Based on an 18-month, 8 percent (semiannual) coupon Treasury note selling at par. If interest rates increase by 20 basis points (i.e., ΔR = 20 basis points), use the duration approximation to determine the approximate price change for the Treasury note.

Question

Quizplus · Accepted Answer

We can use the duration approximation formula to estimate the price change:

Approximate price change = - Duration x ΔR x (Price / (1 + YTM/2))

Where Duration = (1/2) x (Time to maturity in years) x (1 + YTM/2)^(-1) = (1/2) x 1.5 x 0.98302 = 0.724
ΔR = 20 basis points = 0.20%
Price = 100 (since selling at par)
YTM = 0.08 = 8%

Plugging in these values, we get:

Approximate price change = - 0.724 x 0.002 x (100 / 1.04) = -0.017

So the approximate price change is -0.017, or $0.2672 per $100 face value. Therefore, the best choice is D.

Based on an 18-Month, 8 Percent (Semiannual) Coupon Treasury Note