O ne area where investors and even experts get themselves into a muddle is currency risk – specifically when it comes to the currency that a fund is priced or denominated in.

Currency risk itself is pretty straightforward, and familiar to anyone who has ever been on holiday or who owns a property abroad.

Lets say youre a British resident whos headed to the U.S. for a vacation in three months. You decide to take some dollars with you, and you opt to convert a whopping £1,000 into dollars because youve heard that youll need to tip big to avoid a lynching.

Youre also very old-fashioned, so you want to get this sorted out three months in advance. Ignoring transaction costs 1 :

• At a rate of £1:$1.60, your £1,000 buys you $1,600 dollars

Lets suppose that before your holiday, the pound strengthens so that £1 now buys $2. But youve already changed your money, at the old rubbish rate!

• At the new rate of £1:$2, your $1,600 is now worth (1,600/2) = £800

Ouch!

It could have gone the other way. Currency risk has upside as much as downside.

Currency risk and the underlying assets

Converting holiday money is straightforward – and exactly the same thing happens when you make overseas investments .

Lets say that rather than going on holiday, you do what Id do – being a tightwad – and put £1,000 into a tracker fund that follows the US market instead.

All the stocks in the tracker fund are based in the US, listed on the US markets, and priced in dollars as youd expect. Your US tracker fund is therefore buying a bunch of US dollar denominated assets.

At the £1:$1.60 exchange rate:

• Your £1,000 investment buys $1,600 of dollar assets 2

Three months later, the exchange rate is £1:$2. If the US stock market has not changed over the period, youd log on to your broker and see:

• Your investment is now worth $1,600/2 = £800

Of course its more likely the market would also have moved over three months, as well as the exchange rate. If the US market had gone up 10%, your investment would be worth £880. If it had fallen 10%, youd be looking at a princely £720.

In fact, its usually stock market moves not currency moves that will dominate your returns. (Also, currency changes usually – though not always – happen more slowly than in my example, which I just dialed to high to make my point.)

Fund denominations dont matter

Safari, so-goody, as Christopher Biggins used to say in a kids TV program that has me showing my age.

Where people get confused is when they buy a fund that is denominated in a currency other than that of the underlying investment .

A typical example would be a UK-traded ETF that tracks the Japanese market, but is denominated (/priced) in euros.

The mistake people make is they think they are exposed to multiple currency risks – in this case the euro as well as the Japanese yen.

This is wrong – you are only exposed to the underlying assets currency.

Lots of people make this slip. For example, Morningstar has an article up as I write that states:

unless, of course, you really know what you’re doing when it comes to forex and, for example, you want to take a bet that emerging market currencies will appreciate against the euro, that the euro will appreciate against sterling, and that these events will converge in time for when you choose to sell your shares.

The implication of this quote is that a UK investor who buys an emerging market fund thats denominated in euros faces a double-whammy of two currency risks – the pound versus the euro, as well as versus the emerging market currencies.

Thats incorrect. As a UK investor youre only exposed to emerging market currency risk in buying the euro-denominated fund. The exchange rate between the pound and the euro is irrelevant!

Currency risk: The science bit

Ill show why its the underlying asset currency that matters in two different ways.

First Ill use a bit of algebra, and then well go through a real-life example.

Algebra first.

Lets say you are a UK investor who has rather oddly decided to buy a euro-denominated ETF that holds only UK shares. 3

The Euro-priced ETF holds UK-listed assets – BP, Tesco, Lloyds, and so on – that are denominated in sterling.

(1) The quoted price of the ETF in euros:

= Value of UK holdings * (pound/euro exchange rate)

Now lets say you log into your UK fund platform to find out what your ETF investment is worth today in pounds – your native currency.

Clearly its £ value is equal to the value of the ETF in euros, adjusted for the euro/pound exchange rate.

(2) In other words, the value of the ETF in £:

= Price of ETF in euros * (Euro/pound exchange rate)

Now we can substitute (1) into equation (2) to give us the value in pounds as:

= Price of ETF in euros * (Euro/pound rate)

= (1) * (Euro/pound rate)

= (Value of UK holdings * (Pound/euro rate)) * (Euro/Pound rate)

= Value of UK holdings * (Exchange rates cancel out) 4

= Value of UK holdings

In other words, as a UK investor who is investing pounds, this fund of UK assets is worth its value in pounds, regardless of whether its priced / denominated in euros, yen, or Malaysian ringgits.

What about if you were a UK investor buying a euro-priced ETF that invested in the Japanese stock market?

Here the underlying assets are Japanese, so the exchange rate that matters for a UK investor is the pound/yen exchange rate.

To see this, we can modify my equation above to take the value of the ETF in pounds to be:

= Value of Japanese holdings * (Pound/euro rate) * (Euro/Yen rate)

= Value of Japanese holdings * (Pound/Yen rate)

Again, the pricing currency (here its euros) is irrelevant and vanishes from the equation. The euro introduces no extra currency risk.

Note: Some funds hold a lot of cash. which may introduce an additional currency risk. If for example you own a European-based investment trust that invests in Japanese equities but that holds 10% of its assets as cash in euros, then as a UK investor you do face currency risk on those euros, as well as on the much larger exposure to the Japanese yen. Cash held by ETFs and trackers is usual trivial, however, and can be disregarded.

Currency risk in the real-world

Lets really drive the point home with a real-world worked example.

Imagine the Japanese tracking ETF mentioned above comes in two denominations – the original euro-denominated ETF that we looked at above, and another one denominated in pounds sterling.

As a UK investor, youd be naturally drawn to the ETF denominated in pounds. But in theory it makes no difference which one you buy 5 .

Lets look at the pound denominated Japanese tracking ETF first, using real data from Google Finance for historical stock market levels and exchange rates.

Its 6 Jan 2012 and you decide to invest £1,000 into this Japan-tracking ETF.

At the time of your investment:

The Japanese stock market is at 8,390

£1 buys 119.5 yen 6

You invest £1,000, which means you invested in yen terms:

1,000*119.5 = 119,500 yen

On 4 January 2013 you decide to cash out. Over that time the Japanese stock market rose to 10,688 – a gain of 27.4%.

So your investment in local yen terms is:

= 119,500 yen plus the 27.4% gain

= 152,243 yen

We now have to convert back into pounds. Turning again to Google Finance. I see that on 4 January 2013:

£1 buys 141.6 yen

So your investment is worth in pounds:

= 152,243 / 141.6

= £1,075

Notice that although the local market went up 27.4%, you ve only gained 7.5% in pounds. Thats because the pound strengthened against the yen, which meant your yen bought fewer pounds when converted back into sterling. This is true currency risk in action.

Hopefully that was pretty easy to follow. But what if youd bought the euro-denominated ETF ?

Trickier to work out, as we need to know a couple more exchange rates.

On 6 January 2012:

One pound bought 1.21 euros

One euro bought 98.6 yen

So – deep breath! – you again invest £1,000:

£1,000 = 1,210 euros

1,210 euros = 119,472 yen

As we saw, the Japanese market rose 27.4% over the year.

This time your investment in local terms:

= 119,472 yen plus a 27.4% gain

= 152,208 yen

Checking on Google Finance. I see on 4 January 2013:

One pound bought 1.23 euros

One euro bought 115.2 yen

So converting back:

152,208 yen = 1,321 euros

1,321 euros = £1,075

Magic! Again you have ended up with £1,075, despite the fact you invested via a euro-denominated ETF.

The exchange rate changes between the pound and the euro have disappeared from the equations. It is the exchange rate between your currency and the currency of the investment – in this case the yen – that matters, and determines your currency risk.

Why this happens: Related currency pairs are perfectly inter-connected, which is what enables the denominating currency to disappear above. If this wasnt the case, then you could profit when currency exchange rates got out of kilter. For example, you could might be able to convert pounds into yen, and then convert those yen into euros, and then convert those euros back into your original currency, pounds, for a profit. You cant do this because the currency markets are extremely liquid, deep, and efficient, and any miniscule opportunities like this are immediately arbitraged away.

Currency risks and rewards

Dont be surprised if you see people saying something different to the above. Theyre wrong and Im right, as the worked example I plodded through above proves, even if you werent convinced by my elegant algebra.

Check the figures with Google Finance if you dont believe me! And see this similar example that uses the Thai baht.

The takeaway should be clear:

• Currency risk is determined by the local currency of your foreign asset.

• Even if you buy a vehicle that is priced in your own currency, such as a UK investor buying a UK-listed ETF thats denominated in pounds, if the fund invests in overseas stocks then youre exposed to the currency risk of the underlying assets.

Despite the scary name, currency risk isnt necessarily a bad thing, as you can win as well as lose. Also, its another kind of diversification and so can reduce risk .

You dont want to completely ignore your home currency. If youre going to be a UK pensioner, it would be madness to have all your assets in Japan. One day youll need to spend pounds in the shops and you dont want to be completely at the mercy of the prevailing pound/yen exchange rate when you retire.

But as part of the global diversification of a well-constructed long-term portfolio. currency risk is not something to be afraid of.

Thanks for reading! Monevator is a simply spiffing blog about making, saving, and investing money. Please do check out some of the best articles or follow our posts via Facebook, Twitter, email or RSS.

The costs of exchanging money at airport booths and so on are massive in the real world, and you should explore all the different ways to pay abroad – but thats another article. [↩ ] Again ignoring any transaction costs. [↩ ] An ETF targeted at European investors, in other words. [↩ ] One small caveat is there may be money changing charges made by the fund or charged by your broker when converting from one currency to another racked up along the way. But that is a separate issue. [↩ ] As throughout this article Im ignoring small currency related transaction costs that are a different issue [↩ ] I am going to ignore small rounding errors throughout for clarity. [↩ ]