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This is not homework. I am trying to calculate the implied interest rate of one currency (C2) using an FX swap and the interest rate of another currency (C1 - base). I have the following:

Spot: 7.7587 (C2 per unit C1)
Buy Notional (spot) C1: 12,888,757.14
Sell Notional (spot) C2: 100,000,000.00

Start date: 6-May-13
End date: 7-May-14

Buy Notional (forward) C2: 100,000,000.00
Sell Notional (forward) C1: 12,905,390,58
Forward FX rate: 7.7487

I have a borrowing in C1 for 0.9650% for the year.
Using interest rate parity: $$ F_0 = S_0 \frac{1+r_{C2}}{1+r_{C1}} $$
I solve for $ r_{C2} = 0.8349\%$.
However, I am told that the right answer is $0.8486\%$.
Which should be the implied interest rate in currency C1. Am I crazy or missing something?

Do I need to consider FX basis?

EDIT
If I use ACT/360 for C1 and ACT/365 for C2 with $ACT=365$ I get actually pretty close $(0.8483\%)$. Is that it? Is the difference caused by daycount?

C1 is USD
C2 is HKD
(I believe these are the correct day-count convention based on a paper by UBS). Not sure where to find the "official" declaration.

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well, its impossible to say if you dont tell us which day count conventions must be applied. The question, wherever it is coming from should make a mention of that. –  Matt Wolf Jun 28 '13 at 4:44
    
Apologies. I clarified the currencies in the edit. –  PBD10017 Jun 28 '13 at 5:41
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1 Answer 1

up vote 1 down vote accepted

Because the day count of your inquired date is 366 days:

  • Hkd daycount is act/365 therefore 366/365
  • Usd daycount is act/360 therefore 366/360

$$ \frac{7.7487}{7.7587} = \frac{1+r_2(\frac{366}{365})}{1+0.00965×\frac{366}{360}} $$

Solving for $r_2 = 0.8486$.

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Awesome! How did you find out the conventions? Thanks. –  PBD10017 Nov 11 '13 at 5:23
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