### CFA Practice Question

There are 206 practice questions for this study session.

### CFA Practice Question

A firm sells a 5 x 8 FRA, with a NP of \$300MM, and a contract rate of 5.8%. On the contract expiry date, the 3 month spot LIBOR is 5.1%. The firm will receive ______.

It is calculated as: [(300,000,000 x (0.058 - 0.051) x (90/360)] / [1 + 0.051 / (360/90)]

User Comment
george2006 the numerator= 300M * (0.007)* 90/360 = 0.525 M
discounted to time t1 = 5months, it should be somewhat smaller than 0.525 M.

Or the diff might be attributed to rounding errors?
katybo The firm is a seller!
ganone the answer is correct. you discount at 5.1% the underlying rate. The number of day is 90 days as it is on 360 day basis.
Bibhu The general formula for this

Notional Principal x [(Floating - Spot) Days/360]/ [1+ Floating x days/360]
Floating : 5.8% Spot 5.1%
omer123 The firm takes the short position so it can borrow at the low underlying interest rate 5.1% and receive the contract rate 5.8%, it would have been reversed if the firm was the buyer.
aakash1108 ...i.e. it can borrow at 5.1% and lend at 5.8% and earn the spread in between i.e. 0.7%. However, the firm will earn this spread at the end of 3 months. Thus, it discounts that spread i.e. [\$300MM X 0.7% X (90/360)] = \$525,000 to todays value.

Therefore, with discounting:
PV=525,000/(1.051)^(90/360) = \$518,511 (*)

(*) Rounding error minimized.
asthildur If you look in the notes the denominator should be 1+ (0.051*90/360) and you will get the right result of \$518,390. It's because you are discounting for the time period of 90 days with the annual interest rate of 5.1% which is changed to a 90 days rate.
viannie The firm sells.
Using the standard formula gives negative but because the firm is the seller, the one in short position in a decreasing interest rate situation gains. Therefore the firm gets paid \$518,390 (round off)
TheHTrader What does 5 x 8 FRA mean in this case?
TheHTrader Never mind. 5=effective 5 months from now, 8=terminated 8 months from now, based on 3-month LIBOR
tschorsch The discounting in the denominator is simple multiplication, i.e. 1+rate*(n/360) because the quoted rates are the appropriate period (i.e. 3 month LIBOR in this case) and do not need to be compounded. I.e. the rate quoted was correct for the period. If you compound, you will discount by the annual yield.
jpducros Rates decrease from 5.8 to 5.1 => the seller/short wins.
ZoltanPongracz the formula says underlying-FRA rate and .058 was used for underlying and then the underlying figure in the denominator is .051? why is that??
rocyang [(300,000,000 x (0.058 - 0.051) x (90/360)] / [1 + 0.051x (90/360)].
johntan1979 Good luck, you all. It's not as hard as it seems. More practice will do the trick.
jimmyvo You are wrong, Bibhu and rocyang. Your equations. The denominator equation should be "360/days" NOT "days/360"
jimmyvo tschorsch is also wrong. equation in denominator.
mtsimone The short is Float – FIxed, the Long FRA is Fixed – Float.

The short made out since: Notional(Fixed – Float)(days/360/[1+(Float*days/360)] = 5118,390.

The convention in IR FRAs is simple interest, noty compounded interest.
mtsimone Boneheaded error: I meant the Short is Fixed – Float in the first sentence, but the calculation has it right.

Rocyang has it right.
ashish100 Jimmy vo multiplied by 90/360 same as divide by 360/90