Question

Calculate the realized compound yield for a 10 percent bond with 20 years to maturity and an expected reinvestment rate of 8 percent.

Answer 1

Let's assume bond par value is $1,000 and interest is paid semi-annually.

realized compound yield = (bond proceeds/par value)^{1/(maturity*2)} - 1

bond proceeds = total coupon received with reinvestment return + par value

semi-annual coupon will be $1,000*10%/2 = $50 and there will be 40 semi-annual coupon payment.

Future value of coupon payments @ 8% reinvestment rate = PV*[(1+reinvestment rate/2]^maturity*2 - 1]/(reinvestment rate/2) = $50*[(1+0.08/2)^20*2 - 1]/(0.08/2) = $50*[(1+0.04)⁴⁰ - 1]/0.04 = $50*[(1.04⁴⁰) - 1]/0.04 = $50*(4.8010206279366502738209561852126 - 1)/0.04 = $50*(3.8010206279366502738209561852126/0.04) = $50*95.02 = $4,751

bond proceeds = $4,751 + $1,000 = $5,751

realized compound yield = ($5,750/$1,000)^1/(20*2) - 1 = 5.751^1/40 - 1 = 5.751^0.025 - 1 = 1.0447 - 1 = 0.0447

0.0447 is semi-annual. annual realized compound yield = 0.0447*2 = 0.0894 or 8.94%

realized compound yield is 8.94%.