Question

Both Bond Sam and Bond Dave have 10 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 17 years to maturity. (Do not round your intermediate calculations.)

   

Requirement 1:

(a)	If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Sam?
	(Click to select)9.78% -10.54% -9.51% 10.85% -9.53%

    

(b)	If interest rates suddenly rise by 4 percent, what is the percentage change in the price of Bond Dave?
	(Click to select)42.28% -25.71% 29.71% -34.60% -25.69%

    

Requirement 2:

(a)	If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Sam be then?
	(Click to select)9.78% 10.88% 10.81% 10.83% -9.48%

    

(b)	If rates were to suddenly fall by 4 percent instead, what would the percentage change in the price of Bond Dave be then?
	(Click to select)42.24 % 42.26% 42.31% -25.66% 29.71%

Answer 1

In the question, initially both bonds are priced at par, so the YTM for both bonds = coupon rate = 10%.

Assume par value of both bonds to be $100.

Price of a bond is mathematically represented as:

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

For Bond Sam, C = 10/2 = 5 (semi-annual), n = 3 * 2 = 6 semi-annual periods, M = $100

For Bond Dave, C = 10/2 = 5 (semi-annual), n = 17 * 2 = 34 semi-annual periods, M = $100

a) When interest rates rise by 4%, YTM = 10% + 4% = 14%. i = 7% (semi-annually)

For Bond Sam,

P (Sam) = $90.47

% Change in price of Sam = (90.47 - 100)/100 = -9.53%

For Bond Dave,

P (Sam) = $74.29

% Change in price of Sam = (74.29 - 100)/100 = -25.71%

b) When interest rates fall by 4%, YTM = 10% - 4% = 6%. i = 3% (semi-annually)

For Bond Sam,

P (Sam) = $110.83

% Change in price of Sam = (110.83 - 100)/100 = 10.83%

For Bond Dave,

P (Sam) = $142.26

% Change in price of Sam = (142.26 - 100)/100 = 42.26%