How exposed are you to currency risk?

If you're a British investor who puts money into international investments either directly or through a fund you're exposed to "currency risk".This means that your returns depend on how sterling performs against foreign currencies. For example, let's assume you buy US stocks. If the dollar rises against sterling, your US investments are worth more in sterling terms. If it falls, they are worth less.

That's fairly straightforward. But let's make it more complicated. For example, lets assume that you buy European stocks through an exchange-traded fund (ETF) that's priced in US dollars. How does having another layer of currency movements affect your returns?

Most investors assume that you are then dependent on how the other currency performs. For example, with our European ETF, you need to worry about how sterling performs against the dollar as well as how strong the euro is. But this isn't usually true. What matters is still how sterling performs against the euro. The dollar is irrelevant. To see why this is, let's look at an example.

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Two ways to get the same result

Imagine that at the beginning of 2014 you put £10,000 into an ETF priced and traded in sterling that invests in Europe. At the time, the EUR/GBP exchange rate was 1.2038, meaning that you invested a total of €12,038.

The MSCI Europe index rose by around 4.1% during the course of 2014. By the end of 2014, the EUR/GBP exchange rate was 1.2876. Your return in euro terms was, of course, 4.1%, giving you a totalof €12,530 by the end of the year.

Your return in sterling terms was unfortunately worse, due to the fall in the euro against the pound. By the end of 2014, your fund was worth £9,732 (€12,5301.2876) a loss of 2.7%.

As an alternative, let's assume you put your £10,000 into an otherwise entirely identical ETF that is priced and traded in US dollars. At the start of 2014, the USD/GBP rate was 1.6566 and the USD/EUR rate was 0.7268. So your £10,000 initially becomes $16,566. That's then converted into euros and you end up with €12,040 the same amount as before, subject to a small rounding error.

As we've already seen, the MSCI Europe index rose by 4.1% in 2014 and your ETF was worth just over €12,530 by the end of 2014. The euro depreciated against the dollar during the year, with the exchange rate falling to 0.8266. But the dollar appreciated against sterling, rising to 1.5577. That means that in US dollar terms, the ETF was worth $15,162 by year end (€12,5300.8266), a fall of around 8.5% on its original value.

That reflects both the rise in the MSCI Europe over the year and the loss from the weaker euro. To calculate your return in sterling terms, we then convert that back into pounds and get £9,733 ($15,1621.5577), which is again a loss of 2.7% on your original sterling investment.

The currency triangle

Why do we get the same result either way? To understand this, you need to keep in mind that our three exchange rates (EUR/GBP, USD/GBP and USD/EUR) are not separate numbers, but a triangular relationship. When you change one exchange rate, you must change one or both of the others in a way that keeps the relationship consistent.

Imagine that sterling rises against the dollar. If USD/EUR does not change, sterling must also rise by an equal amount against the euro. Alternatively, EUR/GBP may remain constant, in which case the euro must rise by an equal amount against the dollar. Or more likely in reality all three rates will change to differing extents.

If this didn't happen, currency traders would be able to earn risk-free profits from arbitraging exchange rates. Imagine that USD/GBP rose by 10%, while the other two rates remained unchanged.In that case, you could earn a guaranteed 10% by buying dollars with sterling, then buying euros with dollars, and finally buying sterling again with euros.

Obviously, this isn't possible. The foreign-exchange market is highly liquid and highly efficient, so even the very small arbitrage opportunities that emerge as exchange rates move are traded away very quickly. So we find that howeverwe move around this triangle of FX rates, we must come to the same result.Going sterling to euros and back to sterling must produce the same result as sterling to dollar to euro to sterling.

So for a British investor in euro-denominated investments, it is just the change in the EUR/GBP rate that matters. Whether the fund is quoted in sterling or dollars and what path the money takes when it's changing currencies makes no difference.

In fact, the vast majority of global foreign-exchange trades take place through the US dollar in any case. So even if you invest in a sterling-denominated fund that invests in European stocks, there's a chance that your money will be converted into US dollars before being converted into euros and the same on the way back. That will almost certainly be true if you're investing in something in a more exotic currency.

The impact of hedging

Of course, this only applies where the fund isn't hedging the currency. If our USD-denominated European ETF hedged the euro-dollar exchange rate, the result would be different. Our return in that case would be equal to the return of the MSCI Europe in euro terms, plus the change in the USD/GBP rate (minus the cost of hedging).

In that case, the change in sterling versus the dollar would affect our returns. So if you are investing in a hedged currency fund, you need to be aware of this. But in most cases, the currency that the fund is priced in doesn't matter. All you need to take into account is how sterling moves against your investment's home currency.