Question

Bond Dave has a 8 percent coupon rate, makes semiannual payments, a 4 percent YTM, and 25 years to maturity. If interest rates suddenly rise by 1 percent, what is the percentage change in the price of Bond Dave? Enter the answer with 4 decimals (e.g. 0.0123).

Answer 1

Price of a bond is mathematically represented as:

where P is price of bond with periodic coupon C, n periods to maturity, M face value, and periodic YTM i.

For this question,

M = $1000, n = 25 * 2 = 50 semi-annual periods, i = 4%/2 = 2% (semi-annual), C = 8%/2 * $1000 = $40 (semi-annually)

P = 1256.94 + 371.53

P = $1,628.47

When YTM = 4% + 1% = 5%

i = 2.5% (semi-annually)

P = 1,134.49 + 290.94

P = $1,425.43

% change in price of bond = (1,425-43 - 1,628.47)/1,628.47 = -12.4680%