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Bond duration convexity practice problems (answers)

# Bond duration convexity practice problems (answers) -...

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UNIVERSITY OF ILLINOIS College of Business - Department of Finance Finance 300 (Financial Markets) Coupon Bond Prices & YTM Changes (Duration & Convexity) (t periods) Coupon (C\$) PV (C\$) Duration ( D i ) Convexity ( C i ) 1 \$30.00 \$29.41 0.0253 0.0506 2 \$30.00 \$28.84 0.0496 0.1487 3 \$30.00 \$28.27 0.0729 0.2916 4 \$30.00 \$27.72 0.0953 0.4764 5 \$30.00 \$27.17 0.1168 0.7006 6 \$30.00 \$26.64 0.1374 0.9616 7 \$30.00 \$26.12 0.1571 1.2570 8 \$30.00 \$25.60 0.1761 1.5845 9 \$30.00 \$25.10 0.1942 1.9417 10 \$30.00 \$24.61 0.2115 2.3267 11 \$30.00 \$24.13 0.2281 2.7373 12 \$30.00 \$23.65 0.2440 3.1716 13 \$30.00 \$23.19 0.2591 3.6276 14 \$30.00 \$22.74 0.2736 4.1036 15 \$30.00 \$22.29 0.2874 4.5979 16 \$30.00 \$21.85 0.3005 5.1088 17 \$30.00 \$21.42 0.3130 5.6347 18 \$30.00 \$21.00 0.3250 6.1741 19 \$30.00 \$20.59 0.3363 6.7256 20 \$30.00 \$20.19 0.3470 7.2878 Face Value = \$1,000.00 \$672.97 11.5679 242.9261 Bond Price (∑ PVCF) = \$1,163.51 ∑/2 = Duration (Years) ∑/4 =Convexity (Years 2 ) 7.859 75.459 Years to Maturity Coupon Rate Market Rate (YTM %) Current Yield Modified Duration Price Change (MD Only) Convexity Correction Price Change (MD +C.C.) -Duration/[1+y/n] + 1.00% YTM 1/2 *[Convexity/ (1+y/n) 2 ] + 1.00% YTM 10.00 6.00% 4.00% 5.16% -7.705% -\$89.65 36.264 -\$85.43

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Semi-Annual Coupon Bond Convexity \$400.00 \$600.00 \$800.00 \$1,000.00 \$1,200.00 \$1,400.00 \$1,600.00 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% Yield Estimate Actual Price Duration Only C.C. Estimate Actual Price Duration Only Estimate YTM % MD + CC Estimate Actual Price M. Duration Only Estimate 0.0% \$1,589.61 \$1,600.00 \$1,515.21 1.0% \$1,470.43 \$1,474.69 \$1,427.28 2.0% \$1,359.69 \$1,360.91 \$1,339.36 3.0% \$1,257.38 \$1,257.53 \$1,251.44 4.0% \$1,163.51 \$1,163.51 \$1,163.51 5.0% \$1,078.09 \$1,077.95 \$1,075.59 6.0% \$1,001.10 \$1,000.00 \$987.67 7.0% \$932.55 \$928.94 \$899.75 8.0% \$872.44 \$864.10 \$811.82 9.0% \$820.76 \$804.88 \$723.90 10.0% \$777.53 \$750.76 \$635.98 11.0% \$742.74 \$701.24 \$548.05 12.0% \$716.38 \$655.90 \$460.13 Face Value (FACE) Coupon Rate (CR) Market Rate (YTM) Maturity (t) # Coupons (n) \$1,000.00 6.00% 4.00% 10.00 Semi-Annual 1 2 3 [1 * 2] + 3 1/[1+YTM/n)^(t*n)] 1-[1/(1+YTM/n)^(t*n)] [C (\$)]/[YTM/n]
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