Question

What is the total return of buying a 30 year treasury bond with 3% coupon now at a 4% yield, and selling it after 3 years at 4.5% yield (right after you get the 6th coupon payment), assuming you don't reinvest the coupons?

		-7.18%
		1.22%
		2.20%
		3.72%

Answer 1

Face Value of Bond = $ 1000, Current Tenure = 30 years or 60 half-years and Yield = 4 % per annum or 2 % per half-year

Coupon Rate = 3 %, Semi-Annual Coupon Payout = 1000 x 0.5 x 0.03 = $ 15

Current Buy Price = 15 x (1/0.02) x [1-{1/(1.02)^(60)}] + 1000 / (1.02)^(60) = $ 826.196

New Yield After 3 years = 4.5 %

New Price after 3 years = Sale Price = 15 x (1/0.0225) x [1-{1/(1.0225)^(54)}] + 1000 / (1.0225)^(54) (remaining tenure is 27 years or 54 half-years) = $ 766.911

Capital Gains = (766.911 - 826.196) = - $ 59.285 and Total Coupon Gain = 15 x 6 = $ 90

Total Net Gain = 90 - 59.285 = $ 30.715

Total Return = [30.715 / 826.196] x 100 = 3.717 % ~ 3.72 %

Hence, the correct option is (d)