an investor buys a three-year bond with a 5% coupon rate paid annually. The bond, with a yield-to-maturity of 3%, is purchased at a price of 105.657223 per 100 of par value. Assuming a 5-basis point change in yield-to-maturity, the bond's approximate modified Duration is closest to:

Question

Quizplus · Accepted Answer

First, we need to calculate the bond's present value factor:

PV Factor = (1 + Yield) ^ (-Number of periods) = (1 + 0.03) ^ (-3) = 0.942596

Next, we can calculate the bond's full price:

Full Price = Annual Coupon Payment x PVIFA(Yield, Number of periods) + Par Value x PV Factor
Full Price = 5 x 2.870772 + 100 x 0.942596
Full Price = 18.539352 + 94.2596
Full Price = 112.798952

The bond's modified duration can then be calculated as:

Modified Duration = (-1 / Full Price) x [PVIFA(Yield + 0.0005, Number of periods) - PVIFA(Yield - 0.0005, Number of periods)]
Modified Duration = (-1 / 112.798952) x [2.827275 - 2.91457]
Modified Duration = (-0.008859) / (112.798952)
Modified Duration = -0.0000785 or approximately 2.78

Therefore, the closest choice is A.

An Investor Buys a Three-Year Bond with a 5% Coupon