Question

You buy a 6% semi-annual coupon-bond for $1122.47 with a one-year maturity. Six months later six-month rates are 5% (actually 2.5% return over a six-month period). Diagram the cash flows and calculate the actual realized return with coupon reinvested.

Answer 1

Assumed Bond Par Value = $ 1000, Bond's Purchase Price = $ 1122.47, Bond Tenure = 1 year or 2 six-month period, Bond Coupon = 6%, Coupon Frequency: Semi-Annual

Semi-Annual Coupon = 0.06 x 1000 x 0.5 = $ 30

Yield 6-month later = 5 % per annum

Therefore, Bond Sale Price = S = [Par Value + Coupon] (both at bond maturity 6-month later) / (1.025) = [1000+30]/(1.025) = $ 1004.878

Final Wealth Value at the end of first 6-months = Coupon Received + Sale Price = 30 + 1004.878 = $ 1034.878

Initial Investment = Bond Purchase Price = $ 1122.47

Therefore, Actual Realized Return = [(1034.878 - 1122.47) / 1122.47] x 100 = - 0.078 or -7.8 % over a 6-month period

Annualized Actual Return = - 7.8 x 2 = - 15.6 %