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 andhave the same coupon rate of 1% and a face value of $1,000.

1. Calculate the prices of the three (3) bonds.

2. (i)        Calculate the expected 1-year interest rate for year 2.

(ii)       Calculate the expected 1-year interest rate for year 3.

3. Tommy does not understand why yields differ among Singapore government securities and when compared to the yields on securities issued by other governments. Explain why this might be the case.

Answer 1

(a) Interest Rate: 3 - Year = 3%, 4 - Year = 4 % and 5 - Year = 6 %

Coupon Rate = 1 % and Face Value = $ 1000

Annual Coupon = 0.01 x 1000 = $ 10

Therefore, 1-Year Bond Price = (1000 + 10) / (1.03) = $ 980.58

2-Year Bond Price = 10 / (1.03) + 1010 / (1.04)^(2) = $ 943.51

3-Year Bond Price = 10 / (1.03) + 10 / (1.04)^(2) + 1010 / (1.06)^(3) = $ 866.97

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

1-Year Rate during Year 2 = f1 = [(1+r2)^(2) / (1+r1)] - 1 = [(1.04)^(2) / (1.03)] - 1 = 0.050097 or 5.0097 % ~ 5 %

(ii) 2-Year Spot Rate = r2 = 4% and 3-Year Spot Rate = r3 = 6%

1-Year Rate during Year 3 = f2 = [(1.06)^(3) / (1.04)^(2)] - 1 = 0.10116 or 10.116 % ~ 10.12 %

(c) Yields for bonds issued by the Singapore and other governments differ owing to the perceived default risk of the issuing government, the maturity risk and liquidity risk of the government's domestic market and the expected inflation in the issuer's home country.