Question

A five-year 2.4% defaultable coupon bond is selling to yield 3% (Annual Percent Rate and semi-annual compounding). The bond pays interest semi-annually. The risk-free yield is 2.4%. Therefore, its current credit spread is 3% -2.4% = 0.6%. Two years later its credit spread increases from 0.6% to 1% while the risk-free yield doesn’t change. Assuming the face value of the coupon bond and risk-free bond is 100.

a)What is the return of investing in this bond over the two year?

Answer 1

Semi annual coupon = 100 *2.4%/2 = 1.2

No of coupons = 5*2 = 10

Semiannual yield = 3%/2 = 1.5%

So, Price of the bond = 1.2/0.015*(1-1/1.015^10)+100/1.015^10 = 97.2333

So, today the bond can be purchased at 97.23

After two year, semiannual yield of the bond = (2.4%+1%)/2 = 1.7% and there are 6 coupon payments remaining

So, price of bond after two years = 1.2/0.017*(1-1/1.017^6)+100/1.017^6 = 97.1707

Bond is sold after two years at 97.17

Semiannual Holding period return (r) is given by

1.2/r*(1-1/(1+r)^4) + 97.17/(1+r)^4 = 97.23

Solving for r, we get

r = 0.0121833

So , annual return of investing in this bond over the two year period = 0.0121833 * 2 = 2.4366%