Question

A “three-against-six” forward rate agreement (FRA) has an agreement rate of 4.05% on the three-month LIBOR interest rate. You believe the three-month LIBOR interest rate will increase to 4.35% within the next three months. You decide to take a speculative position in the FRA with a $1,000,000 notional value. There are 90 days in the FRA period.

If the three-month LIBOR is 4.00% in three months, then what will your profit/loss be? Use a 360 day-count convention

Show your workings and the correct answer in the space provided below and also specify which party (purchaser or seller) makes a profit and which party makes a loss.

One of the following answers will be correct:

a. -$378.88

b. $480.77

c. $378.88

d. -$480.77

Answer 1

We use Formula For final settlement

N(RR-FR)(days of maturity/total days) /(1+RR)*(days of maturity/total days)

Given

Notional value=$1000000

Days of maturity =90days (3months)

Total days=360

FR=agreed rate=4.05%

After 3 months

LIBOR=4% (libor is used as reference rate called RR)

Lets put the values

=1000000*((4-4.05)*90/360) /(1+4%)*90/360

=1000000*(-0.05*90/360) /1.04*90/360

=1000000*-0.0125/0.26

= -125/0.26

= -480.77

Correct answer is D

Lets understand the question also in a summarised form

FRA are a form of agreements where purchaser/seller aims to save his position from any fluctuation of interest rate.There is a reference rate eg market interest rate libor etc which is fluctuating and there is a FRA a rate on which the parties agree

IF LIBOR>FRA (seller has to pay)

LIbor

now see the position described

Purchaser thought libor would rise in future he speculated hence FRA agreed was 4.05% however libor on maturity turned out to be 4%

now -0.05% of LOSS FOR PURCHASER as LIBOR

Hence seller gains purchaser loses in this contract.

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