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Long-run currency risks

Exchange rates tend to mean-revert. Even so, long-run currency risk is significant
March 15, 2018

Many of you are saving to buy a property overseas or are hoping to retire there. You therefore face long-run exchange rate risk – the danger that the currency of the country you hope to move to will rise, and so your money won’t go as far as you’ve planned. How great is this risk?

In theory, we can quantify it if we make a few assumptions. Let’s take the euro. Since 1993 the monthly standard deviation of the €/£ rate (or ecu/£) has been 2.27 percentage points. If we assume that the best estimate of the future exchange rate is the current one and that past volatility is a guide to the future, this implies that there’s a roughly one-in-six chance of the euro rising 2.27 per cent or more in a month.

If we then assume that exchange rates follow a random walk – so one month’s changes are unrelated to the next month’s – we can derive long-run risk from this. We do so simply by multiplying monthly volatility by the square root of the number of months in our time horizon. So the volatility of 12-month changes should be 2.27 multiplied by the square root of 12, which is 7.86 percentage points. And the volatility of three-year changes should be 2.27 times the square root of 36, which is 13.6 percentage points. This tells us there’s around a one-in-six chance of the euro rising 13.6 per cent or more over a three-year period. That’s enough to significantly increase your cost of living or house price if you’re hoping to move to Spain.

Now, you’ll notice there’s a lot of assumptions here. There’s one in particular I want to test – that exchange rates are a random walk, with monthly changes independent of each other.

We can test this easily. To see how, imagine the exchange rate strongly mean-reverted so that a fall in one month was reversed the next. Two-month volatility would then be less than one-month volatility. Long-term exchange rate risk would then be less than short-term risk.

If, on the other hand, there was momentum in exchange rates – with falls leading to further falls – two-month volatility would be greater than one month. Long-run exchange rate risk would then be proportionately greater than short-run risk, unless the momentum was reversed over the long run.

By comparing the actual volatility of two, three, or four-month changes to those implied by a random walk, we can check whether exchange rates are in fact a random walk. My chart does this for moves in the euro/pound (€/£) and dollar/pound ($/£) rates for horizons ranging from two to 60 months based on monthly changes since 1993.

Take the $/£ rate. Short-term moves – up to 10 months – are slightly more volatile than a random walk predicts. This is consistent with small momentum effects. Longer-term changes, however, are less volatile.

For the euro, the picture’s less clear. In the short term (up to 10 months) there’s a little mean-reversion, but there’s momentum over around 18 months, giving way to slight mean reversion.

Other currencies show a similar pattern to the dollar. The yen/pound rate is more volatile than a random walk predicts over around two years, but less volatile over five. So, too, to a lesser extent, is the Swiss franc.

All this is consistent with exchange rates having a simpleish pattern. In the nearish-term they have momentum; changes feed on themselves. But this means they overshoot fair value and so eventually mean-revert, causing longer-term changes to be less volatile.

This behaviour is very different to equities. My chart shows how the All-Share performs on the same test. It has more momentum than currencies, and this momentum isn’t corrected even over five years. Bull and bear markets in equities are stronger and longer-lasting than those in currencies. Does this mean currencies are relatively safe over longer periods?

No. My chart shows only quite small deviations from the random walk. Actual five-year volatility in the €/£ rate has been 17 percentage points – more than enough to make that holiday home unaffordable. And for another thing, my chart shows only what’s happened since 1993. It’s possible that this history is an unreliable guide to the future in two ways.

One is simply that past volatility, even over 24 years, needn’t be a good guide to future volatility at least over the time horizon that matters to you. In the jargon, exchange rates might be non-ergodic.

Secondly, it’s easy to imagine an event that causes a permanent fall in sterling. Anything that depresses the UK’s long-run growth rate relative to other countries, such as a messy Brexit, would have this effect.

Long-run exchange rate risk is, therefore, significant – even though we might not be able to quantify it precisely. Those of you who are exposed to it should consider protecting yourself by holding the currency of the country you plan to move to.

My story, though, is about market dynamics. The evidence suggests there are momentum and mean-reversion effects in currencies – albeit perhaps weakish ones – which is consistent with the idea that exchange rates overshoot their fair value. In this sense, FX markets are not like stock markets, where momentum effects are stronger and longer.