微信：
QQ：
A Look At The Turtle Trading System
[font=Arial][color=#000][size=13px][font=Arial][color=#000000][size=16px]Cho Sing Kum[/size][/color][/font][font=Arial][color=#000000]12th Mar 2004[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000][i]
This article was initially written for the March 2004 issue of Chartpoint magazine which unfortunately wound down operation recently and this article was not published. It is now re-edited and produced here.[/i][/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#0000ff]
[/color][/font][font=Arial][color=#000000][b]Check out our Turtle Trading Software, TurtleFarm, that is programmed to the Turtle Rules.[/b][/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#0000ff][/color][/font][font=Arial][color=#000000][size=16px][b]
It All Began In 1983[/b]
[/size][/color][/font][font=Arial][color=#000000]
The year was 1983. I had just decided that I wanted to go full-time into technical analysis. I took a sabbatical from work in October to learn on my own, not having gone any where with technical analysis since early 1982.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]The Singapore representative for Compu-Trac happened to be back in Indonesia so I was helping him out here. It was from this connection that I got to know people at Drexel Burnham Lambert’s Singapore office. They were a bunch of very nice guys and the office was having problem setting up the computer to download data from Commodity Systems, Inc. in the USA.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
They were asking me why I did not go to Chicago. They were telling me I should go and handed me a newspaper cutting. You see, about that time, Richard Dennis and Bill Eckhardt had put out advertisement for trainee traders for the Turtles program. I gave it some thought but because I was not in a position to relocate to Chicago, it never crossed my mind to apply. Six months into my sabbatical I was offered a job at Drexel which I took up. Since then I was always curious about the Turtle trading method.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]Not A Well Kept Secret[/b]
[/size][/color][/font][font=Arial][color=#000000]
The Turtles were sworn to secrecy. While the Turtle method appeared to be a well kept secret, it was actually not. Channel breakout was growing in popularity in the 1980s. So was volatility adjusted risks. In the late Bruce Babcock Jr’s 1989 book, The Dow Jones-Irwin Guide to Trading Systems, bits and pieces of what could be the Turtle trading methods in one form or another were scattered in the pages. All these were well known market knowledge. But while I was hearing about the successes of the Turtles, I never knew that their method was already out in the market. I was still looking out for it.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]The 1923 Book[/b]
[/size][/color][/font][font=Arial][color=#000000]
I finally went to Chicago in 1986. I went not for any Turtle program but for company orientation that took me to New York, Chicago and Tokyo a year after I joined Merrill Lynch Capital Markets. It was something I did during this trip that had a big impact on my learning. I went to the bookshops around the Chicago Board of Trade and bought all the trading books I could carry. Once back home, I ordered more books from Traders Press Inc. by mail order.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
Good and often lesser known trading books were hard to come by in Singapore bookshops in the 1980s. I could not remember whether I bought this book in Chicago or from Traders Press. Wherever it was, I was very fortunate to have bought the book, Reminiscences Of A Stock Operator, first published in 1923. It was actually a biography of Jesse Livermore, one of the most respected stock and commodity market speculators of all time.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
I was so fascinated by this book that I included many quotes of wisdom from it in the daily market closing commentaries I was writing. I wrote the Nikkei, Hang Seng, Chicago Treasury Bonds and Eurodollar futures closing commentaries. These daily commentaries were sent out by telex to Merrill Lynch’s Asian customers.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Now you may wonder what has this book to do with the Turtle method. In my opinion it has a lot to do although I did not know initially.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Fast forward your clock seventeen years to April 2003.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]The Turtles Revealed Their Secrets[/b]
[/size][/color][/font][font=Arial][color=#000000]
That month I was pointed to the website [url]www.originalturtles.org.[/url] It was a new website wherein the claimed Original Turtles Trading Rules were revealed by Curtis Faith, one of the Turtles in the first class in Dec 1983. Before this I already knew about the 20-day entry and 10-day exit rules which were based on Richard Donchian’s work. I also knew about True Range and Average True Range from J. Willes Wilder Jr’s 1978 book, New Concepts in Technical Trading Systems. And not forgetting Bruce Babcock’s use of Average True Range as stops. What I did not know was how these were put together to form the Turtle Trading Rules.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]My Most Important Discovery[/b]
[/size][/color][/font][font=Arial][color=#000000]
And now the most important of my discovery - the combination of these parts resulted in what I would call the actualization of all that Jesse Livermore wrote in his 1923 book into a complete trading system! This was what the Turtle method was to me - a 1983 actualization of a 1923 book. I mean I could relate them. I certainly did not know whether Richard Dennis intended this but I could feel the resemblance, or rather Livermore’s experience, filtering into the Turtle methodology.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]So it was that twenty years later, I finally got to learn the Turtle method after all. But Livermore’s experience was already available for eighty years, so what was twenty years. It’s always better to be late then never. Naturally, I gave the Turtle Trading Rules a thorough check out.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]The Turtle Trading System[/b]
[/size][/color][/font][font=Arial][color=#000000][i]
“The Turtle Trading System was a Complete Trading System. Its rules covered every aspect of trading, and left no decisions to the subjective whims of the trader. It had every component of a Complete Trading System.”[/i][/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
This quote is taken from the published “The Original Turtles Trading Rules” at the OriginalTurtles.org website. I agree with this. It is further stated that it covers each of the following decisions required for successful trading:[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
1) Markets – What to buy or sell[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]2) Position Sizing – How much to buy or sell[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]3) Entries – When to buy or sell[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]4) Stops – When to get out of a losing position[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]5) Exits – When to get out of a winning position[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]6) Tactics – How to buy or sell[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
For this article I will skip components one and six. I will cover the other four. Not that I don’t find them important but choosing the markets to trade is important especially that the Turtle Trading System is a trend-following system and not a for-all-market-types system! Tactics, well you will learn this through experience.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]I will also not explain the details of the rules and the mathematics behind the calculation. You can find these in the published rules and are strongly encouraged to download the rules from the website mentioned above.
[i][Edited: The rules in pdf format used to be available for free download but not anymore. The website is also no longer hosted on its own and is now part of a commercial website. A compulsory donation is now required to support that commercial website infrastructure. I feel this goes against the intended objective of the Free Rules Project which has the support of Richard Dennis. Here is quoted from an earlier download of the rules: [/i][/color][/font][font=Arial][color=#0000ff][i][b]The Original of the Free Rules Project[/b]. This project had its seed in various discussions among a few of the original Turtles, Richard Dennis, and others regarding the sale of the Turtle Trading System rules by a former turtle, and subsequently, on a website by a non-trader. It culminated in this document, which discloses the Original Turtle Trading Rules in their entirety, free of charge.[/i][/color][/font][font=Arial][color=#000000][i]]
[/i][/color][/font][font=Arial][color=#000000][size=16px]
[b]The Turtle Rules In TradeStation 2000i[/b]
[/size][/color][/font][font=Arial][color=#000000]
There are two Turtle trading systems which are called System 1 and System 2. I have coded both systems into TradeStation indicators and signals/system. In the examples that follow I will be using these for illustration. There are two features that I have not programmed. They are:[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
1) Pyramid of the 4th unit[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]2) Alternate Whipsaw Stop Strategy[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
EasyLanguage does not have a feature to retrieve the entry prices of all respective pyramid positions. It only allow for the first entry price of any pyramid entry strategy using the EntryPrice command and the average entry price of all pyramid entries using the AvgEntryPrice command. As such, I have to do backward calculation to derive the subsequent pyramid entry prices.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
There are certain entry situations where it is not possible to calculate the entry price of the 3rd unit, for example, when the 2nd and 3rd units were entered on the same day (when using daily historical data for testing). While the entry prices can be assumed using the ½ N pyramid rules, this is never a good practice. Without any reliable method of calculating the entry price of the 3rd unit it is not possible to enter the 4th unit. So I only program the codes to pyramid up to a maximum of 3 units only.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]The ½ N Alternate Whipsaw Stop is too small for proper testing on historical daily data.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]These aside, the other challenging part is coding the Last Losing Trade Filter. So in the process I programmed four indicators to show the properties of all theoretical trades to guide me. See Fig 1. The four indicators are:
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]1) The first shows the 20-day channels as blue dots. The 2N-stop and 10-day channel exit are red dots. These dots are superimposed on the price chart to give visual representation of all theoretical trades (no pyramid).[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]2) The second shows the unrealized and realized position profit/loss of all theoretical trades based on 1 contract position size.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]3) The third shows the market position of all theoretical trades.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]4) The fourth shows the N values from which the N on the day before a position entry is captured and used for the entire duration of the position for calculation of the 2N-stop and ½ N profit.
[attach]4677[/attach]
[/color][/font][/size][/color][/font][font=Arial][color=#000][size=13px][font=Arial][color=#000000]Fig 1. Turtle’s Indicators
[/color][/font][font=Arial][color=#000000][size=16px]
[b]Position Sizing – How much to buy or sell[/b]
[/size][/color][/font][font=Arial][color=#000000]
The position size or unit rather, is based on a concept called N. N is the price distance of one Average True Range of the last 20 days. The Turtle’s calculation differ from the normal method of averaging where you add up the last 20-day and divide this total by 20 to get the average number. Instead the Turtle’s method uses what is commonly called the Wilder’s smoothing method.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Wilder explained in his 1978 New Concepts book that this method of “averaging” saves the amount of work required for manual calculation. Now remember in 1978, personal computers were not common yet. His method of averaging when applied to the Turtle’s N is to multiply the previous day’s N by 19, add to this value today’s True Range and then divide the total by 20.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
This method has the advantage that it is somewhat weighted, that is, it changes faster to more recent price behavior yet doesn’t swing as wildly as the normal method of averaging. See Fig 2.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
[attach]4678[/attach]
Fig 2. Turtle’s N and ATR
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Since the dollar value of N represent 1% of account equity therefore this concept normalized volatility across different market. A market with higher volatility will have a bigger N and dollar value hence smaller position size while low volatility produce a smaller N and dollar value hence a bigger position size. Please refer to the published Turtles rules for detailed explanation if you don’t understand this.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]Entries – When to buy or sell[/b]
[/size][/color][/font][font=Arial][color=#000000]
There are two systems. Both are channel breakout systems. System 1 is shorter-term based on a 20-day breakout while System 2 is longer-term based on a 55-day breakout. Very briefly, System 1 would go long on a break above the 20-day high or go short on a break below the 20-day low. System 2 would go long or short on a break of the 55-day high or 55-day low respectively.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
In System 1, there is a filter rule which is not applicable in System 2. System 1 will only initiate a position provided the last theoretical trade is a loss. If the last theoretical trade is a winner, then System 1 will only enter when price breaks out of the FailSafe breakout point of 55-day high (for long) or 55-day low (for short) to avoid missing major moves. Let’s take a look at this visually on the March 2004 Soybean Oil chart in Fig 3.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
[attach]4679[/attach]
Fig 3. FailSafe Breakout
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]At point A, System 1 went short on a breakout of the 20-day low. This position was liquated at point B when price breaks above the 10-day high. A few days later at point C, price breaks above the 20-day high. This would have been a long entry but because the last trade was profitable, this trade was therefore not taken. About a month later at point D, price has traded higher to break above the 55-day high. System 1 then went long so as not to miss the bigger move that followed.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
Fig 3 shows the system without pyramid so as not to clutter the chart for clarity. The same system is shown again in Fig 4 with the Turtles’ method of pyramiding. The Turtles pyramid to maximum of 4 units at every ½ N profit. Now because of a limitation of TradeStation EasyLanguage where I cannot reliably get the 3rd unit entry price (to allow a 4th unit to be added) so I programmed the trading system to pyramid to a maximum of 3 units.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]The Turtles’ method of adding additional units with the stops tightened is very logical. It lowers overall position risks and yet enjoys maximum benefits when it catches good trend moves. However there will be times when this may pose a problem.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
[attach]4680[/attach]
Fig 4. Pyramid entries[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
If you study Fig 3 and Fig 4 carefully, you will notice that there was an extra exit in Nov marked by the label “lxN”. This was followed by a long re-entry in early Dec. Explanation of the Turtles’ stops and exits will make this clearer.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]Stops and Exits – When to get out[/b]
[/size][/color][/font][font=Arial][color=#000000]
Like with any well planned trading system, the Turtles’ too have money management stops and normal trade exits.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]The money management stops are placed at 2N away from the entry price of the last unit entered. The position risk for a 1 unit position is 2N. Since the 2nd unit pyramid is added when price has moved ½ N in favour, the position risk for a 2 unit position is 3½ N (2N + 1½ N). Similarly, the total position risk for a 3 unit position is 4½ N (2N + 1½ N + 1N). The total risk for a full 4 unit position will then be 5N (2N + 1½ N + 1N + ½ N). Basically the stops for earlier positions are tightened up on pyramiding. Since 1 N represents 1 percent of account equity, therefore the respective risks are 2, 3½ , 4½ and 5 percent.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Now some will have problem with these risk numbers. If you recall in the last year’s July issue of Chartpoint, I wrote that my answer of 5 percent as the risk I would take in a position has caused my chance of a job opportunity with Commodities Corporation. So bear in mind that 5 percent is a very high number. But this is the way the Turtles trade and their high risk appetite may be the reason behind their tremendous record in such short period of time in the 1980s.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Trade exits are 10-days against for System 1 and 20-days against for System 2. This means that for System 1 when price violates the 10-day low, longs are exited, vice versa for shorts. For System 2, use the 20-day against. Therefore in short, System 1 is 20 in, 10 out while System 2 is 55 in, 20 out.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Okay now let’s see what exactly happened in Fig 3 and 4 that resulted in the additional exit and long re-entry.
The charts are reproduced in Fig 5.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
[attach]4681[/attach]
Fig 5. Tightening of stops when adding units can result in whipsaw.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
In the first situation shown on the top chart in Fig 5, the system was run without pyramiding, meaning only 1 unit was entered long on the Friday before 17 Nov. Immediately, the money stop was placed 2N below the entry price. This stop, represented by the red dots, was never hit and was eventually replaced by the 10-day low exit. This 10-day low exit condition was met on 22 Dec and the position exited as shown.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
In the second situation shown on the lower chart in Fig 5, the system was run with pyramiding up to 3 units. The first unit was entered as above on Friday 14 Nov. The market then rose in favour of the position and when it hit the ½ N and 1N profits, the 2nd and 3rd units respectively were added according to the Turtles’ pyramid rules. The money stop was tightened (raised) so that it is 2N below the entry price of the 3rd unit. See Fig 5. Unfortunately, the market retraced enough to trigger this 2N stop from the 3rd unit entry price. The entire position of 3 units was stopped out as a result. The long position was re-entered when price broke out of the 20-day high again in Dec and exited as in the first example on 22 Dec.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]This is one situation you have to live with when pyramiding. It doesn’t happen all the time but it does happen. Notice that in the example, the market did not retrace to the original 2N-stop calculated from the 1st unit entry price.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]How Do You Add Units Or New Positions?[/b]
[/size][/color][/font][font=Arial][color=#000000]
While there are rules on maximum position limits for single market (4 units), closely correlated market (6 units), loosely correlated markets (10 units) and total limits (12 + 12 units), what I feel that is not properly explained in the published Turtle rules but which is very important is whether there are rules pertaining to adding units or new positions when trading a portfolio.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Adding units at every ½ N profits is fine when trading only a single instrument or even 2 instruments. Although the rules did stipulate a maximum of 12 units long and 12 units short for a total of 24 units (obviously this has to be a portfolio), this could translate into a total portfolio risk of 30 percent, assuming 3 long positions of 4 units each and 3 short positions of 4 units each. (Earlier, you have seen how a 4-unit position represents 5 percent risk.) In the event that all this positions turned out wrong, the portfolio will be down by 30 percent!
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Is this acceptable? What if this is a new portfolio without any profit cushion? I think you have to use your own techniques since this part of the Turtles’ training was not revealed in the published rules.
[/color][/font][font=Arial][color=#000000][size=16px]
[b]Indeed A Complete Trading System, And A Very Good One[/b]
[/size][/color][/font][font=Arial][color=#000000]
The Turtle trading system is indeed a very good complete trading system. But if you want to get some testing done with the presently available technical analysis software, you will be disappointed. All available software can’t test trading system against a stable of instrument but only with single instrument. Nevertheless, the logic is very sound, risk is systematically managed, and the result can be proven.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]The Japanese Yen was one of my anchor trading instruments for many years so naturally I was interested in what type of result the Turtle System 1 would produce. The following are two sets of results – Fig 6 is without pyramiding while Fig 7 is with pyramiding. These are hypothetical runs on historical data for the purpose of system testing and evaluation. These are purely computer runs where no actual trades were done.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
The tests was based on spot US Dollar/Japan Yen data and did not take into consideration FX swaps which would need to be done to carry spot FX positions overnight and would have effect on the profit and loss performance.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]Both hypothetical accounts started with USD 100,000 converted to Yen on the first bar of data. All figures are in Yen.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
I am very impressed.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
[attach]4682[/attach]
Fig 6. Turtle System 1 without pyramiding.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
[attach]4683[/attach]
Fig 7. Turtle System 1 with pyramiding.[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#000000]
[/color][/font][font=Arial][color=#ff0000][b]Important Disclaimer:[/b][/color][/font][font=Arial][color=#000000]
Currencies, Stocks, Futures and Options trading have large potential rewards, but also large potential risk. You must be aware of the risks and be willing to accept them in order to invest in the currencies, stocks, futures and options markets. Don't trade with money you can't afford to lose. This is neither a solicitation nor an offer to buy/sell currencies, stock, futures or options. No representation is being made that any account will or is likely to achieve profits or losses similar to those discussed on this web site. The past performance of any trading system or methodology is not necessarily indicative of future results.
[/color][/font][font=Arial][color=#000000][size=16px]
[/size][/color][/font][font=Arial][color=#ff0000][b]CFTC RULE 4.41
[/b][/color][/font][font=Arial][color=#000000]HYPOTHETICAL OR SIMULATED PERFORMANCE RESULTS HAVE CERTAIN LIMITATIONS. UNLIKE AN ACTUAL PERFORMANCE RECORD, SIMULATED RESULTS DO NOT REPRESENT ACTUAL TRADING. ALSO, SINCE THE TRADES HAVE NOT BEEN EXECUTED, THE RESULTS MAY HAVE UNDER-OR-OVER COMPENSATED FOR THE IMPACT, IF ANY, OF CERTAIN MARKET FACTORS, SUCH AS LACK OF LIQUIDITY. SIMULATED TRADING PROGRAMS IN GENERAL ARE ALSO SUBJECT TO THE FACT THAT THEY ARE DESIGNED WITH THE BENEFIT OF HINDSIGHT. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFIT OR LOSSES SIMILAR TO THOSE SHOWN. [/color][/font][/size][/color][/font]
页:
[1]