isn't this an error?

[Shazam023]

John C. Hull
Chapter 5 (Determination of Forward and Futures Prices)
Example No. 5.1

Consider a 4-month forward contract to buy a zero-coupon bond that will mature
1 year from today. (This means that the bond will have 8 months to go when the
forward contract matures.) The current price of the bond is $930. We assume that
the 4-month risk-free rate of interest (continuously compounded) is 6% per annum. Because zero-coupon bonds provide no income, we can use equation (5.1)
with T- 4/12, r- 0:06, and S0- 930.

T suppose to be time left to maturity. So how T= 4/12. Either it shud be 8/12 or 12/12=1.
m confused here. plz help.

 

[Dr. Jayanthi Sankaran]

Hi @Shazam023,

The relationship between the Forward contract on an investment asset, with price S(0) that provides no income is given by:

F(0) = S(0)*e^rT

Here, T = Time until delivery date in a forward (or futures) contract (in years)
r = risk-free rate of interest per annum with continuous compounding
F(0) = forward price or Futures price today. Put another way, it is the long forward contract to purchase the zero-coupon bond in 4 months
S(0) = Price of the asset underlying the forward or futures contract today

Applying the above formula with T = 4/12, r = 0.06 and S(0) = $930

F(0) = 930*e^.06*4/12 = $948.79: This is the delivery price in a contract negotiated today.

Thanks
Jayanthi

 

[Shazam023]

@Jayanthi Sankaran
thnkx for reply...... but cn u explain the interpretation of this statement "will mature
1 year from today. (This means that the bond will have 8 months to go when the
forward contract matures.)"

i'm not getting this.. its obvious a 4 month contract will expire in 4 months only not in 1 yr... (Confused)

 

[Dr. Jayanthi Sankaran]

Hi @Shazam023,

The forward contract on the underlying zero coupon bond has a maturity of 4 years, today. The zero coupon bond by itself has a maturity of 1 year from today. And so, at the end of four months, the forward contract expires and delivers the underlying zero coupon bond which has a maturity of eight months, at the end of the maturity of the forward contract.

Thanks
Jayanthi

 

[Shazam023]

thnkx alot... i missed the part "to buy a zero coupon bond".. my bad..

once again thnkx for ur help @Jayanthi Sankaran