Question

A 4 year maturity bond making annual coupon payments with a coupon of 8% has a duration of 3.607 years and a convexity of 16.08. The bond currently sells at a yield of 4%. What is the actual price of the bond if the YTM immediately increases to 6%? Round you answer to the nearest penny. Answer:

Answer 1

Price of bond before yield change = 80 × PVAF(4%,8years) + 1000 × PVF(4%,8years) = $1146.51

Here given duration is Macaulay duration.we find modified duration.

Modified duration = Duration / (1+y) = 3.607 / (1+0.04) = 3.4682692308.

% of price change = - modified duration × % of yield change + (1/2) × convexity × (% of yield change)²

= - 3.4682692308 × 2% + 0.5 × 16.08 × (0.02)²

= - 0.0693653846 +0.003216

=- 0.0661493846

% of price change = - 6.661493846%

Actual price after yield change = $ 1146.51 × (1 - 0.0661493846) = $ 1,070.6690690623.