Question

Suppose that at t=0, you purchase a six year, 8% coupon bond paid annually that is priced to yield 9%. The face value of the bond is $1000.

a) What will be your holding period return if you decide to hold the bond til its maturity and the market interest rate remains constant at 9% throughout your holding period of 6 years? b) What will be your holding period return if you decide to hold the bond til its maturity, but the market interest rate decreases to 8% during the first year of your bond purchase and it remains at that level for the next 5 years?

Answer 1

(a) Bond Tenure = 6 years, Coupon Rate = 8%, Yield = 9% and Face Value = $ 1000,

As the market interest rate remains constant at 9 % throughout the bond's tenure of 6 years, the bond's effective holding period return should equal this yield of 9%.

(b) In this scenario, the initial applicable market interest rate on the bond is 9% and the same changes to 8 % at the end of Year 1. It remains at this level for the next 5 years.

Bond Tenure = 6 years, Face Value = $ 1000, Yield = 9% and Coupon Rate = 8%

Annual Coupons = 0.08 x 1000 = $ 80

Bond Price = 80 x (1/0.09) x [1-{1/(1.09)^(6)}] + 1000 / (1.09)^(6) = $ 955.14

If the market interest rate goes down to 8% at the end of Year 1, the bond coupons are assumed to be reinvested at this applicable rate of 8%.

Therefore, Reinvestment Value of Coupons at Maturity = 80 x (1.08)^(5) +...................+ 80 = 80 x [{(1.08)^(6)-1}/{(1.08)-1}] = $ 586.87

Redemption Value at Maturity = Face Value = $ 1000

Total Final Wealth Value = 1000 + 586.87 = $ 1586.87

Holding Period Return = [(1586.87/955.14)^(1/6)-1] = 0.08829 or 8.829 % ~ 8.83 %