Hi everyone,
Can someone please clarify how to identify in an FRA the m and h?
Seems like there are two instruments, the underlying LIBOR and the FRA or something, I’m not really understanding how to come up with those two variables
(plus I have the formula’s memorized so it would really suck not being to do the calculations over something that seems to be silly)
Would appreciate your help - thanks!
i posted sth a couple of days ago - which does this from basic principles - and without using Don Chance’s complicated formula.
http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91319368
apply that – it works all the time.
when you use it on the cfai eoc problems - note that there are rounding errors.
thanks for your reply…
I’m still confused how to get h and m given different scenarios…
Example 1 (CFA 2013 derivatives Q10): manger hedges his exporer with an FRA that expires in 90 days and based on 90 day LIBOR … I udnerstand that’s a 3 FRA 6 … so the first number of the notation = FRA expirary
But…in another example, it says there’s an 8 year project that needs funding 6 months from now… and in that case, it is a 6 FRA 8 (notation in years)…
If you look at the two examples, in the 2nd example, wouldn’t the first number of the notation also be when the FRA expires, why would it expire if the project funding starts then?
– Good detailed example in the other post but for me it is just easier to plug h and m into the formulas i’ve worked hard on memorizing hehe
I appreicate your help!
Make sure that you get the notation correct: it’s not a “3 FRA 6”; it’s a “3 × 6 FRA”.
The second one’s worse: you cannot use months for half the notation and years for the other half; it’s not a “6 FRA 8”; it’s a “6 × 96 FRA”. Using the correct notation may be difficult at first (especially if you’ve been using something different), but ultimately it will solidify your understanding. Take my word for it.
Opps, i should have fixed that - I did realize it.
Can you please clarifiy the differences in the two examples I provided? 
Would it be FRA 6x96? I doubt that you would have a LIBOR for 96 months.
Probably not. But, then, there’s also no risk-free interest rate in the real world.
You need to understand the theory.
hey ext, first of all if you can follow cpk’s example I would go back and have a look as it is very good. Second, be aware that memorizing something like this is dangerous, because CFA likes to test things conceptually. If you understand why the formula is correct you will likely have a better chance at getting any quesiton about FRA’s they could throw at you correct.
Let me try and break down valuing an FRA simply. I would try and follow this and forget about “h and m”
Let’s say I am a corporate treasurer and I know that for working capital purposes I need to borrow $1 at LIBOR, 30 days from now, for 90 days.
Let’s also so that the current LIBOR term structure is as follows:
30 day LIBOR - 3%
60 day LIBOR - 4%
90 day LIBOR - 5%
120 day LIBOR - 6%
First thing I need to know (because my market maker will quote me this rate when I give him a call to put on the contract) is the LIBOR forward rate, starting in 30 days, for a 90 day loan. The forward rate is of course the rate that would make indifferent between borrowing for 120 days, or, borrowing for 30 days and rolling over the loan for another 90 days.
To solve for the 90 day forward rate all I need to do is divide (1+ the 120 day rate) / (1 + the 30 day rate).
Here is how I do it:
(1+6%*120/360) / (1+3%*30/360) = (1+x%*90/360)
solving for x I calculate 1.745%
Re-annualizing this rate = 1.745%*360/90 = 6.98%
This rate - 6.98% is the 90 day forward LIBOR rate, starting in 30 days. This is the rate that I can lock in today as the corporate treasurer to borrow for 90 days, starting in 30 days.
Ok, so step number 1 is over, I know the rate I can borrow at.
so the market maker says to me on the phone, do you want to do this? I am as the corp treasurer am worried about rising interest rates so I say, ok let’s do the deal.
Now, lets say 10 days have past and the current LIBOR term structure looks like this:
20 day LIBOR- 1%
50 day LIBOR - 2%
80 day LIBOR - 3%
110 day LIBOR - 4%
Now the companies auditors come by and want to know what is the market value of the FRA we put on ten days ago. Just by quickly glancing at the market, I can tell the trade I put on ten days ago is out of the money because we are borrowers and have locked in a borrowing rate of 6.98%, starting 20 days from now.
But by how much are we out of the money? In order to figure out how much we have lost on our position, we need to answer this question - what loss would we lock in right now if we took the exact opposite position?
So in order to take an exactly opposite position, what I need to do is I need to lend $1 for 90 days, starting 20 days from now, in order to match the exact time frame of the borrowing.
So what I do now is call up my market maker and offer to loan him the same $1 for 90 days, starting 20 days from now. he says ok and makes me a market for the same time frame as the above trade. The investment I just placed with my market maker was quoted at a rate that was calculated in the exact same way as above - by first solving for the prevailing forward rate from the LIBOR term structure, but this time for a 90 day loan, starting in 20 days for a total time frame of 110 days.
From the above term structure:
(1+4%*110/360) / (1+1%*20/360) = (1+x%*90/360)
solving for x I calculate 1.17%
Re-annualizing this rate = 1.17%*360/90 = 4.66%
Ok so now I know that in 20 days, I am going to borrow for 90 days at 6.98% and lend for 90 days at 4.66%, I am going to pay interest on the loan in 110 days when it matures and I am going to receive interest on the investment in 110 days when it matures. Hopefully by now you see where I am going with this…
So in order to determine the value on these two positions, I use the following formula to first determine the net cash flow at time 110 days
$1*(4.66%-6.98%)*90/360 = -0.0058
Notice now that this is a locked in cash flow and of course, notice that I will not owe this cash flow to the market maker until 110 days from now, so account for the time value of money I need to discount this back to today. But at what rate? The rate I use is the prevailing LIBOR rate for the entire time frame - the 110 day LIBOR rate of 4%
Discounting this cash flow = -0.0058 / (1+4%*110/360) = -0.00573
This is the marked to market value on my position.
hope this helps!
carthurj