r=8%) cash x pi 7.70% 7.80% 7.90% 8.00% 8.10% flow 106.71 1 108.84 108.13 107.41 106.71 106.01 9 106.25 0.93 8.33 108.22 107.56 106.9 106.25 105.6 9 105.75 0.86 7.72 107.56 106.95 106.35 105.75 105.15 9 105.21 0.79 7.14 106.84 106.29 105.75 105.21 104.67 9 104.62 0.74 6.62 106.06 105.58 105.1 104.62 104.15 9 103.99 0.68 6.13 105.23 104.82 104.4 103.99 103.58 9 103.31 0.63 5.67 104.33 103.99 103.65 103.31 102.97 9 102.58 0.58 5.25 103.37 103.1 102.84 102.58 102.32 9 101.78 0.54 4.86 102.33 102.15 101.96 101.78 101.6 9 100.93 0.5 4.5 101.21 101.11 101.02 100.93 100.83 109 0 0.46 50.49 0 0 0 0 0 106.71 2.13 1.42 0.7 0 -0.7 0.02 0.01 0.01 0 -0.01 PV by dis price change from 8% 2.13 1.42 0.7 0 -0.7 price change per 10 basis point change from 8% 0.71 0.71 0.7 0 -0.7 duration and convexity at 8% interest (note: duration depends on interest rate) Small changes around ano period cash flow discountd disc*t* D/1.08 disc*cash* F/(1.08^2) iyr cash flow cash flow cash flow *t*(t+1) 1 9 8.33 8.33 7.72 16.67 14.29 1 2 9 7.72 15.43 14.29 46.3 39.69 0 3 9 7.14 21.43 19.85 85.73 73.5 0 4 9 6.62 26.46 24.5 132.31 113.43 0 5 9 6.13 30.63 28.36 183.76 157.54 0 6 9 5.67 34.03 31.51 238.2 204.22 0 7 9 5.25 36.76 34.04 294.08 252.13 0 8 9 4.86 38.9 36.02 350.09 300.15 0 9 9 4.5 40.52 37.52 405.2 347.4 0 10 109 50.49 504.88 467.48 5553.69 4761.39 0 sum 106.71 757.38 701.27 7306.03 6263.74 sum/PV 7.1 6.57 68.47 58.7 avg life mod dur avg life ^ 2 convexity first order approximate price change = (dPV/dr)(dr) -0.30% -0.20% -0.10% 0% 0.10% 0.20% 0.30% 0 0 0 0 0 0 0 dP 2.13 1.42 0.7 0 -0.7 -1.39 -2.08
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(dPV/dr)dr 2.1 1.4 0.7 0 -0.7 -1.4 -2.1 0.03 0.01 0 0 0 0.01 0.03 values of 1yr and 10 yr 7.70% 7.80% 7.90% 8.00% 8.10% 8.20% 8.30% 0.08 0.08 0.08 0.08 0.08 0.08 0.08 1-yr 0.93 0.93 0.93 0.93 0.93 0.92 0.92 1yr change 0 0 0 0 0 0 0 10-yr 0.48 0.47 0.47 0.46 0.46 0.45 0.45 10yr chang 0.01 0.01 0 0 0 -0.01 -0.01 what ratio of 1 yr treasuries to $100 face of 9% coupon ond? take ratio of derivatives, or ratio of avg 1yr ratio 817.97 10 yr ratio 163.51 dP bond dp 1yr 2.11 1.41 0.7 0 -0.7 -1.4 -2.1 dp 10yr 2.14 1.42 0.7 0 -0.7 -1.39 -2.07 1yr error 0.02 0.01 0 0 0 0.01 0.02 10yr error 0 0 0 0 0 0 0 pv 1 yr 759.49 758.78 758.08 757.38 756.68 755.98 755.28 p cash -650.67 -650.67 -650.67 -650.67 -650.67 -650.67 -650.67 sum 108.82 108.12 107.41 106.71 106.01 105.31 104.61 pv 10yr 77.87 77.15 76.44 75.74 75.04 74.35 73.67 cash 30.97 30.97 30.97 30.97 30.97 30.97 30.97 sum 108.85 108.13 107.41 106.71 106.01 105.32 104.64 second derivatives of first derivative matching portfolios portfolio second deriv 1 year 1298.66 9% bond 6263.74 10 year 7142.6 replicating first and second derivatives 1 yr bonds 123.02 10yr bonds 138.92 cash
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This note was uploaded on 12/08/2009 for the course ECON 251 at Yale.

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15b_duration_spread_sheet - Consider 9% coupon bond at 8%...

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