The expected return on forex exposure is very low. If your base currency is pound sterling and you invest, say, 10% of the portfolio in US dollars, what you might gain in higher interest rates would in theory be lost in the accompanying higher inflation that would result in depreciation of the currency - a zero sum game. However, in practice, exchange rates do not just follow real interest rate differentials. They are much more volatile. So you do not get any increased return but you get a big increase in volatility. That is why, in my humble opinion, forex exposure is a mug's game.

"The idea is that forex exposure is not quite a zero-sum game"

Having said that, there is something called the â€˜universal hedging' ratio that suggests the optimum percentage of overseas equity exposure that you should hedge is not 100% but more like 77%. The maths behind this is a bit intricate but is set out in Universal Hedging: Optimizing Currency Risk and Reward in International Equity Portfolios written by Fischer Black, and published in the Financial Analysts Journal in 1995.

The idea is that forex exposure is not quite a zero-sum game and that there is some positive utility to it. Going back to the example portfolio; let us say the US dollar exposure can double or halve with equal probability (for someone in the US this is the equivalent of saying that the sterling position can halve or double with equal probability); then for a Â£100m portfolio, the dollar exposure is going to be worth Â£20m or Â£5m with equal probability, for an expected value (mean) of Â£12.5m. This means the expected value of the portfolio is Â£102.5m!

In reality however, currencies do not double or halve, so the expected gain is much less, but it is still a gain. This is known as â€˜Siegel's Paradox' which can be resolved by thinking of two portfolios, one in dollars and one in sterling, but in common currency terms (either dollar or sterling would do). The apparent gain of Â£2.5m is wiped out by one of the currencies always being weaker than the other.

But in the forex world it is real, as you as an investor can only have one base currency (so looking at it from two perspectives is irrelevant) and therefore some forex exposure (not hedging everything) is a good thing.

It is worth mentioning by the way, that this does not apply to foreign bond exposure where relative bond volatilities mean that the recommended ratio spat out by the formula is 100%.

Published in Investment Week

The views expressed in this communication are those of Peter Elston at the time of writing and are subject to change without notice. They do not constitute investment advice and whilst all reasonable efforts have been used to ensure the accuracy of the information contained in this communication, the reliability, completeness or accuracy of the content cannot be guaranteed. This communication provides information for professional use only and should not be relied upon by retail investors as the sole basis for investment.

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