Correlation Explained

Margined Forex trading is a risky form of investment. As such, it is only suitable for individuals aware of and capable of handling the associated risks. Funds in an account traded at maximum leverage may be completely lost if suitable stop loss practices and procedures are not employed. Given the possibility of losing one’s entire investment, speculation in the Foreign Exchange market should only be undertaken with risk capital that, if lost, does not significantly affect the investor’s financial well being. I offer no guarantee that those who read the following information will make money. Readers use this information entirely at their own risk. The author and publisher of this information accept no responsibility or liability with regard to any loss or damage incurred from the use of this information. All intellectual property rights in this document remain the property of the author and publisher. The author will not be held responsible for the reliability or accuracy of the information available in this document. The content provided is put forward in good faith and believed to be accurate. However, there are no implicit or explicit guarantees that the readers of this document will make profit by trading currencies. The reader agrees not to hold the author liable for decisions that are based on the information presented in this document. © 2004-2009 Phil McGrew Rev. 4 All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording or otherwise, without prior permission of Phil McGrew.

CO R R E L A T I O N EX P L A I N E D

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TABLE OF CONTENTS

INTRODUCTION ......................................................................................................................................2

CORRELATION DEFINED ...........................................................................................................................3

LENGTH OF DATA ...................................................................................................................................5

CORRELATION IN MICROSOFT EXCEL ...........................................................................................................5

CORRELATION TABLES .............................................................................................................................7


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INTRODUCTION

Correlation, or more accurately, the lack of respect for correlation is a silent killer of Forex

accounts. Before I define correlation and trust me, I am going to drag you through the

definition, let me give you an example.

Let’s say you are a stock trader and you want a diversified portfolio. You know that by

diversifying you will minimize your exposure to the poor performance of any single company or

industry. So, you buy the following: Chevron, Occidental, Conoco Phillips, Exxon Mobil, Royal

Dutch Shell, and British Petroleum. These companies are all global petroleum producers. Are

you diversified? Clearly, you are not! Now, let’s look at a typical Forex trader. He might go long

on the GBPUSD and EURUSD and simultaneously be short the USDCHF. Is he diversified? Again,

the answer is clearly NO! All 3 of those currencies have the US Dollar in them and as such, any

movement in the dollar will clearly affect all 3 pairs.

OK, but you are smarter than that. You decide to trade the EURJPY and the USDCAD at the

same time. There is no common currency so that is a safe plan right? Not so fast gentle trader,

as I write this they are highly negatively correlated (they may or may not by the time you read

this). I have no idea why they are correlated and I’m not wasting any time thinking about it. The

answer could be anywhere from coincidence to soybeans. The point is that they (currently)

have a tendency to move in the exact opposite direction of each other. If you took these two

trades the gains and losses would offset each other and you would make no progress!

You can’t assign currencies to a group like you can stocks or commodities. The relationships

between countries and their currencies are constantly changing and that is why you must know

to what degree they are correlated.


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CORRELATION DEFINED

Correlation is a statistical term that indicates the strength and direction of a linear relationship

between two sets of random variables. In simpler terms, the correlation formula draws a “best

fit” straight line through a random set of data, which in our case are the various closing prices

of a currency, and compares it to a second line drawn through the additional set of data which

in our case is a second currency pair. To make matters more confusing there is more than one

correlation formula and the results of correlation are often expresses as a correlation

coefficient rather than a true correlation. After researching, I found that the Pearson product-

moment correlation coefficient was the most accurate for trading applications. This is the same

exact correlation formula used in Microsoft Excel and I will prove that later in this chapter. But

first, the formula:

As you can clearly see, the correlation is simply the covariance of the two data sets, X and Y,

divided by the standard deviations of X and Y. A visual example should help clear things up. In

the introduction I mentioned the relationship between the EURJPY and the USDCAD. Here is a

chart of those two pairs:


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When 2 currency pairs are plotted together it is much easier to view them as a line connecting

the closing prices rather than as individual candles. The correlation indicator is applied to the

bottom of this chart and has an indicated value of -0.65on a scale of -1.00 to +1.00. This is often

displayed in whole numbers and when done, would indicate a value of -65 on a scale of -100 to

+100. They are the same thing.

From this chart you can intuitively see that in the recent past the two pairs did indeed have a

tendency to move in opposite directions. The point of correlation is to mathematically say “how

much” of this tendency exists at any given time. To simplify this we will categorize the degree of

correlation into broad categories and use this information to make smarter trading decisions.

The correlation indicator that ships with TradeStation is actually incorrect and they have

acknowledged this. If you want the correct coefficient of correlation indicator for TradeStation

let me know. Some platforms do not support the simultaneous plotting of two currencies and

for this reason, I have not converted the indicator to other platforms.


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LENGTH OF DATA

Calculating correlation requires a “lookback period” much like any moving average calculation

would. There is no standard answer or formula that we can use to determine how much data to

consider when calculating correlation. The amount of data considered is a compromise

between extremes; if you consider too much data then the value will not be responsive to

changes in the market and if you consider too little data then the value would be too

responsive and not represent the overall trend. I have seen arguments that a value of 50

periods will yield good results, make the formula responsive and respect the past market. It

pains me to use a non-scientific number in a statistical formula but I am left with no choice. The

bottom line is that the formula looks back 50 periods.

CORRELATION IN MICROSOFT EXCEL

It’s a little known fact that Microsoft Excel is capable of performing correlation calculations. You

might find this exercise cumbersome and painful because it would require you to enter (or

import) a lot of price information to perform the calculation. Continuing with the previous

example, I have imported the data and I’ll show you a portion of the excel spreadsheet. The

formula used in excel is

=CORREL (array1, array2)


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Here is the same calculation in Excel for the last 50 data points:

From this table you can see that the calculated correlation value of -0.6473 matches very well

with the TradeStation calculated value of -0.65.


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CORRELATION TABLES

Despite the importance of correlation there is very little useful data on the internet that is

helpful to us as traders. To solve this problem, I hired several programmers (3) to solve various

parts of the problem and ultimately produce correlation tables that covered more currency

pairs and more time frames than anything I could find on the internet. The correlation tables

can be found here:

http://www.currensys.com/ctables.php

To continue with our original EURJPY / USDCAD example, I have taken a screen shot of a portion

of the applicable table. You can see that the highlighted row and column intersect at the

EURJPY / USDCAD cell. You can also see the value of -65 in the upper left corner.

.


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I will discuss the general features of the table and then we will continue with our example. The

table is set up as a matrix of 30 currencies. The same currencies that are listed in the first row

are duplicated in the first column. Because this table is larger than most monitors, I listed the

10 most popular currencies first (upper left quadrant of the table). The remaining 20 currencies

are listed in alphabetical order.

To determine the correlation of any combination of pairs simply locate one pair on the black

horizontal row and the other currency on the black vertical column. It doesn’t matter which

currency is horizontal and which is vertical. You will arrive at the same value either way.

You will notice that there aren’t actually any numbers in the individual cells. The numbers

aren’t actually all that important. As I suggested earlier, knowing the general category of

correlation is good enough for most of us. The cells are color coded as follows:

This combination of currencies shows little to no correlation.

This is a white box that has been selected by clicking on it.

This combination of currencies shows moderate correlation

This is a moderate box that has been selected by the user

This combination of currencies shows a high degree of correlation

This is the highly correlated box that has been user selected

Basically, there are 3 colors: White, Tan, and Copper. The other 3 boxes are the same but have some dimension to them to highlight user selections.

White boxes represent correlations between -40 and +40. This represents non-correlation and combinations of pairs may be traded without concern of dependence upon each other.


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Tan boxes represent correlation values between -69 and -40 or +40 and +69. It’s OK to trade these pairs but be careful. The lower the number (closer to zero) the better.

Copper boxes represent high correlation values. Do not trade highly correlated pairs! Seriously,

don’t do it.

In my opinion, knowing the category and making trading decisions off of that category is good

enough. However, some people want to know the actual value of correlation and I have

accommodated that request.

I have added a couple numbers to the table to point out some of the features.

1. Correlation Value Box – If you mouse over any cell the actual correlation value will be displayed in this box. This box is repeated in all 4 corners of the table so that no matter where you are you will still see the number.

2. Multiple Time Frames – Since most of us agree to trade the system on one or more of four different time frames I thought it was important to support correlations in each of those times. When you mouse over any of the four times the chart will automatically reload the values and colors for that table. If you go back to the original table your selections will still be present.

3. Selectable Fields – You can select any row or column by clicking on the appropriate black box. This is particularly helpful if you are in a trade and would like to look at other currencies for additional opportunities.. A second click will deselect the row or column. If you click on an internal cell it will highlight the entire row and column that combine to mark your selection. Again, a second click will undo this action.

The correlation tables update every 15 minutes but new values cannot be generated more

frequently than the time frame they represent. For example, even though the 240 minute

charts are updated every 15 minutes the values will only change once every four hours.

You should also be aware that the correlation web pages do not refresh automatically. Please

refresh your browser to pull in the latest values.

Correlation Explained

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