Question

On May 15, 2000 you enter into a 1-year forward rate agreement (FRA) with a bank for the period starting November 15, 2000 to May 15, 2001. You will receive the forward rate and pay the floating rate in the FRA. You know that currently the price of the 6-month zero coupon is $96.79 and the price of the 1-year zero coupon is $93.51.

(a) What is the agreed-upon forward rate in the transaction?

(b) What is the value of the forward at inception?

Answer 1

Hi,

The concept of FRA is as follows,

A bank that sells an FRA agrees to pay the buyer the increased interest cost on the principal amount if market interest rate is above the stipulated forward rate on the settlement date. Similarly Buyer agrees to pay the Bank any decrease in the interest cost on the principal amount is Market interest rates fall below the Forward rate.

But in the given question we need to find the forward rate, i.e. The forward rate is the interest rate an investor would have to be guaranteed between the first investment maturity and the second maturity to be indifferent (at least in terms of returns) between picking the shorter or longer.

Since we have price of Zero Copoun bonds, we need to find the YTM of both the bonds. We need to use the following formula,

Bond Price	=	C1 / (1+YTM)1	+	C2 / (1+YTM)2
C = coupon payment per period P = par value of bond n = number of periods until maturity YTM = yield to maturity

(in given question since it is 6 month and 12 month we have 2 periods of 6 months each)

Hence the YTM of 6 - month zero copoun bond is as follows,

96.79 = 100/(1+YTM)¹ So, (1+YTM) = 100/96.79 Thereby (1+YTM) = 1.03316 Hence YTM = 0.03316 or 3.316%

Similarly the YTM of 12- month Zero copoun Bond is as follows,

93.51 = [100/(1 + YTM)¹ ]   So, deriving the equation just as above we get, YTM = 0.0694 or 6.94%.

a. Therefore the Forward rate = (1.0694/1.03316) - 1 = 0.03507 or 3.507%

At a date where (T) is equal to zero, the value of the forward contract is also zero. This creates two different but important values for the forward contract: forward price and forward value. Forward price always refers to the dollar price of assets as specified in the contract. This figure is fixed for every time period between the initial signing and the delivery date. The forward value begins at storage cost and tends toward the forward price as the contract approaches maturity.

b. Therefore the value of Forward at the inception is Zero.