Calculating the actual FRA rate

[danielo1]

Hi David. I was intrigued by something as I watched your tutorial about FRAs.
So I understand clearly how it works and what it is for. I was wondering, however, how do you actually calculate the stipulated rate? In your Excel example you locked in a 3% interest rate against the LIBOR, but I would like to learn how you actually got that number and what information you need.

I am aware that a mathematical equation is used for this matter, but I am not familiar about which one is long term interest rate, short term interest rate (t1 interest rate and t2 interest rate?) and, if you want to use the interest rate when the contract expires, how do you calculate it?

Thank you very much David, I appreciate your help and deeply respect your work.

Most respectfully,

Dan Ortega

 

[David Harper CFA FRM]

Hi Dan,

(Thanks for your kind words, really appreciate that!)

As I have been blogging Hull questions for FRM candidates, today's happened to be an FRA problem.
You might find helpful: http://forum.bionicturtle.com/viewthread/1470/
And the XLS is here: http://sheet.zoho.com/public/btzoho/hull-04-06a

The FRA rate is contractual. Say you know you will borrow @ LIBOR in 1 year, but you don't want the rate risk. So you enter into an FRA with me, to pay me a fixed rate forward, in exchange for me paying you LIBOR. We will contractually decide the rate today but it will proabably be near to the observed forward rate; i.e., the 1 year 3 month forward rate, because that is the best estimate of the prevailing rate in 1 year. So, if that's 4%, we agree to 4% today. Then in 1 year, if LIBOR is 5%, I will pay you the net 1% (i owe you prevaling LIBOR @ 5%, you owe me the agreed-upon 4%). This way you have hedged: you will borrow at 5% LIBOR, as planned, but you offset your total cost by the 1% I pay you. So, the FRA rate is contractual, but looks to the forward rate for a fair deal. Then when the "future arrives" it is compared to the observed, actual "spot" (LIBOR) interest rate. Hope that's helpful - David

 

[danielo1]

Thank you so much for the prompt response!

I took a look at the FRA example you sent, thanks a lot! I guess I must have confused you with my earlier question, though.

I understand the LIBOR is a rate that provides percentages for a determined period of time. For example a 30-day LIBOR could be X%, for 60 days it could be Y%, 180 days Z% and so and so on. My question to you is this:

WHAT IF I AM USING A RATE (OTHER THAN LIBOR) THAT IS NOT FOLLOWING LIBOR'S FORMAT? I AM USING A RATE THAT IS PUBLISHED EVERY WEEK (called the Reference Rate) AS OPPOSED TO PROVIDING CERTAIN RATES FOR THE FUTURE. AND WHAT WILL MY EQUATION TO DETERMINE DE ACTUAL RATE BE?

If using a rate such as LIBOR, I’m aware the equation goes as follows:

(LIBOR Long Term * Number of Days Long Term) – (LIBOR Short Term * Number of days Short Term)
%FRA = ________________________________________________________________________________

Number of days of contract * (1 + LIBOR Short term * (Number of Days Short Term/360))


But what if I’m using a reference rate that is published every week? How will my new equation look like?

Thank you David! Your help means a lot.

Dan