By Jason Van Steenwyk

In part 1 of this series, we introduced Modern Portfolio Theory at a very basic level. Specifically, we looked at the mathematical concept of a correlation coefficient, and at the idea that two or more volatile assets can be combined within the same portfolio and potentially create a reduction in overall volatility and/or a greater expected return than reasonably available with a single risky asset by itself – a phenomenon called the *diversification benefit.*

Those of you who are slightly more mathematically inclined can find a reasonably good discussion in the abstract here, but let’s narrow the focus to currencies for now.

**Euros and Pounds / USD**

The value of the euro and British pound are historically closely-related when translated back into the U.S. dollar. It’s easy to see why: Monetary and fiscal policies and events that tend to strengthen the U.S. dollar tend to strengthen it against the euro and the pound at the same time and for the same reason.

Likewise, the converse is true as well. Events that weaken the dollar will tend to weaken it against the pound and euro alike.

This is part of the reason the long-term correlation of the currency pairs GPB/USD and EUR/USD is relatively high. In recent years, thanks to a currency and sovereign debt crisis that forced the euro down against other currencies, we’ve seen a marked decrease in the correlation between the pound and the euro’s performance against the dollar. But as that crisis gradually resolves it’s reasonable to expect a return to the longer term norm, under the principal of reversion to the mean.

(Whether the crisis is yet resolved, of course, is a much tougher call!)

For you technical trading types, this means that if you get a buy signal with one, you should get a buy signal with the other in short order. If correlations are tight and getting tighter, it also means it doesn’t do you much good to hold a GPB/USD position and a EUR/USD pair at the same time.

Why? It goes back to diversification benefit. Remember that correlation coefficients run from -1 (perfect negative correlation) to +1 (perfect positive correlation). As your correlation coefficient approaches its maximum, +1, your diversification benefit approaches zero.

You’re probably better off doubling down on the position that gives you a stronger signal rather than trying to hold both of them. If you can’t diversify away much risk, go for the return.

So if you have two highly-correlated assets, combining them may add trading costs without much risk reduction benefit or benefit to expected combined returns. If it doesn’t add trading costs, you still most likely are giving up the opportunity for a better trade that can help you reduce risk exposure.

At the same time, if you get a buy signal with one and a sell signal with the other, you will wind up shorting one against the other. If you do this with highly correlated assets, your returns will tend to cancel each other out, and all you’re left with is transaction and carry costs.

Yuck.

Now, if two currency pairs that *should* be highly correlated move in opposite directions for no good reason you can figure out, there is a potential to make a ‘reversion to the mean’ play, but that’s an arbitrage idea, and that’s very different from a pure Modern Portfolio Theory approach.

Instead, an MPT portfolio would suggest that after you have settled on a basic currency pair you are happy with, with some solid expected returns, you then carefully add assets that have a relatively low or even a negative correlation with your base pair.

For example, look at this week’s currency pair correlation matrix:

Graphic: www.forexticket.us

This is the weekly correlation matrix going back 50 periods, from a data aggregation site called forexticket.us. You can see the (updated) chart here.

Obviously, there are a lot more potential currency pairs to choose from, but for the sake of a reasonable display on this web page, here’s a small but useful sample.

Let’s say we took as our base currency pair the GBP/USD position. That is, you sold U.S. dollars and bought British pounds. Since a GBP/USD position is 100 percent correlated with a GBP/USD position, by definition, you wouldn’t get any diversification benefit by staking out the same position again. You would just magnify your returns, positive or negative, as well as your risk

Likewise, taking the inverse USD/GBP position – that is, selling pounds to buy dollars – simply cancels your trade out. The correlation coefficient between the GBP/USD and the USD/GBP position is -1, by definition.

Much better, from the point of view of the Modern Portfolio Theory purist, to look for currency pairs that have low or negative correlation to the existing position, and add those in.

To do so, we look for a position that has a correlation coefficient of, say, 0.65 or less, while still offering attractive potential returns.

By way of a real-world limitation, let’s assume that you only have an initial position of either dollars or pounds to work with. (Remember, you sold dollars to buy pounds. So we’re assuming you own nothing other than dollars and the pounds you bought!)

Looking at the above chart, what seems to have a low recent correlation with the GBP/USD position? AUD/USD looks promising, with a significant negative correlation of -52.9. Of course, that’s very close to the posted correlation between the GBP/USD and EUR/USD pairs, which is -52.9. We know that historically, these two pairs are usually much closer-aligned than they are now.

Let’s take another look, adding some AUD pairs to the matrix:

Graphic: Forexticket.us

We also find that the CHF, or Swiss franc, historically makes for some terrific diversification benefit, as well, against either British pound or euro-based pairs, whether long or short against the U.S. dollar.

And this provides the trader with an opportunity to move back and forth against the Swiss franc, depending on the trader’s appetite for changing his or her position and the economic headwinds. Whether you take a GBP/CHF or a CHF/GBP position, the relatively low level of correlation against the GBP/USD pair provides a diversification benefit either way.

It’s off the display, but the current trailing-50-week correlation coefficient between the base position of GDP/USD and a new position of USD/CHF is -90. Which means it would largely cancel out your original position. The correlation is too strong to the negative to be useful except as a risk management/collaring tool.

But a EUR/CHF position plays off well against GBP/USD pair, with a correlation of just -15.1. Mathematically, anyway, the two pairs are almost *uncorrelated*, that is, their movements are almost random, relative to and therefore should provide some significant benefits when combined together in a portfolio.

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