Investment Horizon, Macaulay Duration, and Interest Rate Risk

A bond investor plans to retire in 12 years and, therefore, invests USD 250,000 in bonds with the same maturity. The bonds provide 6% annual coupons and are currently priced at par. Which of the following is _closest_ to the duration gap for the investor?

Correct. First, calculate the Macaulay duration using the formula: $$\displaystyle \text{MacDur} = \frac{1+r}{r} - \frac{1+r+[N \times (c-r)]}{c \times \left[ (1+r)^N - 1 \right] + r} - \frac{t}{T} $$ The bonds are selling at par. Therefore, the yield-to-maturity is the same as the coupon rate: $$\displaystyle \text{MacDur} = \frac{1 + 0.06}{0.06} - \frac{1 + 0.06 + [12(0.06 - 0.06)]}{0.06[(1 + 0.06)^{12} - 1] + 0.06} - \frac{0}{1} \approx 8.89$$ Finally, the duration gap = $$8.89 - 12 = -3.11$$.

Incorrect. The answer choice appears to compare the investment horizon to modified duration, which is not correct.

Incorrect. Here, the investor has an investment horizon of 12 years and the maturity of the bonds is 12 years. However, duration gap does not compare the yields to maturity to the investor's investment horizon.

–3.62 years

–3.11 years

0 years