2 questions, both relatively simple. So if we are trying to calculate the price of a 1x4 FRA when the current 30 day LIBOR is 4% and the 120 day LIBOR is 5%, we calculate the actual rate on a 90 day loan from day 30 to day 120 by 1+R120/ 1+ R30 = which gives us 5.32%. What the heck is this 5.32%? What does it mean. I’m trying to wrap my head around this concept since you need it to price the FRA but really can’t conceptually think of it other than its the rate on a 90 day loan from day 30 to 120. And I’m just pulling that directly from Schweser.
Secondly, the likely variation we’ll get is pricing that same FRA 10 days in. In Schweser they discount the value back 110 days, while when we were just valuing the 1x4 we discounted it back only 90 days to when the contract starts. Many thanks to whoever can help. Let’s all get through this.
summerside182 said it well. Remember you want the loan 30 days later but you want to know now what rate you are going to pay. No one knows what the rate is going to be, but through this FRA agreement someone is willing to take the risk and offer you the loan for 5.32%.
After 10 days, things change, right? So we are now 110 days away from the loan termination date. At this point, if you want to value the FRA, then you can check to see what its current price is. Just like stocks and bonds, it has a market rate which changes every day. Suppose you find that a new FRA (pricing it using the same formula as before, but now your long rate is the 110 days and your short rate is the 20-day rate) with the same maturity as yours today has a rate of 6% (meaning that if some new guy wants to buy it today, he would have to pay 6%).
You’re lucky because you’ve just locked in a rate of 5.32%. The difference in rates is your profit. However, you will not get that difference of 0.68% just yet…you’ll get at after 110 days. So you need to discount the 0.68% annual rate to today, so it’s 0.68%/4 because it’s a 90-day rate. Good luck.
Another way of thinking about this to help clarify the motivation for this, is to ask yourself:
Should I get the loan today and keep it for 120 days paying 5% at the end? Or should I wait 30 days then get the loan and pay 5.32% at the end of 120 days?.
If you take the loan today at 5%, assume you get $1 million. After 120 days you pay 0.05*120/360 * $1 million = $16,667 in interest.
If you wait for 30 days, get the loan and keep it for 90 days, you pay 0.0532*90/360 * $1 million = $13,300.
