Diversification through Low Correlation
July 18, 2005
Attain Capital believes one of the main ingredients of long term investment success lies in trading a portfolio of lowly correlated trading systems, where losses in one system can possibly be offset by gains in another. Correlation coefficients measure the relationship between two variables (investment returns in this case) during a given period of time. For the purposes of investments, we are especially interested in whether there is a close match between the variables' monthly movements. The last thing we want as an investor is a losing month or quarter by one trading system in the portfolio magnified by an equally bad month in additional systems within the portfolio. While there is an increase in the potential return of two investments closely related; there is even more added risk in two investments which move in tandem.
The statistical method used to measure the correlation of two trading systems is the simple correlation coefficient. The correlation coefficient is a statistical measure of the degree of linear relationship between two variables. While the emphasis in regression analysis is on predicting one variable from the other, the emphasis in correlation studies is on the degree of the relationship between two variables. In regression the interest is directional, one variable is predicted and the other is the predictor; in correlation the interest is non-directional, the relationship is the critical aspect.
The correlation coefficient may take on any value between plus and minus one. The sign of the correlation coefficient (+ , -) defines the direction of the relationship, either positive or negative. A positive correlation coefficient means that as the value of one variable increases, the value of the other variable increases; as one decreases the other decreases. A negative correlation coefficient indicates that as one variable increases, the other decreases, and vice-versa.
Taking the absolute value of the correlation coefficient measures the strength of the relationship. A correlation coefficient of r=.50 indicates a stronger degree of linear relationship than one of r=.40. Likewise a correlation coefficient of r=-.50 shows a greater degree of relationship than one of r=.40. Thus a correlation coefficient of zero (r=0.0) indicates the absence of a linear relationship and correlation coefficients of r=+1.0 and r=-1.0 indicate a perfect linear relationship.
So what correlation are we looking for in putting multiple systems together? Obviously not -1.0, since every dollar made in one system would be offset by a dollar lost on another system. Equally as bad, although not as obvious, would be a correlation of 1.0, which would be great in the good times, but possibly devastating in the bad times, as every dollar lost in System 1 would be matched exactly by a dollar lost in System 2. The goal, therefore, is to get as close to zero as possible, signaling the absence of any linear relationship.
It is important to note that a low correlation does not guarantee two systems will not encounter losses in the same day or month, however. Correlation measurements are lagging indicators, for one, measuring the correlation of two systems PAST results. As the old saying goes, however: Past Performance does not guarantee future results. Well, past correlations do not guarantee future correlations either.
The tables below show the correlation coefficients of several trading system pairs as measured on hypothetically tested monthly results over the entire data set for each system. The first table shows the fifteen system combinations showing the lowest correlations (closest to zero) between them, and the second table shows the fifteen system combinations showing the highest correlations (closest to +1 or -1).
In looking over the first table of lowly correlated pairs, it is interesting to note nearly all of the system pairs contain two systems of different styles. For example, there is long term trend following (Andromeda Index) with day trading (BWT Rock'n Russell), and swing trading (Mesa Bonds) with day trading (Electric Daybreaker ES).
Overall, 60% of the fifteen lowest correlated pairs showed the two systems having different styles (i.e. day trading vs swing trading), 100% showed the two systems working on different markets, and 86% of the fifteen lowest correlated systems showing systems using different logic.
In the second table showing the fifteen highest correlated systems all contain pairs of systems with the same trading style and market focus. You will quickly see that the majority of pairs in the fifteen most correlated list are systems operating on the same time frame. You have Aberration and Andromeda, both long term, trend following systems which focus on multiple markets. There is Impetus eRL and Bounce eRL, which are both day trading systems operating on the same market. And finally, you see many pairs of systems which use the same logic but in different markets - such as Bounce eMD and Bounce eRL, Mesa Bonds and Mesa Notes, and Axiom Index eRL and Axiom Index eMD.
These tables provide hard proof that diversifying between markets, time frames, and developers is more than just a catch phrase - it actually produces low correlated results. Loading up on all of the systems from one developer, trading only swing trading systems, or concentrating solely on S&P futures will create a portfolio of systems which exhibit higher correlation - and that can produce higher volatility and poor performance.
To run your own correlation studies on systems you trade or are interested in - try Attain Capital's Correlation Wizard at www.AttainAccess.com
You will be prompted for the username and password you created when registering on the Attain website. If you have forgotten your username or password, don't worry, we have the info. Click on the following link to enter your email and have your personal username and password emailed to you. http://www.attaincapital.com/access/sendpassword.php
Once inside Attain Access,
1. Go to Correlation Wizard page by clicking on link at top of page
The correlation wizard allows you to enter up to 5 systems to see the correlation between them. Using the simple form shown below, users simply select a system in the left column, and click the >> arrows to move it to the right column.
2. Use Wizard to enter the systems you wish to see correlations for.
Once all the system you want to test are in the right column, hit submit to see the correlations. And Voila! A correlation matrix showing the correlation between each of the systems you selected as well as the correlation of each system with hedge funds, stock, prices, interest rates, and commodity prices (as measured by various indices).
3. View Correlation Matrix for the systems you selected.
IMPORTANT RISK DISCLOSURE
Futures based investments are often complex and can
carry the risk of substantial losses. They are intended for sophisticated investors and are not suitable for
everyone. The ability to withstand losses and to adhere to a particular trading program in spite of trading
losses are material points which can adversely affect investor returns.
Feature | Week In Review | Chart of the Week |
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Feature | Week In Review | Chart of the Week |
Investors continue to be bullish on stocks with both SP futures (+1.22%) and NASDAQ futures (+2.75%) seeing solid gains last week. Surprisingly, the gains have slowed in both the Russell 2000 futures and SP Midcap 400 futures markets as both markets finished the week unchanged from the previous week after hitting new all time highs intra-week.
A slight downward move in the energy markets no doubt helped propel stocks higher. Crude Oil futures fell -2.73% after damage from Hurricane Dennis proved less severe than originally thought. Crude derivatives Heating Oil (-3.14%) and Unleaded Gas (-3.81%) also sold off, however Natural Gas futures rallied gaining +5.11%.
The grain markets continue to be where the action is, as grain futures had a big up week in the face of severe drought conditions across the Midwest. Corn futures led the charge gaining +8.94%, while Soybeans (+6.32%) and Wheat (+3.34%) also were up for the week.
Finally, it seemed like most currency and bond traders took the week off as these markets barely moved all week. There was a late sell off in the bonds on Friday, but the markets ended the week nearly right where they started on Monday.
*Day Trading**
The bulls were charging last week with the S&P 500 Index closing on four-year highs and the Nasdaq Composite closing on its 2005 high. Despite the buying spree, several short term models struggled to turn a profit for the week due to light volume and narrow trading ranges (most of the moves higher happened during off hours).
Only a handful of systems were able to bring home profits last week. BWT Zones Russell added to the stellar month it is having with profits of $500 per contract last week, while RC Success continues to be one of the most consistent day trading systems and gained another $117.50 per contract. Other systems seeing profits included: Clipper eRL, which was good for $95.60 per contract in profits for the week on three trades, Impetus eRL - which traded just once but made $60.40 per contract, and BWT Rock N Russell, which made just $34.30 per money management unit using the position manager.
Elsewhere, systems struggled with choppy trading conditions and shed some of the profits made in the week prior. R-Mesa saw a slight roadblock last week on its way back to 2005 profits, trading three times for a total loss of -$2,031.50. Day Breaker had a hiccup last week as well, dropping -$1,139 for the week on three trades similar to that of R-Mesa. BWT Zones SP usually dominates the low-volatility conditions, but ended up losing -$900 for the week. Compass, meanwhile, was profitable on two of three trades but lost -$418 for the week.
Finally, Helix SP traded less than usual with an average of just one trade per day but lost a total of -$800 (-$380 per ES), RC Miracles traded just three times for a loss of -$40 per emini contract, and the Electric Day Breaker portfolio was unprofitable by -$1,147.50 trading one emini contract on each of the four markets (ES, NQ, eRL and eMD).
**Swing Trading**
Despite last week seeing 2 out of the 5 most actively traded stock index futures hit all time high’s (eMD and eRL), the weeks results ended mixed for the various swing trading systems.
Of the systems that traded last week, Tzar ES turned in the best trade of the week earning +$1,037.50 on a long trade it had held since June 26th. The system is now short the market and losing -$342.50 in open trade equity. Eclipse eRL also traded last week, locking in +$954 when reversing to long. The long trade propelled Eclipse to a new equity high as the eRL hit new highs.
Other swing trading included Tzar eRL which lost -$1,990 on a short trade and Tzar NQ which also lost -$1,320 on the short side of the market. Currently Tzar is holding long the eRL and eMD and short the ES. The Axiom Index system was not active last week; however is currently holding long the eMD and NQ for gains of +$1,815 and +$1330 respectively. The eMD has been holding long since 7/1 while the NQ has been in since 7/8…all other Axiom markets are flat.
Finally, Mesa Bonds and Mesa Notes continued to hold long the financial markets and do not seem to show any sign of reversing. Mesa Bonds lost -$437.50 and Mesa Notes lost -$375 in open trade equity on the week.
**Long Term**
This summer is shaping up to be a long one for farmers across the Midwest. Extreme drought has hampered crops and traders are beginning to position themselves for higher prices. Systems like Aberration Plus, Andromeda, Axiom LT, and SEMA4 Symmetry are also expecting prices to rise as each system has entered a few long grain positions. Axiom LT has been the most aggressive thus far entering long in corn, bean oil, and Minneapolis wheat. As of the close on Friday the system was profitable in 2 out of 3 markets with open trade profits of +$637.50 per contract in corn, +$628.00 per contract in bean oil, and an open trade loss of -$325.00 per contract in Minneapolis wheat.
Aberration has also been active entering long in corn and bean Oil. The system has been moderately successful in these trades to date with open trade profits of +$362.50 per contract in corn and an open trade loss of -$380.00 per contract in bean oil.
Andromeda and SEMA4 Symmetry have to this point only entered long in corn. Andromeda has open trade profits of +$87.50 per contract, while SEMA4 Symmetry entered a new long position this morning.
The bond markets were quiet last week, but they have pulled significantly off their highs of late June. The thirty year bonds are down -2.43% since June 27th and the other treasuries (10 year, 5 year, and 2 year) have followed suit. From a trading system perspective, trend followers are beginning to exit long trades across the board. Last week Andromeda exited a long 10 year note trade for a loss of -$1581.25, and Axiom LT exited a long 2 year note trade for a loss of -$659.38 per contract.
Finally, other system trades from last week include a long entry by Andromeda in crude oil, and long entry by Aberration Plus in sugar.
Please Login to: http://www.attainaccess.com for the latest updated statistics.
IMPORTANT RISK DISCLOSURE
Futures based investments are often complex and can
carry the risk of substantial losses. They are intended for sophisticated investors and are not suitable for
everyone. The ability to withstand losses and to adhere to a particular trading program in spite of trading
losses are material points which can adversely affect investor returns.