### CFA Practice Question

There are 206 practice questions for this study session.

### CFA Practice Question

Which of the following combinations of interest rate options would replicate a 6-month by 9-month forward rate agreement to pay 5% fixed? The LIBOR below refers to the 3-month LIBOR.
A. Long a 6-month call on LIBOR and short a 6-month put on LIBOR.
B. Long a 9-month call on LIBOR and short a 9-month put on LIBOR.
C. Long a 6-month call on LIBOR and long a 6-month put on LIBOR.
Explanation: If LIBOR exceeds 5%, this combination will result in an inflow of funds just like an FRA. If LIBOR drops below 5%, this combination will result in an outflow of funds just like an FRA.

User Comment
tanyak so where does the 9 months fit into all this?
RNAN In 6 months, the spot 3 month LIBOR rate is the focal point. The options (calls and puts) are on the 3 month LIBOR rate that begins in 6 months.
heinzlive The 9 months are the maturity of the contract: begins in 6 months and based on 3-months LIBOR, matures all in 9 months from now.
ljamieson can use put-call parity to construct fwd to. c-p=f-kdf
ramdabom Why not C. Wouldn't the 6-month put pay off in interest rates dropped so you're fully hedged?
hks101 The payout on C is not the same as the payout on A.
Payout on FRA:
FRA locked in at 5%
over 5%, payout is positive
under 5%, payout is negative

option A's payout:
over 5%, excercise call, payout positive
under 5%, long will excercise the put you sold, payout negative
carmentsang wrong! why would you exercise a call when you need to pay out?!
Saxonomy You will agree to pay 5% now if you believed int rates were going up i.e. "long" on I.R.

So, it only makes sense to long a call and short a put. They are both bullish.

Ignore the 9-months. 9-months only tells us that in 6months, consider the 3month LIBOR rate. We don't put 9-months in any of our calcs.
mtsimone Pay fix='long fix' (though you can't be 'long' something fixed, but it's good as a pneumonic)
Pay float: think 'long float'
Since, a synthetic long is a long call and a short put it has to be 'A.'
And vice versa, of course.