Exchange Rate

CFA Level I
#1

Came across the following question. The answer provided is A but I think B is correct. Can anyone please confirm?

QUOTE

A New Zealand traveler returned from Singapore with SGD 7,500 (Singapore dollars). A foreign exchange dealer provided the traveler with the following quotes:

Ratio Spot Rates

USD/SGD 1.2600

NZD/USD 07670

The amount of New Zealand dollars (NZD) that the traveler would receive for his Singapore dollars is closest to:

A. NZD 7,248

B. NZD 7,761

C. NZD 4,565

Answer = A

The NZD/SGD cross-rate is NZD/USD x USD/SGD = 0.7670 x 1.2600 = 0.9664

The traveler will receive: NZD0.9664 per SGD; NZD0.9664 x SGD7,500 = NZD7,248

QUOTE

#2

Answer is A. Instead of multiplying SGD7500 by 0.9664 you multiplied it by its reciprocal 1.0348. When dealing with conversion make sure that the the currency you want to convert is the base currency not the price currency. Since you want to convert 7500 SGD to NZD, your SGD currency must be the base currency. Think about it mathematically:

7500 SGD * 0.9664 NZD/SGD. SGD need to “cancel” out to get NZD so it has to be the base currency.

#3

Thanks cfageist.

I’m still a little confused. Referring to the USD / SGD cross-rate, I understand this to mean 1 USD = 1.2600 SGD (since USD is stronger than SGD). In the same vein, I would have thought NZD / SGD = 0.9664 would imply that 1 NZD = 0.9664 SGD (i.e. SGD is stronger than NZD). Accordingly, the amount of NZD that the traveler would receive = 7,500 / 0.9664 = 7,760 NZD.

Am I missing something here?

#4

In order to find the amount of SGD per USD you would need the reciprocal. Everything is expressed relative to the base currency. In this case 1 USD is actually equal to 0.7937 SGD expressed as 0.7937 SGD/USD.

If you have 1 USD you will be able to buy 1.26 SGD. Similarly, if you have 1 SGD, you will be able to buy 0.7937 USD.

Also keep in mind that when you are calculating appreciation and depreciation in percentage or forward points, it is always expressed relative to the base currency. If you need to find it for the price currency, find the reciprocal first and then calculate percentage change or forward points/percentages.

#5

Sorry for taking up so much of your time but it seems that the two sentences below are inconsistent?

"In this case 1 USD is actually equal to 0.7937 SGD expressed as 0.7937 SGD/USD.

If you have 1 USD you will be able to buy 1.26 SGD. Similarly, if you have 1 SGD, you will be able to buy 0.7937 USD."

Based on the calculations, I still get B as the answer.

#6

Sorry typo, the second sentence is accurate. The first sentence should say 0.7937 USD is equal to 1 SGD expressed as 0.7937 SGD/USD

#7

Thanks cfageist! Very helpful

#8

I don’t quite agree with the above solutions, can someone else verify this?

Here is a live example from the current Spot rates in the market:

USDSGD 1.3345

NZDUSD 0.7025

NZDSGD 0.9375

These are all from a live FX platform quoted as I write this message.

If you convert the USDSGD to SGDUSD , you get 0.7493

So you realize that SGD is stronger than NZD. so if you divide them as below you will get the same answer as above for NZDSGD

NZDUSD 0.7025 / SGDUSD 0.7493 = 0.9375

This basically tells you that 1 NZD is equal to SGD 0.9375. Hence if you have SGD 7500 for example, you would do 7500/0.9375 and get the answer which should be more than 7,500.

For the question above, if you follow the same steps, you get the answer to be B) 7,761

#9

@ gk1309, what I understood was that for the purposes of the exam, FX rates are always expressed as price currency / base currency - i.e. number of units of price currency for each unit of the base currency.

Anyone else please feel free to correct me if I am mistaken or if you agree with my understanding.

#10

When CFA Institute writes USD/GBP 1.3358, it means that USD1.3358 = GBP1.0000.

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#11

So in this example, USD/SGD 1.2600 means SGD 1 = USD 1.2600?

#12

Yes.