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# Effective Bond Duration; effective convexity; price change

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Problem:

5.Calculate the effective duration of a bond to a 100 basis point change in interest rates with a 6-1/4 coupon, 10-years remaining to maturity, and an asking quote of 110.7811 (decimal, not 32nds).

Calculate the effective convexity to a 100 basis point change of the bond in Question 5.

Calculate the total percentage price change (duration and convexity) to a 65 basis point decrease in interest rates for the bond in Questions 5 and 6.

#### Solution Preview

Please refer attached file for complete description. Some of formulas may be missing here.

Solution:

Calculate the effective duration of a bond to a 100 basis point change in interest rates with a 6-1/4 coupon,
10-years remaining to maturity, and an asking quote of 110.7811 (decimal, not 32nds).

Face Value of bond=100
Price of bond Po=110.7811
Coupon rate 6.25% of face value=6.25
Time to maturity=10 years

Let us calculate YTM of a bond using IRR function in MS Excel

Year End Cash flow
0 -110.7811 (Price of bond)
1 6.25 Coupon payment
2 6.25 Coupon payment
3 6.25 Coupon payment
4 6.25 ...

#### Solution Summary

Solution describes the steps for calculating effective bond duration, effective convexity and total percentage price change.

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