# Can anyone devise a formula for valuing FRA before maturity?

Schweser gives a very complicated explanation on page 213, book 5, for valuing an FRA prior to settlement. Can someone tell me what a formula would be that I can memorize so that I don’t have to spend another hour staring at this? The example they give is, “Value a 5.32% 1 X 4 FRA with a principal amount of \$1 million 10 days after initiation if 110-day LIBOR is 5.9% and 20-day LIBOR is 5.7%.”

Calculate the new FRA Rate R110=(1 + 0.059 * 110/360) R20=(1+0.057*20/360) (R110/R20 - 1)*360/90 = new Rate Amount Long Gets Part 1: ( New Rate * 90/360 - 0.0532 * 90/360 ) * Notional = Amount of money Long gets due to Interest Savings at the end of the contract. Right now we are at day 10 - which is 110 days away from the end of the contract. So current amount = Amount Long Gets Part 1 / R110 R110= 1.018027778 R20=1.003166667 New Rate = 0.0593 = 5.93% Amount Long gets part 1: ( 0.0593 * 90/360 - 0.0532 * 90/360 ) * 1 Million = 1525\$ Amount Long gets final = 1525 / 1.018027778 = 1497.99\$ subject to rounding…

rellison Wrote: ------------------------------------------------------- > Schweser gives a very complicated explanation on > page 213, book 5, for valuing an FRA prior to > settlement. Can someone tell me what a formula > would be that I can memorize so that I don’t have > to spend another hour staring at this? > > The example they give is, “Value a 5.32% 1 X 4 FRA > with a principal amount of \$1 million 10 days > after initiation if 110-day LIBOR is 5.9% and > 20-day LIBOR is 5.7%.” There are some complicated formulas in CFAI book. They are too difficult to remember so I never read. Schweser have a point to neglect them. Take some time to understand the few pages in Schweser. It is just based on simple concept of present value. Draw a time line will be helpful. First find the new 90 days rate at expiration of FRA, from the 110 and 20 day LIBOR. Compare the new 90 days rate with the FRA 90 days rate. If the new rate is higher, you gain. How much? Calculate from 1m principal, rate difference, 90 days. Because you gain this amount only when you have lend the money for 3 months, at the termination of the loan. So, discount it back to today, i.e. 90+20 days. At what rate? The most current rate, today’s 110 days LIBOR. From cpk123’s reply, you can see that all are intuitive calculation. Change of annual rate to quarterly rate, discount and compounding, etc.