FRA at Expiration - Can't Understand Answer

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aedgar

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Assume that at FRA expiration, 150 day Euribor is actually 7.5%. Given NP of $20m, value of short position is closest to:
Answer: $14,001.40
NP * (Mkt Rate - FRA rate) * (t/360)
————————————————
1 + [Mkt Rate * (t / 360)
FRA Rate from previous answer is 0.0767
Thus,
Numerator = $20M * (0.075 - 0.0767) * (150 / 360) = $-14,166.67
Denominator = 1 + [0.075 * (150/360) = 1.03125
When i Divide the numerator and denominator, I get -$13,737.38
How are they getting the $14K answer that I bolded at the top? What step am I missing? I understand to convert the negative to positive as they are doing a short position, but I’m not understanding the $14K calculation.
Thanks in advance.
 
Wiley question in Derivatives Reading 47 - Lesson 3 Forwards on Fixed Income Securities and FRAs.
 
Working backwards, if i divided the numerator of -$14,166.67 by -$14,001.40 and subtract 1, this gives me the market rate after applying the % of t that the loan occurred (i.e. 270 /360). If i then divide the answer by that %, I get a 2.8% market rate so the math just isn’t adding up in my opinion.
 
So is my figure correct, based on my math?
 
Actually, it’s a rounding issue. The set of questions involving that particular FRA was probably created and calculated in Excel. If you calculate the FRA price in Excel then use that result in the payoff formula you get the same answer as in the Wiley guide.
Gotta love Excel and large notional principals eh?
 
Yup: that’s what it is.
Get a couple more decimal places on the FRA price and you get the correct answer.
Good job, JayWill! I was just using the numbers that aedgar had in his original post.
 
That big of a rounding issue worries me though. Could this occur on the exam or would they not provide an answer that would be carried out through Excel?
Thanks for the input JayWill
 
Or don’t round the numbers at all. Use the STO and RCL buttons to keep inputs raw.
 
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