 # FRA confusion

I thought I understood FRA’s but I guess not. can some one explain this to me please? 30 days ago, J. Klein took a short position in a \$10 million 90-day forward rate agreement (FRA) based on the 90-day London Interbank Offered Rate (LIBOR) and priced at 5%. The current LIBOR curve is: 30-day = 4.8% 60-day = 5.0% 90-day = 5.1% 120-day = 5.2% 150-day = 5.4% The current value of the FRA, to the short, is closest to: A) −\$15,495. B) −\$15,280. C) −\$15,331. D) −\$15,154.

I get D. 1/(1+.05(60/360) - (1+.05(90/360))/(1+.054(150/360)) = 15,154 to long = loss to short.

D is my guess, I got 15,160 T/G

Niblita got D, so it must be true. There is no trick to FRAs, just memorize the formulas and do all the practice problems in the CFA book. T/G

The answer is \$15,154 Can some one explain this to me?

The value is the interest savings by entering into the FRA. So you just have to difference what you paid and the actual rate and the PV it.

can anybody else show a different calculation than niblita…

zephyr, can you give the schweser explanation or the question ID

Ok, since 30 days has already passed, this is a 2X5 FRA correct? So the contract starts in 60 days. Since the contract starts then, does the float or fixed make a payment on that day or do they not make a payment until the next settlement date which would be 150 days from now?

I already answered this one a couple of days ago… Re: FRA… why can’t I solve this one? Posted by: Jack (o’-'o) (IP Logged) Date: May 14, 2008 06:10AM I thought this was a very poorly phrased question… He basically took out a 3x6 FRA 30 days ago @ 5%. 30 days later (i.e. now) we’ll need to work out the 2 x 5 FRA rate: 60 day rate annualised = 0.05 x (60 / 360) = 0.00833 150 day rate annualised = 0.054 x (150/360) = 0.0225 The 2 x 5 FRA rate = (1.0225 / 1.00833) - 1 = 0.01405 The price of the 3 x 6 is 5% or annualised to 0.0125 The difference between the traded 3 x 6 FRA and the current equivalent 2 x 5 FRA = -0.00155 -0.00155 x 10,000,000 = -15,500 Discount this back to present value = -15,500 / 1.054^(150/360) = \$-15,164 Please let me know if I got that wrong… Jack EDIT: difference due to rounding error.

thanks jack, that was driving me nuts

jack, how do you get that it’s a 3x6 FRA from the question given?

so basically buddy takes a 3x6 contract 30 days ago. its priced at 5% now the contract is a 2x5, and we need to value this ish. get the price of a 2x5 subtract the 5% and multiply it by the principle value to get the value then discount that ish to today using the 150 day rate.

the shorter will pay the libor valued as 1 at 60 days later (float rate always converge to 1 at rate setting date), and receive 1+5%*90/360 in 150 days. so today’s value is a discount of this CF: that is (1+5%*90/360)/(1+5.4%*150/360)