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Calculate the MacCaulay Duration for a $1$ year fixed rate coupon bond paying $6$ % semiannually. You know that the yield of the bond is $6.72$ %.

$D_{mac}= \frac{\frac{(0.5)(1.5)}{1.0336}+\frac{(1)(1.5)}{1.0336^2}+\frac{(100}{1.0336^2}}{1.5 [\frac{1-(1.0336)^{-2}}{0.0336}]+\frac{100}{1.0336^2}}$

$D_{mac}=\frac{95.733808}{96.459}=0.9924$

But the answer is $0.9854$

Tosh
  • 1,614

1 Answers1

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$\begin{matrix}\text{period} &\text{cash flow} &\text {discount rate} & NPV & \text {Time weighted NPV}\\ 0.5&0.03&(1.0336)&\frac {0.03}{1.0336}&\frac{0.5(0.03)}{1.0336}\\ 1&1.03&(1.0336)^2&\frac{1.03}{(1.0336)^2}&\frac{(1.03)}{(1.0336)^2}\\ \text{Net}&1.06&&0.99315&0.9786 \end {matrix}$

Macauley duration $= \frac {\text{Time weighted NPV}}{NPV} = \frac{0.9786}{0.99315} = 0.9854$

Doug M
  • 57,877