One of the most important aspects of trading also is one of the most difficult to describe. Known as money management, trade management, risk control or a number of other terms, virtually all managers agree that this element is the single most important part of a trading plan. For our purposes, money management will be how trades are allocated across one or more trading systems with a given pool of money. In the first of two parts, we will break down what responsible money management includes and develop a set of meta rules for applying it.
For those still unconvinced of the importance of money management, particularly with regard to profitable core systems, consider a classic coin-toss game. You win $6 when your guess is correct and lose $5 when your guess is wrong. This is a positive expectation game. Mathematically, this is:
(6*0.50) - (5*0.50) = 3.00 - 2.50 = 0.50
On average, we make 10% on each toss. Despite that incredible edge, controlling rules can make you bankrupt, not rich. For example, betting 50%, just three losses in a row would end our game (assuming an 85% loss is bankrupt). Further, there is a 1.56% chance -- a so-called “five-sigma event” -- that we can lose six times in a row. If we bet 30% of our account on each flip, $100 would become $11.77. Even with such strong odds in our favor, if we are betting 30% on each trade, one time in 75, we would lose more than 89% of our equity.
Many brilliant people have fallen victim to poor money management. One of the most well-known is Victor Niederhoffer. Another is Long-Term Capital Management. To see why, consider the other side of the six-sigma event. There also is a one-in-75 chance that our $100 will become $482.68. It’s easy to see how even brilliant minds can become drunk on leverage, confusing variance for genius.
Money management begins with proper performance assessment. If you don’t know how well a system is trading, you can’t begin to manage returns. We can begin this discussion with two terms: beta and alpha.
Beta is calculated using regression analysis. It describes the tendency of a position’s returns to respond to swings in the broader market, usually represented by an index. A beta of 1.00 indicates the position moves with the market. A beta less than 1.00 means that the position is less volatile than the market. A beta greater than 1.00 indicates the position will be more volatile than the market. For example, if a stock’s beta is 1.2, it’s theoretically 20% more volatile than the broader market.
Alpha is a measure of performance on a risk-adjusted basis. Alpha takes the volatility (price risk) of a position and compares its risk-adjusted performance to a benchmark index. The excess return of the fund relative to the return of the benchmark index is a fund’s alpha.
Alpha also is an abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like the Capital Asset Pricing Model (CAPM). A positive alpha of 1.00 means the fund has outperformed its benchmark index by 1%. Correspondingly, a similar negative alpha would indicate an underperformance of 1%. If CAPM analysis estimates that a portfolio should earn 10% based on the risk of the portfolio, while the portfolio actually earns 15%, the portfolio’s alpha would be 5%. This 5% is the excess return over what was predicted in the CAPM model.
In the world of trading system evaluation, we also could consider alpha as excessive returns compared to a standard benchmark system.
Trading advisor benchmarks
Consider a standard benchmark for professional trading advisors, the Barclay Commodity Trading Advisor (CTA) index, the leading industrial benchmark of representative performance of CTAs. There are currently 533 programs included in the calculation of the Barclay CTA Index for the year 2010, which is unweighted and rebalanced at the beginning of each year. This index is not tradeable, so you can’t duplicate its performance.
To qualify for inclusion in the CTA Index, an advisor must have four years of prior performance history. Additional programs introduced by qualified advisors are not added to the index until after their second year. These restrictions, which offset the high turnover rates of trading advisors as well as their artificially high short-term performance records, ensure the accuracy and reliability of the Barclay CTA Index. Due to inclusion qualifications, this index is a measure of all-star performance, not an average CTA.
This index has been tracked since 1980. Yearly statistics are available on Barclay’s website. Let’s look at the combined results of this index and explain some of its concepts (see “All-star traders”).
As we can see, managed futures has a low correlation to stocks and bonds -- the primary focus of many CTAs who strive to offer diversification compared to traditional markets. These programs contain long-term trend following as well as shorter-term strategies. They trade from both the long and the short side. This index will be our bench market.
The MAR Ratio was developed by the Managed Account Reports newsletter. It shortly became a popular tracking metric. The name is simply an acronym for the newsletter. The ratio can be used for comparing CTAs, commodity pool operators (CPOs) or even trading systems and strategies. One of the benefits of the ratio is that you can use it to compare a CTA with a trading system and generally get a good comparison between risk-adjusted returns for the programs over a specific past period of time.
There are a couple of important points to understand when using the ratio.
The longer the results for the trading program, the lower the ratio will ultimately become. Comparing five years of performance of one program against two years of performance of another program is not a valid comparison. You need an equal amount of periods of equal time frames.
The ratio is only a metric of what happened in the past. It has no predictive power. The ratio provides a quick reference for risk-adjusted performance of a period of time in the past. To calculate the MAR ratio, divide the compounded annual return of the program since inception by the worst drawdown since inception. The best hedge funds and CTAs over an extended period of time have MAR ratios between 0.50 and 1.00. For example, a program with a ratio of 0.50 attempting to earn 20% per year will see at least a 40% drawdown:
MAR = CAGR / MDD%.
Beta in sheep’s clothing?
The Barclay CTA Index has a compound growth rate of 11.68% (see “All-star traders”) with a maximum drawdown of 15.66%. This is an MAR of 0.74. Let’s suppose we have a CTA with a 30% compound growth rate, and a 45% maximum drawdown. This CTA is underperforming, as the index is at 0.66 in terms of MAR, so the returns are really “access beta” due to volatility.
The Barclay index is a 30-year index. This is an average of all CTAs, so in actuality this CTA shown by the index does not exist. This is why a CTA who has been in business for 10 years with a MAR in the range of 0.50 to 1.00 is considered a superstar, because this index is made up of many CTAs with great returns for a few years followed by bad returns before they ultimately go out of business. Some claim indexes overstate performance because of this survivorship effect.
An example of this inconsistency is that many CTAs who did well in 2008 did badly in 2009. Consider a baseball analogy. A player who hits 25 home runs has an average of 0.290, which is really not much better than an average player. However, if he does this for 20 years, he has 500 home runs and is a candidate for the Hall of Fame (as long as he didn’t use any performance-enhancing Ponzi schemes).
Alpha is a measure of skill over a baseline. For example, if we were trading a basket of exchange-traded funds, we could use the S&P 500 as a baseline. The Barclay index also can be used as a benchmark and baseline; however, the difference here is that we can’t actually duplicate it. This remains the best way to measure skill for a black-box trading system or program.
If we have access to the system logic, we have other ways of measuring skill. We can look at the performance of the system without the money management concept and develop baseline measures. For example, we can compare a trend-following system to a 20-bar channel breakout as the baseline. Financial-based systems can be compared to buy and hold. If we know that our components themselves offer alpha, it’s more likely that our solution offers alpha. Once we have tested each system, we need to overlay a set of meta rules to control money allocation and trade management.
You can perform this analysis manually. Some software offers automated solutions. For example, TradersStudio has what is called the Session Level, which allows you to test one system and set of parameters on one or more markets. You can test each system against a baseline and see if it provides a true skill-based edge over a baseline system (alpha).
Next, we can combine these using a series of controlling rules. In TradersStudio, this is called a Trade Plan. This allows us to use a pool of money that can be allocated between multiple strategies and markets. You can control how profits are reinvested and also do dynamic rebalancing.
Component benchmarks: A place to start
The below components will compose our baseline methodology. Because the Barclay index is really an index of all-stars, our benchmarks will give us a baseline of average performance. This is another reason for picking the classic simple system with standard non-optimized parameters.
Trend following basket baseline
Strategy: 20-bar channel breakout
Time frame: Day
Markets: Treasury bonds, S&P 500 and Nasdaq
Filter: 200-day moving average long only
Let’s start with the 20-bar channel breakout. The results in “20-bar benchmark” (below) represent a basket trading one lot for each market.
We deduct $75 for slippage and commission. Trade dates are April 2, 1991, to April 8, 2010. We include both good and bad markets because this should be a baseline that represents no skill level. However, using one-lot positions is not good practice because trading a one lot of cotton is not the same as trading a one lot of natural gas, which could lose $20,000 in one day. We can use a volatility-based sizing concept. We provide an example online (see futuresmag.com/murraycode) coded in TradersStudio.
Dynamic margins use a multiplier of TrueRange. For example, we use five times the 50-bar average TrueRange converted to dollars as a proxy for margin. Margins are not changed often and are mostly adapted after volatility shifts have rippled through the markets. We will use 30% of our margin proxy for sizing our positions.
We will use an account of $1 million to ensure all trades are taken from the start and we will also not limit the number of contracts traded. Once again, we will use the period April 2, 1991, to April 8, 2010. Results are shown in “Volatility-adjusted breakout” (below).
If we look at the breakdown on a dollar volatility-adjusted basis, we see that the ratio of the profits is much higher for copper vs. crude. Copper makes more profit than crude, volatility-adjusted, even though crude made more money on a one lot. Lumber also made a higher percentage of profits on this volatility-adjusted portfolio than it should have made.
A risk-balanced approach produces significantly different results. We can next take the same process and develop our financial and bond market baselines.
There are two ways to add alpha to a trading program.
The first way is to use a system that adds trading skill, meaning simply developing better rules for entry and exit. The problem is the more complex the systems get, the more likely they are not going to perform as well as in the future as historical results suggest.
The other way is to use meta rules to control risk, filter trades and rebalance portfolios. One example of this would be to limit how many long vs. short trades are allowed. We could limit correlation. The problem is that these correlations change when large sigma events occur. We would expect, for example, gold and T-bonds to be negatively correlated; however, if rates are dropping too quickly and bond prices are going up, the relationship can invert, and gold can rally due to inflation fears. The concept means that diversity does not really exist, and during times of disaster uncorrelated portfolios can become correlated.
This concept also explains the main problem with modern portfolio theory. If you have a portfolio of different sectors of stocks and rotate them, you might think you are safe; however, in the case of a major world crisis, you might as well have invested all your money in the S&P 500 index. All world stocks become correlated during such events -- the Russian crisis of 1998, the aftermath of September 11, 2001, and the financial meltdown of 2008.
In our next article, we will discuss common trade and risk-control methodologies, as well as how to use better systems to show development of trading programs that generate true alpha.
Murray A. Ruggiero Jr. is the author of “Cybernetic Trading Strategies” (Wiley). E-mail him at firstname.lastname@example.org.