Advanced FRA Question without

dvilayphet

So we have to unannualize and reannualize rates, how can we do this without using compounding in our FRA formula? What am I missing?

yospaghetti

I don't believe there is any compounding in the FRA formula... Could you be more specific, please?

Are you referring to the pricing or valuation mid-contract?

RMontgomery

Well the techinical correct way to do it is to use compounding. For instance, if there is a 90 day rate = 5.0%, that number is annualized. To get the actual amount of interest paid, you raise it to the .25 = 1.23%.

However, with LIBOR rates, it is assumed 360 days are in a year. If you take the ratio of days/360, it will give you a real close approximation of the rate. In this case, 5.0%*(90/360) = 1.25%.

On the real thing, I would first use the technically correct way of compounding. If your answer isn't one of the listed choices, recalculate using the approximate measures.

luda002

but with LIBOR there is NO ANNUALIZING. Look it up.

it is an ADD-ON Rate, not a compounded rate.

Schweser does throw in a few problems on SWAPs with Spot Rates - but that is just Schweser.

There is no annualizing.

1+0.05*90/360 = 1.0125

(1.05)^0.25 = 1.01227

not too much of a difference... but on bigger amounts and multiplied / divided could make a lot of difference to the answer.

CP

flyinggirl

Ok so the technically correct way is to multiple by the respective d/360 and NOT compund at that ratio?

Houjichasan

cpk, does "add-on" rate just mean you use simple interest and not compound interest?

giants2010

A couple things. "Add-on interest" refers to the fact that LIBOR is not quoted at a discount where Treasury bills are, which is called "discount interest". (CFAI, Vol. VI, pp. 14,15)

Next, here is the CFA formula for valuing an FRA mid-contract to the long (ibid, pp. 37)


Vo = Notional Principal multiplied by --->

1 / [1 + (new short-term rate x days/360)] - [1 + (FRA rate x days/360)] / [1 + (new long-
term rate x days/360)]

5566

I remember from Lvl I that the way a rate is quoted is by convention .


Strictly speaking the TVM calculation would NOT treat a rate over a longer period as a simple linear increase over a shorter period:

R1 = 1+ (R * 90/360)
R2 = 1+ (R * 180/360)

The add-on rates are simple multiples of the base annualized rate at a point of time.

That's the way the LIBOR rates are quoted and used . So lets not argue about that.

TVM would say:

R2 = Sqrt( (1+R1)^2) - 1

But LIBOR does not use a TVM calc for quoting , it uses the above "add-on" way.