Question

you wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days. the price of a 150-day zero coupon bond is 0.9823 and the price of 310 day zero coupon bond is 0.9634. Which one of the following methods is the correct method to create the synthetic FRA? explain

A) borrow one 150-day bond and invest in 1.02 of the 310-day bonds.

B) borrow two 150-day bonds and invest in 0.98 of the 310-days bonds.

C) lend one of the 150-day bonds and borrow 1.02 of the 310-day bonds

D) lend two of the 150-day bonds and borrow 0.98 of the 310-day bonds.

Step by step

Answer 1

You need to lock in return of FRA between 150 and 310 days.

So, funds outflow should be on 150th day and inflow should be on 310th day (since you are investing from 150 to 310).

Cashflow on day 0 should be nil

So we will borrow funds for 150 days and invest the on same day for 310 days.

In this way, cash outflow on day zero will be nil.

And we will be able to lock in our returns.

If we borrow 1 150 days bond, inflow = 0.9823

We need to invest the same amount in 310 days bond.

No of 310 days bonds to be bought = 0.9823/0.9634 = 1.02 bonds

Therefore option A is correct.

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