Question

An investor buys a three year bond With a 9% coupon rate paid annualy The bonds yeld to-maturty is 6%. Assume a 4 basis point change in yeld to-maturty.

Step 1: Calculate PVO, PV- and PV to 6 decimal places per 100 of par value.
Step 2 What is the bond's approximate modified duration? (round your answer to 2 decimal places)

Answer 1

Step 1: Calculate the present value of the bond using the yield to maturity rate. Step 2: Calculate the approximate modified duration using the formula (PVO - PV+) / (2 * PVO * (∆YTM)).

Step-by-step explanation:

Step 1: To calculate the present value of the bond, we need to discount each cash flow at the yield to maturity rate. The coupon payment of 9% is received annually and the face value is received at the end of the third year.

PVO = (9 / (1 + 0.06)) + (9 / (1 + 0.06)^2) + (109 / (1 + 0.06)^3) = 8.491667 + 8.017921 + 90.532726 ≈ 106.042314

PV- = 106.042314 - 0.0004 * 106.042314 ≈ 105.997726

PV = PV- / 100 ≈ 1.059977

Step 2: To calculate the approximate modified duration, we need to use the following formula:

Modified Duration ≈ (PVO - PV+) / (2 * PVO * (∆YTM))

∆YTM = 0.0004, PVO = 106.042314, PV+ = 105.997726

Modified Duration ≈ (106.042314 - 105.997726) / (2 * 106.042314 * 0.0004) ≈ 0.0125309 ≈ 0.01 (approximate to 2 decimal places)