Question

You are given the following benchmark spot rates:

Maturity	Spot Rate
1	2.90%
2	3.20%
3	3.60%
4	4.20%

a) Compute the forward rate between years 1 and 2.

b) Compute the forward rate between years 1 and 3.

c) What is the zero price today of a five-year zero-coupon bond if the forward price for a one-year zero-coupon bond beginning in four years is known to be 0.9461

d) Calculate the price of a 4% annual coupon corporate bond with two years remaining to maturity has a Z-spread of 200bps. Assume interest paid annually.

Answer 1

	Maturity	Spot Rate
	1	2.90%
	2	3.20%
	3	3.60%
	4	4.20%
	a)	Forward rate between year 1 and 2				(1+3.20%)^2/(1+2.90%)-1
		Forward rate between year 1 and 2				3.50%
	b)	Forward rate between year 1 and 3				((1+3.6%)^3/(1+2.9%))^0.5 - 1
		Forward rate between year 1 and 3				3.95%
	c)	Forward rate of 1 year bond between yr 4 & 5					1/.9461 - 1	5.70%
		So Price of zero coupon bond =				1/((1+4.20%)^4*(1+5.70%))
		So Price of zero coupon bond =				0.802517
	d)	Yield is 3.20% + 2% = 5.20%
		Price is	$977.75	PV(5.2%,2,4%*1000,1000,)