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

Answer:

a.

3.51%

b.

0%

Explanation:

a.

First, we need to calculate the YTM of 6 months zero-coupon bond by using the following formula

Price = Face value / ( 1 + YTM )^numbers of years

96.79 = 100 / ( 1 + YTM )^1

1 + YTM = 100 / 96.79

1 + YTM = 1.0331646

Now calculate the YTM of 1 Year zero-coupon bond

93.51 = 100 / ( 1 + YTM )^1

YTM = 1.0331646 - 1

YTM = 0.0331646

YTM = 3.31646%

YTM = 3.316%

1 + YTM = 100 / 93.51

1 + YTM = 1.06940

YTM = 1.06940 - 1

YTM = 0.06940

YTM = 6.940%

YTM = 6.94%

Hence the forward rate is calculated as follow

Forward rate = [ (1 + YTM of 1 year zero coupon bond ) / ( 1 + YTM of 6 months year zero coupon bond ) ] - 1 = ( 1 + 6.94% ) / ( 1 + 3.316% ) = [ 1.0694 / 1.03316 ] - 1 = 1.03508 - 1 = 0.03508 = 3.508% = 3.51%

b.

At the time of inception the formward rate is 0.