# The Quick and Dirty Guide to Modern Portfolio Theory – For Currency Traders – Part 1

You have heard it said that you have to take risks to make money. And there is truth to that. You may have also heard it said that if you want greater returns, you have to expose your portfolio to greater risk. Traditional economic theory suggested, in the past, that expected returns were something that had to be purchased at the cost of the primary coin of the realm of investing – increased risk.

As it turns out, with apologies to George and Ira Gershwin, it ain’t necessarily so.

Modern Portfolio Theory, first formally introduced to the finance community by Harry Markowitz in the 1950s, sketches out the mathematical argument that two or more assets, combined in a portfolio, can and frequently do provide superior risk-adjusted returns than a single asset by itself.

Markowitz showed mathematically that by combining multiple assets in a portfolio that were not highly correlated with one another, the investor could, in theory, reduce his risk exposure without giving up expected returns. Conversely, he could also increase expected returns at a given level of risk.

The result: The theoretical ability to increase expected returns… with no increase in expected volatility.  Or, as economic theorists more colloquially refer to it – a free lunch.

Correlation

The key to understanding the “free lunch” and where it comes from lies in the mathematical concept of correlation. In a nutshell, correlation simply refers to the tendency of two different assets to move together.

Correlation is measured using a term called correlation coefficient, which plots the likelihood of two assets moving in tandem along a continuum between +1 and -1.  A correlation coefficient of +1 indicates the two assets always moved together during the testing period. A correlation coefficient of -1 indicates that the two assets always moved in opposite directions during the period of time examined. And a correlation coefficient of 0 indicates a random relation, or no relationship at all.

A Very Simple Example

Imagine two streams of income, one comes from a ski resort in Colorado and the other comes from a beach resort on Cape Cod, Massachusetts. Both will have very uneven cash flows because of the innate seasonality of the business. Cape Cod will make all its money during the summer months, and probably lose money during the winter. The Colorado ski resort, on the other hand, will make all its money during the winter months, and probably lose money over the summer.

Since one asset tends to make money when the other asset is losing money, the correlation coefficient between the two is negative.

It’s probably not perfectly negative. The closest thing to a perfect negative correlation in the investment world is shorting a long position (or vice versa).

Now, suppose you sold the ski resort and used the money to buy a hotel in Daytona Beach. Well, then your cash flows would be very highly correlated with one another.

Put another way:

Asset Pairs in a Two-Asset Portfolio        Correlation Coefficient

Colorado Ski Resort     /     Utah Ski Resort                                    0.85

Colorado Ski Resort    /      Cape Cod Beach Resort                    -0.75

Correlation Coeff: +1.0                        -0.75

Cape Cod Beach Resort / Utah Ski Resort                                  -0.80

Daytona Beach Resort / Cape Cod Beach Resort                     +0.75

Correlation Coeff: +0.85              -0.75

Now, most people can grasp intuitively that if overall expected return over the course of many years is roughly the same across each of these four assets, it is better to own a (northern hemisphere) ski resort and beach resort in tandem than it is to double down on any one investment, or to own either two ski resorts or two beach resorts in the same hemisphere. A five year old can grasp that by owning two assets that are not highly correlated in the same portfolio, the overall volatility of cash flows goes way down – without a reduction in expected returns. Over the long haul, the portfolio should still make money – and in about the same long-term rate of return it did for a single asset – again assuming profitability, cash flows, etc. are equivalent.

The difference: Each investment, though profitable in itself over the long term, cancels out the others’ volatility in the short term.

There you have it: Reduced volatility, with no commensurate reduction in expected return.

The free lunch.

The extent of the free lunch is known as the diversification benefit. The lower the correlation coefficient between a portfolio and a new asset being added to that portfolio, the greater the diversification benefit.

Is it possible to overdo diversification benefit? Yes. If your goal is profit, you mix two assets with a perfect negative correlation coefficient of -1.0, you haven’t done yourself much good. Your new asset simply cancels out your old one for as long as you own both. But you are still out your transaction costs and costs of carry.

Meanwhile, you are also out money you could have profited by selling some or all of your pre-existing asset and putting it in a money market or some other essentially risk-free investment.

It’s a good short-term risk management technique, if you want to lock in a certain price point for a brief period in time without incurring short-term capital gain taxes (or ordinary income tax, if you fall under active trader rules) by selling your entire long position. But it’s not something you want to do indefinitely if you are looking to make money!

Applying MPT to FOREX

Just as other assets, such as income streams from ski resorts and beach hotels, can be compared with one another for covariance and correlation, so can currencies. Or, more specifically, currency pairs. Since its currency pairs that generate profits in the FOREX world – that is, it’s how currencies bounce off one another that matters to the FOREX trader. So a FOREX trader would compare the profits or losses from two currency pairs against one another for a specific period of time in order to determine a correlation coefficient.

It sounds more complicated than it is, but if you have a series of returns for both pairs, it’s an easy operation to do in an Excel spreadsheet.

But fortunately, you won’t have to. A number of media outlets actually publish the correlation coefficients of various currency pairs over various trailing time periods.

Here’s one from Investing.com.

Here’s a video that teaches you how to create your own correlation display in matrix form.

Some software packages or subscription services will stream correlation data for you and display it as a matrix as well. And OANDA publishes correlations in matrix form, using prior 1-hour, 1-day, 1-week, 1-month, 3-months, 6-months and 1-year time periods, in three different formats. Here it is in decimal form:

A snapshot of the correlation coefficients of various currency pairs from FXTrade.oanda.com

Looking at this matrix, you can quickly grasp that the USD and the Swiss Franc are very strongly negatively correlated. This was consistent over all examined time periods. They have historically tended to move in the opposite direction from each other. As long as past trends continue, their inverse relationship seems not only predictable, but substantial: The correlation coefficient didn’t dip to a number less significant than -.88.

Meanwhile, both the euro and Japanese yen currency pair and the USD and British Pound Sterling demonstrate fairly substantial positive correlation over the last several trailing time periods, going back a year.

In Part Two of this series, we’ll look at some ways you can use this data, and your grasp of diversification benefit, correlation coefficients, and reversion to the mean to help you not only reduce your risk, but also potentially identify and unlock profitable trading opportunities.

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