Back tested results can be used to get an idea of how much capital you need to trade a particular strategy. As of April 23, 2007, the largest draw-down has been about 10 points. (The draw-down is the difference between the previous highest cumulative profit and a subsequent low point. For example, the cumulative pr

You apply this strategy consistently, without variation, as often as possible. The positive expectancy asserts itself in the long run and profits accrue, although there will be bad runs which cause short term losses.

When you look at examples like tossing a coin or rolling a die, it is easy to see what the Probability of Winning is, but in real trading situations it is far from obvious. The only way of determining system parameters is by estimating them from samples of market action.

The usual way of doing this is by obtaining historical data and back-testing your strategy to see how it performed in the past, or by paper trading the strategy for a test period. In either case, your objective is to get reliable estimates of the system parameters.

There are some important caveats to emphasize:

• Small samples provide unreliable estimates of system parameters! Your test period should include a minimum of 20 trades, and preferably 50 or more.
• A strategy may not work in all market conditions. If you back-test your strategy in different periods when market conditions vary (bull market, bear market, sideways market), your parameter estimates are more reliable.
• The greatest trap of all is curve fitting.
  • This occurs when you define rules in your strategy to optimize results obtained in a test period. If you look at any particular set of historical data, you can often specify trading rules which produce magnificent results applied over that period. (If only we could trade in the past, we would all be wealthy.)
  • Curve fitted strategies can usually be recognized by their complexity and large number of rules and exceptions.
  • Curve fitting is a very natural thing to do, so it is vital that you are on guard against it. The problem is that markets are infinitely variable, and a strategy optimized on data from one time period is most unlikely to perform well in other periods.
  • The other problem with curve fitting is that the sample estimates of system parameters are no longer accurate, since they have been deliberately optimized.
  • The best way of avoiding curve fitting is to define a strategy based on a trading idea (I will look at some of these in future articles). A strategy based on an idea of how markets work, or other traders react to certain events, can be developed independent of past data. If you then back-test that strategy, the results will not be curve fitted.
  • But if, as a result of observations you make during the test period, you decide to make adjustments to the strategy, that is the time to beware. Any change you make must have a logical trading rationale - otherwise you will be falling into the curve fitting trap.

Consider a soybean futures strategy traded at the Chicago Board of Trade (CBOT). The strategy is based on the simple idea of trading price breakouts which occur during the first 30 minutes of the trading day. If no breakout occurs, there is no trade for the day. Otherwise the market is entered with a Buy or Sell order in the direction of the price breakout.

(A price breakout occurs when the price moves out of a previously established trading range.)

The target profit for the trade is determined from the chart pattern forming the trade setup, and the stop loss is set at an equal amount. In other words, the amount risked is equal to the potential profit in this strategy. If neither the profit target not the stop loss are reached during the trading day, the position is closed at the end of the session.

Results for trading this strategy since Feb 6, 2007, are recorded in this spreadsheet.

For each date when the setup occurs, the trade result is entered as a number of points. In the soybean market, each point is worth $50, so the first result of -4.25 points represents a loss of $212.50 on the trade.

The third column shows the number of contracts traded. Next is a column showing the cumulative profit (in points), followed by the contract code (ZS).

Then there is a column indicating whether the trade is a win or a loss. Note the runs that occur here. It is interesting that 4 out of the first 5 trades were losers, although the strategy as a whole has proven successful. This illustrates the futility of relying on small samples for useful information.

Next come columns showing the cumulative winning amount, cumulative loss amount, number of wins and number of losses. This enables calculation of the Average Win and Average Loss.

Finally, the three highlighted columns show the ratio of the average win to average loss, the probability of winning, and the Expectancy.

As results for each day are added, the sample size gets larger and a better picture of performance emerges. Note how the estimates in the highlighted columns vary a lot in the first few rows, but settle down as the number of results increase. After about 20 trades, the numbers do not change much, giving confidence that they are converging to good estimates of the system parameters.

On the date of writing this article, 23 April, 2007, the Win/Loss ratio is estimated at 0.97. This means the average win is about the same as the average loss.

The Probability of Winning is estimated at 0.66. In other words, the strategy wins about 2 out of 3 times.

The expectancy is estimated at 1.1 points (1 point = $50). So, on average, the strategy has made just over 1 point every time it is traded. Brokerage costs of about $5 would have to be deducted from this.

This is an example only. It shows how testing can be used to estimate the Expectancy for a trading strategy. It may be possible to improve this strategy in a number of ways.

• You can improve your win/loss ratio by using a tighter stop loss. For example, instead of risking the same amount as the target profit, you might choose to risk only one quarter of that amount before quitting the trade. That would mean your Average Win should come out at about four times the Average Loss, which is certainly a good thing. Unfortunately the Probability of Winning will also reduce, because some trades which are winners at the moment would hit the tighter stop loss point, and be closed for a loss.
• Alternatively you could increase the Probability of Winning by specifying a smaller Profit Target, leaving the stop loss amount unchanged. For example, if the profit target is reduced to just 1 point, then some trades which currently end up as losers would reach this reduced target, changing them to winners. However, the higher Probability of Winning will be offset by a reduced Win/Loss ratio because your average winning amount will be smaller.
• At this point you might be tempted to program your computer to work through all the different combinations of Profit Target and Stop Loss levels to see which gives the best Expectancy during the test period. However, this would be an example of curve fitting.
• The point is that the original trading idea puts the stop loss point just beyond a major support or resistance area on the chart. It is a logical thing to do because it is known that other players in the trading game will perceive the support or resistance areas as a barrier. That barrier would have to be penetrated before the stop is triggered. This trading idea is arrived at quite independently of the test data.
• However, if your computer analysis shows that a fixed stop loss level of (say) 1.5 points would have doubled returns during the test period, and you change the rules of your strategy to incorporate this value instead of the original rule, you are guilty of curve fitting!
• Remember this concept. You can not use test results to optimize a strategy and still expect those same test results to provide valid estimates of the underlying parameters for the strategy.
• If you truly understand this point, you will save yourself a lot of wasted effort. You will also look at the results quoted for advertised trading systems with a jaundiced eye, because many of them rely on curve fitting to achieve high returns.
• I will continue to update this spreadsheet with trading results on a daily basis. It will be interesting to see if the key parameters remain consistent as time passes and the market moves through different conditions.

Back tested results can be used to get an idea of how much capital you need to trade a particular strategy. As of April 23, 2007, the largest draw-down has been about 10 points. (The draw-down is the difference between the previous highest cumulative profit and a subsequent low point. For example, the cumulative pro

Consider a soybean futures strategy traded at the Chicago Board of Trade (CBOT). The strategy is based on the simple idea of trading price breakouts which occur during the first 30 minutes of the trading day. If no breakout occurs, there is no trade for the day. Otherwise the market is entered with a Buy or Sell order in the direction of the price breakout.

(A price breakout occurs when the price moves out of a previously established trading range.)

The target profit for the trade is determined from the chart pattern forming the trade setup, and the stop loss is set at an equal amount. In other words, the amount risked is equal to the potential profit in this strategy. If neither the profit target not the stop loss are reached during the trading day, the position is closed at the end of the session.

Results for trading this strategy since Feb 6, 2007, are recorded in this spreadsheet.

For each date when the setup occurs, the trade result is entered as a number of points. In the soybean market, each point is worth $50, so the first result of -4.25 points represents a loss of $212.50 on the trade.

The third column shows the number of contracts traded. Next is a column showing the cumulative profit (in points), followed by the contract code (ZS).

Then there is a column indicating whether the trade is a win or a loss. Note the runs that occur here. It is interesting that 4 out of the first 5 trades were losers, although the strategy as a whole has proven successful. This illustrates the futility of relying on small samples for useful information.

Next come columns showing the cumulative winning amount, cumulative loss amount, number of wins and number of losses. This enables calculation of the Average Win and Average Loss.

Finally, the three highlighted columns show the ratio of the average win to average loss, the probability of winning, and the Expectancy.

As results for each day are added, the sample size gets larger and a better picture of performance emerges. Note how the estimates in the highlighted columns vary a lot in the first few rows, but settle down as the number of results increase. After about 20 trades, the numbers do not change much, giving confidence that they are converging to good estimates of the system parameters.

On the date of writing this article, 23 April, 2007, the Win/Loss ratio is estimated at 0.97. This means the average win is about the same as the average loss.

The Probability of Winning is estimated at 0.66. In other words, the strategy wins about 2 out of 3 times.

The expectancy is estimated at 1.1 points (1 point = $50). So, on average, the strategy has made just over 1 point every time it is traded. Brokerage costs of about $5 would have to be deducted from this.

This is an example only. It shows how testing can be used to estimate the Expectancy for a trading strategy. It may be possible to improve this strategy in a number of ways.

• You can improve your win/loss ratio by using a tighter stop loss. For example, instead of risking the same amount as the target profit, you might choose to risk only one quarter of that amount before quitting the trade. That would mean your Average Win should come out at about four times the Average Loss, which is certainly a good thing. Unfortunately the Probability of Winning will also reduce, because some trades which are winners at the moment would hit the tighter stop loss point, and be closed for a loss.
• Alternatively you could increase the Probability of Winning by specifying a smaller Profit Target, leaving the stop loss amount unchanged. For example, if the profit target is reduced to just 1 point, then some trades which currently end up as losers would reach this reduced target, changing them to winners. However, the higher Probability of Winning will be offset by a reduced Win/Loss ratio because your average winning amount will be smaller.
• At this point you might be tempted to program your computer to work through all the different combinations of Profit Target and Stop Loss levels to see which gives the best Expectancy during the test period. However, this would be an example of curve fitting.
• The point is that the original trading idea puts the stop loss point just beyond a major support or resistance area on the chart. It is a logical thing to do because it is known that other players in the trading game will perceive the support or resistance areas as a barrier. That barrier would have to be penetrated before the stop is triggered. This trading idea is arrived at quite independently of the test data.
• However, if your computer analysis shows that a fixed stop loss level of (say) 1.5 points would have doubled returns during the test period, and you change the rules of your strategy to incorporate this value instead of the original rule, you are guilty of curve fitting!
• Remember this concept. You can not use test results to optimize a strategy and still expect those same test results to provide valid estimates of the underlying parameters for the strategy.
• If you truly understand this point, you will save yourself a lot of wasted effort. You will also look at the results quoted for advertised trading systems with a jaundiced eye, because many of them rely on curve fitting to achieve high returns.
• I will continue to update this spreadsheet with trading results on a daily basis. It will be interesting to see if the key parameters remain consistent as time passes and the market moves through different conditions.

Back tested results can be used to get an idea of how much capital you need to trade a particular strategy. As of April 23, 2007, the largest draw-down has been about 10 points. (The draw-down is the difference between the previous highest cumulative profit and a subsequent low point. For example, the cumulative pr

Results for trading this strategy since Feb 6, 2007, are recorded in this spreadsheet.

For each date when the setup occurs, the trade result is entered as a number of points. In the soybean market, each point is worth $50, so the first result of -4.25 points represents a loss of $212.50 on the trade.

The third column shows the number of contracts traded. Next is a column showing the cumulative profit (in points), followed by the contract code (ZS).

Then there is a column indicating whether the trade is a win or a loss. Note the runs that occur here. It is interesting that 4 out of the first 5 trades were losers, although the strategy as a whole has proven successful. This illustrates the futility of relying on small samples for useful information.

Next come columns showing the cumulative winning amount, cumulative loss amount, number of wins and number of losses. This enables calculation of the Average Win and Average Loss.

Finally, the three highlighted columns show the ratio of the average win to average loss, the probability of winning, and the Expectancy.

As results for each day are added, the sample size gets larger and a better picture of performance emerges. Note how the estimates in the highlighted columns vary a lot in the first few rows, but settle down as the number of results increase. After about 20 trades, the numbers do not change much, giving confidence that they are converging to good estimates of the system parameters.

On the date of writing this article, 23 April, 2007, the Win/Loss ratio is estimated at 0.97. This means the average win is about the same as the average loss.

The Probability of Winning is estimated at 0.66. In other words, the strategy wins about 2 out of 3 times.

The expectancy is estimated at 1.1 points (1 point = $50). So, on average, the strategy has made just over 1 point every time it is traded. Brokerage costs of about $5 would have to be deducted from this.

This is an example only. It shows how testing can be used to estimate the Expectancy for a trading strategy. It may be possible to improve this strategy in a number of ways.

• You can improve your win/loss ratio by using a tighter stop loss. For example, instead of risking the same amount as the target profit, you might choose to risk only one quarter of that amount before quitting the trade. That would mean your Average Win should come out at about four times the Average Loss, which is certainly a good thing. Unfortunately the Probability of Winning will also reduce, because some trades which are winners at the moment would hit the tighter stop loss point, and be closed for a loss.
• Alternatively you could increase the Probability of Winning by specifying a smaller Profit Target, leaving the stop loss amount unchanged. For example, if the profit target is reduced to just 1 point, then some trades which currently end up as losers would reach this reduced target, changing them to winners. However, the higher Probability of Winning will be offset by a reduced Win/Loss ratio because your average winning amount will be smaller.
• At this point you might be tempted to program your computer to work through all the different combinations of Profit Target and Stop Loss levels to see which gives the best Expectancy during the test period. However, this would be an example of curve fitting.
• The point is that the original trading idea puts the stop loss point just beyond a major support or resistance area on the chart. It is a logical thing to do because it is known that other players in the trading game will perceive the support or resistance areas as a barrier. That barrier would have to be penetrated before the stop is triggered. This trading idea is arrived at quite independently of the test data.
• However, if your computer analysis shows that a fixed stop loss level of (say) 1.5 points would have doubled returns during the test period, and you change the rules of your strategy to incorporate this value instead of the original rule, you are guilty of curve fitting!
• Remember this concept. You can not use test results to optimize a strategy and still expect those same test results to provide valid estimates of the underlying parameters for the strategy.
• If you truly understand this point, you will save yourself a lot of wasted effort. You will also look at the results quoted for advertised trading systems with a jaundiced eye, because many of them rely on curve fitting to achieve high returns.
• I will continue to update this spreadsheet with trading results on a daily basis. It will be interesting to see if the key parameters remain consistent as time passes and the market moves through different conditions.

Back tested results can be used to get an idea of how much capital you need to trade a particular strategy. As of April 23, 2007, the largest draw-down has been about 10 points. (The draw-down is the difference between the previous highest cumulative profit and a subsequent low point. For example, the cumulative pr

The Probability of Winning is estimated at 0.66. In other words, the strategy wins about 2 out of 3 times.

The expectancy is estimated at 1.1 points (1 point = $50). So, on average, the strategy has made just over 1 point every time it is traded. Brokerage costs of about $5 would have to be deducted from this.

This is an example only. It shows how testing can be used to estimate the Expectancy for a trading strategy. It may be possible to improve this strategy in a number of ways.

• You can improve your win/loss ratio by using a tighter stop loss. For example, instead of risking the same amount as the target profit, you might choose to risk only one quarter of that amount before quitting the trade. That would mean your Average Win should come out at about four times the Average Loss, which is certainly a good thing. Unfortunately the Probability of Winning will also reduce, because some trades which are winners at the moment would hit the tighter stop loss point, and be closed for a loss.
• Alternatively you could increase the Probability of Winning by specifying a smaller Profit Target, leaving the stop loss amount unchanged. For example, if the profit target is reduced to just 1 point, then some trades which currently end up as losers would reach this reduced target, changing them to winners. However, the higher Probability of Winning will be offset by a reduced Win/Loss ratio because your average winning amount will be smaller.
• At this point you might be tempted to program your computer to work through all the different combinations of Profit Target and Stop Loss levels to see which gives the best Expectancy during the test period. However, this would be an example of curve fitting.
• The point is that the original trading idea puts the stop loss point just beyond a major support or resistance area on the chart. It is a logical thing to do because it is known that other players in the trading game will perceive the support or resistance areas as a barrier. That barrier would have to be penetrated before the stop is triggered. This trading idea is arrived at quite independently of the test data.
• However, if your computer analysis shows that a fixed stop loss level of (say) 1.5 points would have doubled returns during the test period, and you change the rules of your strategy to incorporate this value instead of the original rule, you are guilty of curve fitting!
• Remember this concept. You can not use test results to optimize a strategy and still expect those same test results to provide valid estimates of the underlying parameters for the strategy.
• If you truly understand this point, you will save yourself a lot of wasted effort. You will also look at the results quoted for advertised trading systems with a jaundiced eye, because many of them rely on curve fitting to achieve high returns.
• I will continue to update this spreadsheet with trading results on a daily basis. It will be interesting to see if the key parameters remain consistent as time passes and the market moves through different conditions.

Back tested results can be used to get an idea of how much capital you need to trade a particular strategy. As of April 23, 2007, the largest draw-down has been about 10 points. (The draw-down is the difference between the previous highest cumulative profit and a subsequent low point. For example, the cumulative pr

Back tested results can be used to get an idea of how much capital you need to trade a particular strategy. As of April 23, 2007, the largest draw-down has been about 10 points. (The draw-down is the difference between the previous highest cumulative profit and a subsequent low point. For example, the cumulative profit on 16 Mar reaches 31 points and then subsides to a low of 20.25 points on 5 April. That is a draw-down of 10.75 points, equivalent to $537.50 per contract traded.)

Conservatively, you should be able to withstand a draw-down of at least five times that experienced in a relatively small sample like this, so think in terms of around $3,000 risk capital to trade this strategy with one contract. Some brokers require $2,000 in your account before you can trade, so you would need a $5,000 account to feel comfortable trading the strategy. With $8,000 you might trade 2 contracts, with $11,000 you could look at 3 contracts, and so on.

The results also indicate that this strategy has quite a good level of opportunity to profit, with most market days yielding a trade opportunity.

Finally, you can see that the strategy produced a profit of over 40 points ($2,000) in the period from 6 Feb to 23 April, 2007. On a $5,000 trading account, that would be a 40% return in less than 3 months, giving you an idea of the rate of return anticipated for this particular trading game!