CFA Level 1 Bond Duration Change | Test Prep

Bond Duration Change Calculation

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Question

Consider an annual coupon bond with the following characteristics:

For a 75 basis point change in interest rates, the bond's duration is:

Answers

Explanations

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A. B. C. D.

B

Since the bond has an embedded option, we will use the formula for effective duration.(This formula is the same as the formula for modified duration, except that the "upper price bound" is replaced by the call price.) Thus, we only need to calculate the price if the yield increases 75 basis points, or 0.75%.

Price if yield increases 0.75%: FV =100, I/Y =7.25= 6.50 + 0.75, N =12, PMT =6.5, Compute PV = 94.12

The formula for effective -

jjoachim_SS15_1_C_j_duration

Where:

V-

= Call price/price ceiling

V+

= estimated price if yield increases by a given amount, y

V0 -

= initial observed bond price

y

= change in required yield, in decimal form

Here,effective duration = (101.75 "" 94.12) / (2 * 100 * 0.0075) = 7.63 / 1.5 =5.09 years.

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