### Implied interest rate from FX swap

• 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)
Sell Notional (spot) C2: 100,000,000.00

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

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.

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.

Apologies. I clarified the currencies in the edit.

8 years ago

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 $r_2 = 0.8486$.

Awesome! How did you find out the conventions? Thanks.