Forward Rate agreements Exam 1

[Anonymous]

An FRA trader entered into an FRA agreement in which he will pay 6%(assuming quarterly compounding) between 3 months and 6 months. The principal for the trade is $3 million. The 6 month LIBOR spot rate is 5.8%. If the trader had a gain of $2550 at the end of the period, The 3 month LIBOR rate would be?

A. 5.30%
B. 6.30%
C. 5.25%
D. 2.51%

The correct answer is A. how do we get there??????????????????

[Anonymous]

Hi,

Could you please mention the PRM handbook and page number please so I can try to help you.

Thanks

[Anonymous]

I got the question from edupristine mock tests 11-11-2012

[Anonymous]

This is the explanation given but still cant get it.

Draw out all the known and unknown on a timeline.

Step 1: Given that the profit is 2550, find the underlying rate (floating rate) associated between T=3 and T=6 when the fixed is 6%. Let that rate be y%

Step 2: Using 5.8% between T=0 and T=6 and y% between T=3 and T=6, find x% which is the 3 Month LIBOR.

Please remember they are asking the 3 Month LIBOR, not the floating rate in the question.

[Anonymous]

Hi,

If I follow you steps, I get the following:

1. y= 2550 * 365/93 / 3000000 * 100 = 0.33% (0.333602)

2. (1 + x/100 * 93/365)(1 + (6+y)/100 * 93/365) = (1 + 5.8/100 * 186/365) (no arbitrage condition)

thus x = 100 * [1 + 5.8/100 * 186/365)/(1 + (6+0.333602)/100 * 93/365))-1]*365/93 = 5.18276%

I don’t know how they get 5.3% unless I missing something on the profit…

[Anonymous]

Hi,

If I follow your steps, I get the following:

1. y= 2550 * 365/93 / 3000000 * 100 = 0.33% (0.333602)

2. (1 + x/100 * 93/365)(1 + (6+y)/100 * 93/365) = (1 + 5.8/100 * 186/365) (no arbitrage condition)

thus x = 100 * [1 + 5.8/100 * 186/365)/(1 + (6+0.333602)/100 * 93/365))-1]*365/93 = 5.18276%

I don’t know how they get 5.3% unless I am missing something on the profit…

[Anonymous]

this is it

Let x be the libor rate between the 3 months and 6 months [e^x*.25-(e)^.25*.06]*3000000=2550
[e^x*.25-(e)^.25*.06]=[2550/3000000]=.00085
(e)^x*.25=1.015113
(e)^x*.25=1.01596
.25x=.015836
x=6.334%
3 month libor as of today=(e)^.5*.058/(e)^.25*.06334=1.0294246/1.015963=1.01325=(e^3 month libor*.25)=>.25*3 month libor=.013163=>3 month libor=.05265=.0527~.053(rounding off to next higher place decimal)

thanks

[Anonymous]

You did not mention to use continuous compounding ! That’s why my result (5,18%) is a little bit off compared to yours (5,26%)!

And by the way, rounding 5.26% to 5,3% is definitely not a market practice….

[Anonymous]

i agree. edupristine said in real practice continuos compounding is used. i am happy that we got the concept though! Its thier options on answers that need to be changed.

[Author]

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