Question

Tommy is examining some risk-free Singapore government securities. The yields to maturity on three government bonds with maturities of 1, 2 and 3 years are respectively 3%, 4% and 6%. The bonds all pay an annual coupon and have the same coupon rate of 1% and a face value of $1,000. (a) Calculate the prices of the three (3) bonds. (b) (i) Calculate the expected 1-year interest rate for year 2. (ii) Calculate the expected 1-year interest rate for year 3

Answer 1

(a) (i) Bond Face Value = $ 1000, Yield to Maturity = 3 %, Tenure = 1 year, Coupon Rate = 1 %

Annual Coupon = 0.01 x 1000 = $ 10

Bond Price = 10 x (1/0.03) x [1-{1/(1.03)^(1)}] + 1000 / (1.03) = $ 980.58

(ii) Bond Face Value = $ 1000, Yield to Maturity = 4 %, Tenure = 2 years, Coupon Rate = 1 %

Annual Coupon = 0.01 x 1000 = $ 10

Bond Price = 10 x (1/0.04) x [1-{1/(1.04)^(2)}] + 1000 / (1.04)^(2) = $ 943.42

(iii) Bond Face Value = $ 1000, Yield to Maturity = 5 %, Tenure = 3 years, Coupon Rate = 1 %

Annual Coupon = 0.01 x 1000 = $ 10

Bond Price = 10 x (1/0.05) x [1-{1/(1.05)^(3)}] + 1000 / (1.05)^(3) = $ 891.07

(b) 1-Year Spot Rate = r1 = 3% and 2-Year Spot Rate = r2 = 4 %

1-Year Spot Rate during Year 2 = [(1+r2)^(2) / (1+r1)] - 1 = [(1.04)^(2)/(1.03)] - 1 = 0.05 or 5 %

(c) 2-Year Spot Rate = r2 = 4 % and 3-Year Spot Rate = r3 = 5 %

1-Year Spot Rate during Year 3 = [(1+r3)^(3) / (1+r2)^(2)] - 1 = [(1.05)^(3)/(1.04)^(2)] - 1 = 0.07029 or 7.029% ~ 7.03 %