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# Moving Abroad: Can We Optimize FX Conversions?

### Enrique Millán

#### 29/09/2021

If you have had the chance to live outside of your home country, you might have faced the dilemma of exchanging currencies. Today we are going to get into the vocabulary of these transactions, and if they are worth optimizing in the scale of a household.

We will follow Teresa on her new adventure to London (GBP). She has just moved from Madrid (EUR), and she will be studying there for the next couple of years. Teresa needs pounds for her daily life: to pay her rent, groceries, etc.; but she receives money back from Madrid, in euros.

Before we run some numbers, let’s set up the vocabulary we would use if we were defining this problem at The Factory.

### Currency Risk

Teresa has to place a tag to each currency in the EURGBP rate: a risk currency and a base currency. The base currency is her home currency, the one in which we will express the results. In this case, euros. The risk currency is the one Teresa is exposed to.

To be exposed to a currency means that she has capital (or has to provide it) in that currency, so she is concerned about the fluctuations in value of that currency (with respect to her base currency). In this case, pounds. To that capital we refer to as exposure.

#### Long vs. Short

Additionally, one needs to define if Teresa is interested in the rise or the fall in value, in currency terms, of her exposure. To capture this idea, we borrow the terms from the stock market, to be long and or to be short.

Because she needs to meet certain recurring payments in London, she has a debt in pounds. Therefore, she is interested in the fall of the pound in face of the euro.

If pounds become cheaper, she will need less euros to meet the same debt.

Her rent is going to remain fixed in pounds, but it could become cheaper in euros if the pound falls.

Summing up, we say “Teresa is Short GBP”.

### Does Timing Matter?

The rent is paid at the beginning of the month. Teresa can naively convert her euros to pounds the day before. Or she could convert smaller amounts the previous four weeks, so that the actual amount is met by the end of the month.

That is, we are going to compare a naive strategy with a dollar-cost averaging one. Since one strategy will trade four times more often than the other one, we have included transactions costs. We took them from a known company which converts money worldwide. They charge a fixed fee of 0.5 EUR and a variable fee of 0.5% of the converted amount. We assume that Teresa’s rent and running costs add up to 2000 GBP, and that she must face them on the first business day of each month.

Let’s have a look at which one is better!

#### Analysis

For the four-year period ranging from september 2013 to september 2017, Teresa would have been better off converting smaller quantities in the previous weeks, rather than converting all the money in a one-off trade.

This is so because at the beginning of the period, the EURGBP rate was declining, hence it was becoming more expensive to pay the same debt. By changing smaller amounts every week, Teresa manages to save up almost 400 EUR after two years.

However, when it becomes cheaper to pay off the debt (when the EURGBP grows), she starts losing money if she converts smaller amounts every week. When this is the case, it would be better to wait until the end of the month, since the price she will have available will be much cheaper than the one she has been facing during the previous weeks.

#### Psychological Impact

As we have seen, depending on the trend endured by the rate, it could be better or not to space out the conversion of base currency to face a debt in another currency.

And yet, there is a hidden benefit that comes from spacing out conversions.

In the previous table we have drawn some basic statistics for the recurring flows of money faced by each strategy. Expectedly, the flows of the dollar-cost averaging strategy are approximately four times smaller than those of the naive strategy. And this is what brings the hidden benefit: the flows of the dollar-cost averaging strategy are less spread out.

The business implications of this fact is that this kind of strategy is less likely to surprise us. From the table, the amount of money we convert every week changes approximately 44 EUR, whereas the flows of the naive one can go up or down by almost 200 EUR! That is, the flows for the dollar-cost averaging strategy will be easier to predict.

### Conclusions

We have compared two alternate strategies to face a debt in a foreign currency. Our hope was that spacing out conversions might bring some additional benefits, but due to the oscillating nature of forex exchange rates, whatever gain is obtained is potentially lost months later.

Nevertheless, breaking down the conversion of the whole amount did add some benefits from the business point of view, allowing for a more accurate financial planning.