A 15-year to maturity bond with a face value of $1000, coupon of 6%, paid annual
ID: 2750782 • Letter: A
Question
A 15-year to maturity bond with a face value of $1000, coupon of 6%, paid annually, is priced at 97 (% of face value).
Consider a 20 basis point increase in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond? Consider a 200 basis point increase in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond? Vice versa, consider a 20 basis point decline in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond? Consider a 300 basis point decrease in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond?
Explanation / Answer
Coupon rate 6% YTM formula = {Interest payment+(Face value-Market price)/Years to maturity}/(face value+2*market price)/3 Discount rate =YTM ? YTM =[60+(1000-970)/15]/(1000+970*2)/3 = Face Value 1,000 YTM =6.33% Current Price 970 Yers to maturity 15 Period Cash Flow Dsicount Factor @6.33% PV of cash flows PV*Period 1 60 0.9405 56.43 56.43 2 60 0.8845 53.07 106.14 3 60 0.8318 49.91 149.73 4 60 0.7823 46.94 187.75 5 60 0.7357 44.14 220.72 6 60 0.6919 41.52 249.10 7 60 0.6507 39.04 273.31 8 60 0.6120 36.72 293.76 9 60 0.5756 34.53 310.81 10 60 0.5413 32.48 324.78 11 60 0.5091 30.54 335.99 12 60 0.4788 28.73 344.72 13 60 0.4503 27.02 351.21 14 60 0.4235 25.41 355.71 15 1,060 0.3983 422.15 6,332.28 969 9,892 Total Macaulay's Duration = 10.21 Years Normal Duration= 9.60 Years % change in price= -Duration *% change in interest 20 basis point=0.20% increase in YTM will result is -9.6*0.20 = 1.92% decrease in in Bond price Period Cash Flow Dsicount Factor @6.53% PV of cash flows PV*Period 1 60 0.9387 56.32 56.32 2 60 0.8812 52.87 105.74 3 60 0.8271 49.63 148.89 4 60 0.7764 46.59 186.35 5 60 0.7289 43.73 218.66 6 60 0.6842 41.05 246.30 7 60 0.6422 38.53 269.74 8 60 0.6029 36.17 289.38 9 60 0.5659 33.96 305.60 10 60 0.5312 31.87 318.74 11 60 0.4987 29.92 329.12 12 60 0.4681 28.09 337.03 13 60 0.4394 26.36 342.74 14 60 0.4125 24.75 346.48 15 1,060 0.3872 410.42 6,156.28 950.26 9,657 Earlier price 970 Current price 950 Reduction 2.0% So Actual price decrease in bond is 2% % change in price= -Duration *% change in interest 200 basis point=2% increase in YTM will result is -9.6*2 = 19.2% decrease in in Bond price Period Cash Flow Dsicount Factor @8.33% PV of cash flows PV*Period 1 60 0.9231 55.39 55.39 2 60 0.8521 51.13 102.25 3 60 0.7866 47.20 141.59 4 60 0.7261 43.57 174.27 5 60 0.6703 40.22 201.08 6 60 0.6187 37.12 222.75 7 60 0.5712 34.27 239.89 8 60 0.5272 31.63 253.08 9 60 0.4867 29.20 262.82 10 60 0.4493 26.96 269.57 11 60 0.4147 24.88 273.72 12 60 0.3828 22.97 275.64 13 60 0.3534 21.20 275.65 14 60 0.3262 19.57 274.03 15 1,060 0.3011 319.21 4,788.13 804.52 7,810 Earlier price 970 Current price 805 Reduction 17.1% So Actual price decrease in bond is 17.1% % change in price= -Duration *% change in interest 20 basis point=0.20% decrease in YTM will result is -9.6*-0.2 = 1.92% increase in in Bond price Period Cash Flow Dsicount Factor @6.13% PV of cash flows PV*Period 1 60 0.9387 56.32 56.32 2 60 0.8845 53.07 106.14 3 60 0.8334 50.00 150.01 4 60 0.7853 47.12 188.46 5 60 0.7399 44.39 221.97 6 60 0.6972 41.83 250.98 7 60 0.6569 39.41 275.90 8 60 0.6190 37.14 297.10 9 60 0.5832 34.99 314.93 10 60 0.5495 32.97 329.71 11 60 0.5178 31.07 341.74 12 60 0.4879 29.27 351.27 13 60 0.4597 27.58 358.56 14 60 0.4331 25.99 363.84 15 1,060 0.4081 432.61 6,489.20 983.77 10,096 Earlier price 970 Current price 984 Increase 1.4% So Actual price increase is 1.4% % change in price= -Duration *% change in interest 300 basis point=3% decrease in YTM will result is -9.6*-3 = 28.8% increase in in Bond price Period Cash Flow Dsicount Factor @3.33% PV of cash flows PV*Period 1 60 0.9678 58.07 58.07 2 60 0.9366 56.20 112.39 3 60 0.9064 54.38 163.15 4 60 0.8772 52.63 210.53 5 60 0.8489 50.94 254.68 6 60 0.8216 49.29 295.76 7 60 0.7951 47.71 333.94 8 60 0.7695 46.17 369.34 9 60 0.7447 44.68 402.12 10 60 0.7207 43.24 432.40 11 60 0.6974 41.85 460.31 12 60 0.6750 40.50 485.98 13 60 0.6532 39.19 509.51 14 60 0.6322 37.93 531.02 15 1,060 0.6118 648.50 9,727.49 1,311.27 14,347 Earlier price 970 Current price 1,311 Increase 35.2% So Actual price increase is 35.2%
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