Question CAD/USD rate

[Anonymous]

Question : Using covered interest parity, calculate the 3 month CAD/USD forward rate if the spot CAD/USD rate is 1.1239 and the three month interest rates on CAD and USD are 0.75% and 0.4% annually respectively.
(a) 1.1278
(b) 1.1200
(c) 1.1249
(d) 1.1229
Your Response was incorrect
The correct answer is choice ‘c’
Forward rates can be calculated from spot rates and interest rates using the formula Spot x (1+domestic interest rate)/(1+foreign interest rate), where the ‘Spot’ is expressed as a direct rate (ie as the number of domestic currency units one unit of the foreign currency can buy). In this case the forward rate will be 1.1239 * (1 + 0.75%*90/360) / (1 + 0.4%*90/360) = 1.1249.

It can be confusing to determine which interest rate should be considered ‘domestic’, and which ‘foreign’ for this formula. For that, look at the spot rate. Think of the spot rate as being x units of one currency equal to 1 unit of the other currency. In this case, think of the spot rate 1.1239 as “CAD 1.1239 = USD 1”. The currency that has the “1” in it is the ‘foreign’ and the other one is ‘domestic’.

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In my understanding, an fx rate noted x and given as ‘CUR1/CUR2’ always means 1 unit of CUR1 equals x units of CUR2, in other words you need x units of CUR2 to buy 1 unit of CUR1. (see http://en.wikipedia.org/wiki/Currency_pair : “This [base/foreign currency] ambiguity leads many market participants to use the expressions currency 1 (CCY1) and currency 2 (CCY2), where one unit of CCY1 equals the quoted number of units of CCY2”)

In that case, a CAD/USD rate of 1.1239 means that 1 CAD = 1.1239 USD. Applying the forward rate formulae, as 1.1239 is the 3-months forward rate, and given the interest rate of each currency, the CAD/USD spot rate is 1.1249. Answer ‘c’ is correct.

[kzg]

Question CAD/USD rate

[Anonymous]

Kzg,

I hear what you are saying. Traders normally just know what they are talking about when they deal, and in real markets because often traders specialize in a few currencies & the shorthand used can be quite different from the way these things may be described in books. For example they often quote only the third and fourth decimal places for some currencies, and not even bother to specify which is currency 1 and 2. I am not an FX trader, have never been one and quite frankly I am unaware of the convention that would apply to different currency pairs.

So the approach I have taken is the safe one for the exam, ie use what the PRMIA handbook describes. For the way they have expressed the formula, my explanation holds correct. Other ways of looking at it may also be right outside of this context – and quite frankly if one understands the concept the formula becomes irrelevant.

For whatever it is worth – hope it helps. There is no shortage of ways to get completely confused and lose one’s head – thanks to Google.

But thank you for your time and making the effort to highlight this.

Mukul

[Anonymous]

Hi Mukul,

I understand your point, and read again the Handbook, but I confrm that there is indeed a slight mistake (only appearing once in an example, regarding the use of the “CUR1/CUR2” notation).

Simply said : in a “CUR1/CUR2” fx notation, the currency to the left of the slash is the base currency. The base currency is always equal to one unit, and the quoted currency (the one on the right) is what that one base unit is equivalent to in the other currency.

Now, regarding the direct/indirect quote issue : a direct currency quote is simply a currency pair in which the domestic currency is the base currency ; while an indirect quote, is a currency pair where the domestic currency is the quoted currency.

So if you were looking at the CAD as the domestic currency and USD as the foreign currency, a direct quote would be CAD/USD, while an indirect quote would be USD/CAD. The direct quote varies the foreign currency, and the quoted, or domestic currency, remains fixed at one unit. In the indirect quote, on the other hand, the domestic currency is variable and the foreign currency is fixed at one unit.

In the test question, you might ask : “Using covered interest parity between CAD and USD, calculate the 3 month CAD forward rate if the spot CAD rate is 1.1239 vs USD and the three month interest rates on CAD and USD are 0.75% and 0.4% annually respectively.
(a) 1.1278
(b) 1.1200
(c) 1.1249
(d) 1.1229

Thus, to answer this, you need to know that CAD is quoted as a foreign currency and that 1.1239 refers to the USD/CAD rate (1 USD = 1.1239). It would be different with EUR, as you might know that EUR is quoted as a base currency, therefore 1.1239 would refer to EUR/USD quote (1 EUR = 1.1239 USD)

[Author]

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