You wish to create a synthetic forward rate agreement in which you would lock in

Question

You wish to create a synthetic forward rate agreement in which you would lock in the current forward rate on borrowing a loan between day 180 and day 360. The price of a 180-day zero coupon bond is 0.9875 and the price of 360-day zero coupon bond is 0.9798. What are the transactions used to create this instrument?

long the 180-day bonds and short (FV) 0.9922 of the 360-day bonds.

short the 180-day bonds and long in (FV) 0.9922 of the 360-day bonds.

short the 180-day bonds and long in (FV)1.0079 of the 360-day bonds.

long the 180-day bonds and short (FV) 1.0079 of the 360-day bonds.

long the 180-day bonds and short (FV) 0.9922 of the 360-day bonds.

short the 180-day bonds and long in (FV) 0.9922 of the 360-day bonds.

short the 180-day bonds and long in (FV)1.0079 of the 360-day bonds.

long the 180-day bonds and short (FV) 1.0079 of the 360-day bonds.

Explanation / Answer

First, calculate the 180 day forward rate 180 days from now -

0.9875 x forward rate = 0.9798

F = 0.9922

You are borrowing a loan between day 180 and day 360, i.e., creating a long position in the forward market or going long in FV 0.9922. To create a synthetic forward rate agreement, you need to offset this long position by creating a short position. So, you need to go short the 180 dag bonds. Therefore, Option B is correct.

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