The spot rate for three hypothetical zero-coupon bonds (zeros) with maturities o

Question

The spot rate for three hypothetical zero-coupon bonds (zeros) with maturities of one, two and three years are given in the following table (based on annual compounding).

Maturity(T)

1

2

3

Spot rates

r(1)=11%

r(2)=10%

r(3)=9%

(a) Calculate the forward rate for a one-year zero in one year, f (1,1).

(b) Calculate the forward rate for a one-year zero in two years, f (2,1).

(c) Calculate the forward rate for a two-year zero in one year, f (1,2).

(d) Calculate the price for a 3-year treasury bond with par value of $1,000 and having a 5% coupon rate paid annually.

Maturity(T)

1

2

3

Spot rates

r(1)=11%

r(2)=10%

r(3)=9%

Explanation / Answer

Answers:

(a) f (1,1) = 11% (Given)

(b) f (2,1) = F2/F1 = (1.10)^2 /1.11 = 1.09 =9% approx

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