Question

Estimate the price change of a 150-bp increase and decrease on a 15-year, 7% coupon bond
currently trading at par. The bond has a modified duration of 9.115 and a convexity of 114.8.

Answer 1

% change in the price

= - Modified duration x Δi + 0.5 x Convexity x (Δi)²

= -9.115 x Δi + 0.5 x 114.8 x (Δi)²

= -9.115 x Δi + 57.40 x (Δi)²

Case 1: 150 bps increase

Δi = 150 bps = (150/100)% = 1.50%

Hence, % change in the price = -9.115 x 1.5% + 57.40 x (1.5%)² = -12.381%

If we assume the par value of the bond to be $ 1,000, then this will translate into:

price change = -12.38% x P0 = -12.38% x 1,000 = - $ 123.81

Case 2: 150 bps decrease

Δi = -150 bps = (-150/100)% = -1.50%

Hence, % change in the price = -9.115 x (-1.5%) + 57.40 x (-1.5%)² = 14.964%

If we assume the par value of the bond to be $ 1,000, then this will translate into:

price change = 14.964% x P0 = 14.964% x 1,000 = $ 149.64