# FRA... why can't I solve this one?

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 … help!! (#27499)

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

I get 15.160 - but it’s not negative! It must be positive because the FRA gave him a better price than the price today. So I think you got the sign wrong

But he’s short the FRA?

Sorry - didnt see that

Thank you Jack, I misinterpreted the 3x6 thing completely.

Jack (o’-'o) Wrote: ------------------------------------------------------- > > Discount this back to present value = > > -15,500 / 1.054^(150/360) = -15,164 \> \> Please let me know if I got that wrong... Only difference I had was (as libor is add on rate) I did -15500/(1+0.54\*(150/360)) to discount it back - which gives -15,159. But I think we’re close enough for a cigar.

Why doesn’t jack post more? - pretty good explanation up there

Thanks for the compliment Joey!! Means a lot from coming from you! (been on these forums for the last couple of years so seen you post a lot…) I don’t post much as I normally have no clue, just that I covered derivs not long ago so happened to know this so thought I’d help a fellow AFer =)