FURTHER INFORMATION ABOUT AXIOM INDEX

Background

The foundation of what would become AXIOM was first formulated in 1995, using a pool of about 30 commodities as the test sample. In its original version, it was meant to be a multi-market, long term system using daily bars. However, due to capitalization concerns, I did not trade it and instead returned to my interest in the S&P. In August of 2003 I tested the original to see how it would have performed in the intervening years and was pleased to see it had done very well. After August I focused on improving Axiom Long Term, working extensively on improving the basic entry technique. I then tested many, many different types and variations of exit strategies on the original markets: ATRs, Bollinger Bands, variable moving averages, days-in-trade, RSI, dollar volatility, etc. In the end, I settled on simple, fixed-dollar stop strategies: an initial relatively close stop, one or two profit-lock stops, and a profit objective. These did the best job of minimizing risk, letting trades run their course, and protecting profit. With the initial development phase completed, I tested an additional 30 markets, and found results to be excellent.  In March, 2004, I applied the system to intraday data and discovered that it worked very well swing-trading indexes. I also tested the original version of AXIOM, which uses a simpler set of entry cycles, and performance was even better. To this I added a filter which I have found works specifically with indexes, and adjusted the stops to fit the increased dollar volatility of the indexes.
AXIOM Index averages from 2.5 to 7 trades per month, depending upon the index, and it is in a position 50-60% of the time.

AXIOM Long Term versus AXIOM Index

Both versions of AXIOM rely on the observation that markets consist of a variety of trend lengths & that successful trading requires the mutual confirmation of these trends. The original version of AXIOM used 4 trend lengths, & this became AXIOM Index. Adding additional trends proved a better platform for trading non-index markets using daily bars, & this version became AXIOM Long Term. As mentioned, a filter & different stop values further differentiate the index version.

Avoiding Over-Optimization

The fact that the basic logic of AXIOM applies to a wide variety of markets and time frames attests to its robustness and balanced approach to optimization. Also, from the beginning AXIOM Index was developed using four indexes, the S&P 500, S&P Midcap, NASDAQ, and Russell 2000. Using an extended portfolio helps to ensure that no values or rules will be chosen that favor just one or two markets, i.e. curve-fitting is reduced.  Additionally, all of the primary entry values consist of Fibonacci numbers, reducing the extent to which optimization is possible. I don't believe there's any magic to Fibonacci, but by limiting the range of values from which to choose, one limits the amount of curve-fitting possible (e.g. rather than choosing the best value from 1-25, Fibonacci allows only to choose between 1, 3, 5, 8, 13, and 21). Further, both in testing and in the final choices, the dollar values for stops were limited to increments of 250-1000, reducing the "fine-tuning" that can occur at this stage.
I believe strongly that a system should be as simple as possible, avoiding special rules that fit only a few situations or periods: the coding for AXIOM is 35 lines, utilizing only those rules and values that work on a variety of markets over time.
As validation of the AXIOM Index principles, consider the excellent hypothetical results on the Dax, an out-of-sample market. Another example is the Kospi, which is the South Korean Index. An interested party recently sent data for this liquid market, and AXIOM Index does very well trading it (view results here). A final example is the India NSE Index. Such out-of-sample results are the best way to prove the validity of a system.

Realistic Analysis

Two numbers are the key ingredients of my rule and parameter choices: return per risk and k-ratio. I treat the maximum drawdown as the primary risk number, and I measure this using Monte Carlo software. This program allows me to determine not just the maximum drawdown of the single historical equity curve, but to vary that curve thousands of times. From this, I can determine the average maximum drawdown, average percent drawdown, and their standard deviations. Relying on the single historical equity curve leaves one open to engineering an artificially low max drawdown and high profit that is dependent upon that specific equity curve for its good numbers. By tossing the trades together in randomly different orders, such a weakness can be uncovered. The development of AXIOM was predicated upon this approach. In the next step, I divide the net return by two times the average max drawdown to determine the reward per risk. A parameter set may have lower profit, but if it achieves that profit at a lower risk, then I choose it.
The k-ratio, developed by Lars Kestner, measures equity curve smoothness by calculating the deviation of trades in an equity curve from the linear regression line of that curve. According to him, "The K-ratio detects inconsistency in returns" and measures "the consistency of results through time." Essentially, it quantifies the "swinginess" of the equity curve. Investors prefer an equity "curve" that approaches an ascending line, implying less risk. Kestner states that typical values of the ratio fall between -5 and +5 (the higher, the better), & that he looks "for systems with an average K-ratio of 1.0 or better for individual commodities..." The single-commodity k-ratios for AXIOM Index markets are from 3.6 to 6.3, with portfolio k-ratios from 4 to 7.
These two numbers provided most of the basis for my choice of the specifics of AXIOM. Consequently, AXIOM has a high return per risk ratio, and its equity curves exhibit evenness, as evidenced by high k-ratios.