Question

Suppose that a six-month zero coupon bond is currently selling at $925.93 and a one-year zero coupon bond is selling at $797.19. (a.)Determine the annualized six-month spot rate and the annualized one-year spot rate. (b.)Determine the implied annualized six-month forward rate for six-months from now. (c.)Suppose the annualized yield-to-maturity on an eighteen-month zero-coupon bond was 7.00%and the spot yield on a two-year zero was 13.00%. Based on this information and your results from above, describe which theory (or theories) of the term structure would be best able to explain the yield curve you have found.

Answer 1

	(a)	Annualized six month spot rate and annualized one year spot rate
		Current Price of six months zero bond	$925.93
		Amount to be received at maturity	$1,000
		Assume six months interest rate=r
		925.93*(1+r)=1000
		r=(1000/925.93)-1=	0.079995
		Annualized interest rate=((1+r)^2)-1	0.16639
		Annualized interest rate=	16.64%
		Current Price of one year zero bond	$797.19
		Amount to be received at maturity	$1,000
		Assume one year interest rate=i
		797.19*(1+i)=1000
		i=(1000/797.19)-1=	0.254406
		Annualized interest rate=	0.254406
		Annualized interest rate=	25.44%
	(b)	Implied annualized six-month forward rate for six-months from now
		Implied six month forward rate for six months from now =			R
		Spot six months interest rate from (a)	0.079995
		Spot one year interest rate from (a)	0.254406
		As per Unbiased Expectations Theory:
		(1+0.079995)*(1+R)=(1+0.254406)
		1+R=(1.254406/1.079995)=	1.161492
		R=Implied six month forward rate sixmonths from now	0.161492
		Annualized Rate =((1+R)^2)-1=	0.349064
		Annualized Rate =	34.91%
	.(c)	Liquidity Preference Theory
		Investors prefer shorter term bonds
		Bonds with longer terms command a liquidity premium