SS 14 FRA credit risk

jbaldyga

On pages 90-91 of schweser book 4, study session 14, the example states that you must discount back the payment of the FRA based on the loan amount.

Here is the question:

In anticipation of brooiwing $1mm at LIBOR +200 bps for one year, a manager has entered an FRA with a reference rate of 5% and a notional principal of $1mm. it is now three months before the maturity of the FRA, which coincides with the beginning of the loan, and LIBOR has increased to 6%. assuming the risk free rate is 4% determine the value and direction of any credit risk in the FRA.

they are saying that the manager is entitled to a $10k payment, which makes sense but then says that this amount must be discounted back 1 year at 8% (6%(LIBOR)+200bps).

It is then discounted back at the RFR for three months to get to the current time, whcih makes sense.


I dont understand why you would dicount back the $10k by the loan amount as this is a hedge and, to me, should be independent of the loan.

pennyless

Does anyone have an idea on the logic behind this?

Thanks

liangfeng

The FRA payout comes at the end of the loan so you first need to PV it at the individual's cost of capital. You then PV it again at the risk-free-rate to see the present amount of credit risk.

lcw77

Thanks that clears it up a little.

I guess where I am confused is where it says "Under the assumption that LIBOR stays at the current level of 6%, the bank will be required to pay the manager $9,259.26 (which is 10,000/1.08) at the beginning of the loan (i.e., at the expiration of the FRA)"

Why would the bank only have to pay $9,259.26 when the FRA expires. I would think the payment of 10k should be discounted by the reference rate (LIBOR = 6%).

If the two contracts are separate, why would the bank benefit by having they payment dicounted by the loan amount

Iginla2011

Does anyone know the answer to this?

Colum

thanks

Do you know what page in the book this is on? I am looking in book 5 of the CFAI book and cant find it.

thommo77

Think of it this way, the bank is loaning you $1mm. Since you make out on the FRA, the bank basically gives you $1,009,259.26 at the start of the loan, but you only owe $1m.

The extra $9,259.26 is used by you to make up for the extra interest you're facing on the loan now that rates have increased. You can invest this at the RFR and have that extra $10k you owe at the end of the loan now that rates have increased.

In the opposite case, you lose on the FRA. The bank gives you less than $1M, but you owe $1m at the end.

Does that help? you discount back just because TVM, it's paid off at the beginning of the loan, but you will need it at the end of the loan.

mcmc

This is the one thing I am punting out for the exam on Saturday. I looked in the CFAI and they only discuss really credit risk of a option and forward.... not really an FRA.