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 method is the correct method to create the synthetic FRA? Explain. Explain the Long and the Short for each situation

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-day 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

Answer 1

Locking in return between 150 and 310 days mean that investment or outflow would occur on 150 days and inflow on 310 days. Hence, we should invest in 310 day bonds so that inflow occurs on 310 days. But this would mean that outflow occurs now so we have to borrow now so that outflow is cancelled by the inflow now and then the borrowed amount returning will result in outflow in 150 days. Number of 310 bonds=0.9823/0.9634=1.02

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