Any advice on remembering the FRA formula? I tend to get confused with the inputs.
draw out a timeline. Mark the points when it starts and ends. Mark the rates you’re given to their corresponding time periods. Solve for the “X” implied rate by doing some simple division. I think schweser goes over this but not sure, let me know if you want more.
Thanks Andrew. Getting late so I’ll try I out in the morning.
Hi, Actually I am not understanding the formulas and as such cannot recall them. Some help would be much appreciated here…
point me to a problem please
- Find Original Price 2. Find new Price after X amount of days 3. New price * Days of loan/360 - Old price*Days of loan/360 * Notional = Interest Savings 4. Discount interest savings = Gain/loss There is a really good thread floating around… http://www.analystforum.com/phorums/read.php?12,754042,764130#msg-764130 http://www.analystforum.com/phorums/read.php?12,749056,750229#msg-750229
Im not sure which formulas you are referring too, as there are a few different parts. Here is how i do it, start to finish. First, its important to understand the FRA notation: a X b a is the term of the FRA agreement b is the term of the total position: FRA agreement Plus the term of the underlying. So a 1X4 FRA is a 30X120 FRA (30 days till end of FRA, 120 days till the end of the total position, so the underlying iws 120-30 = 90 days) Lets use a 1X4 for an example to make it easier. 1) Find the FRA rate a) find the unannualized rate for 4 (or letter b in the notation). If the quoted rated for 120 days is 4%, we do 4%(120/360) = 1.333%. Then add 1 to this rate. b) find the unnanualized rate for the rate of 1 (or letter a in the notation). If the 30 day rate is quoted as 3%, then it would be 3%*(30/360) = .0025. Add 1 to this rate. c) set up a ratio of the two rates found above, with the 120 day rate (or letter b rate) in the numerator and letter a rate or 30 day rate in the denominator. 1.01333/1.0025 = 1.0108 then subtract 1, to get .0108. Then, we need to annualize this rate to get the rate for the FRA. We annualize by the rate of the underlying (in this case it is 90 days) so .0108*(360/90) = 4.3225% This is the fixed rate of the FRA. 2) Value at Maturity a) The value at maturity is simpler - we need to find the savings or loss for the long for being “able” to borrow at the FRA rate. if this rate is lower than the market rate, the long wins. if it is higher, the long loses. Lets say the rate for a 90 day loan at the end of the FRA (so 30 days) is 5%. Lets say the notional amount is $1M Here is how to calculate the payoff: (Market rate - FRA Rate)(Days of underlying loan/360)(notional amount) = Amount saved by the long ( if this is negative, it is amount lost by the long) In this case: (5% - 4.3225%)(90/360)(1M) = 1693.7 In reality, the savings aren’t actually earned until the underlying loan matures, which occurs in 90 days. So we need to discount the savings by the 90 day unnaualized market rate: 1693.9/(1 + 5%*(90/360) ) = 1672.773 3) The harder calculation is to value it before maturity (although it is a similar calculation). Lets say that we are 10 days into the FRA (so now the FRA notation is 20 days X 110 days), and we want to see the value to the long. The question should give you the current 20 day rate and 110 libor rate as well. Lets say 20 day rate is 3.5% and 110 day rate is 5.5%. a) We calculate the “new price” of the FRA, as done in the step above to get the initial FRA rate: Again, we need to unnanualize the rates, set up the ratio and annualize: 110 day: 5.5% * (110/360) = .016806, then add 1 = 1.0168 20 day: 3.5% * (20/360) = .00194, + 1 = 1.00194 Set up ratio: 1.0168/1.00194 = 1.014832, subtarct 1 = .014832. then we annualize it by the term of the underlying loan, still 90 days. .01483*(360/90) = 5.93%. This is the new “FRA Price” b) Now, we value the contract as we did at maturity, except we use the new FRA rate instead of the maret rate at the end of the FRA (5.93% - 4.3225%)(90/360)(1M) = 4026.02 Now we discount. This part is a little trickier. Make sure to discount by the new FRA rate and by the days left until the entire position matures (110 days in this case) 4026.02/(1 + .0593*(110/360)) = 3954.37, or the value to the long 10 days into the contract. If it was a negative value, then the short would be up this amount. I hope this helps and makes sense.
Spanishek, Thank’s very much for the explanation. I guess it was the “discounting” part that I was not understanding. So, when calculating the value before and at maturity, always discount at actual interest rate on the FRA and wrt the time remaining to the full maturity (At expiry, this should be equivalent to b-a).
Sure thing. Yes, at maturity, discount by current rate of the underlying (b-a days / 360) Before maturity, discount by the days left of the total position (b/360)