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?

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.

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)]

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?

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.