# Simulation And Trading

Traders forecast future prices using some combinations of fundamentals, indicators, patterns, and behavior from the past. They hope that recent history will forecast the future helping them to make some profit. The problem, however, is that nothing that has happened in the past is any guarantee for the favorable results in the future. Basically, profitability of each trade has elements of some randomness and uncertainty. Here is the problem that many people are not equipped with enough knowledge and tools to manage uncertainty, thus mastering the psychology of trading.

At first glance trading may seem quite trivial. You just look at price chart, then buy here and sell there. But it in practice it?s much more complex than that. Trading is about what had happened in the past while trying to predict what will happen in the future. However, no one can precisely know the future in advance. Dealing with random outcomes from each trade, trading is a probability exercise, where a good trader biases the outcomes of each trade in his or her own favor. As, in order to succeed a trader need to have probability on his or her side. Traders use patterns from the past to forecast the future. Forecast doesn?t mean certainty, but it?s about that we know the likely future direction of the market where we are trading. However, we can be certain that in the past when the patterns, fundamentals or indicators have been as they are now, then the probability is in our favor.

At the same time one needs to be very careful with forecasts and gut feeling about the direction of the market, so that one doesn?t get into the trap of gambler?s fallacy when dealing with risk and uncertainty. Some traders hold beliefs that are likely to be wrong. They say that after a string of losing trades success on the next trade is more likely, so position size on the next trade should be increased. This may or may not be true in trading, but for most random events like tossing coins, it is definitely not true. What it implies is that the probability of winning each trade is somehow influenced by the result of the previous trade. This is not true for rolling dice, flipping coins or drawing marbles from an urn ? neither the coin, the marbles, nor the dice have any memory of the outcomes. Each draw or event is completely independent of the previous one. At the same time, it can also be argued that in real life each trade may not be completely independent of the previous trade. For instance, if we are trying to use a break-out system, it may be that after several failures success will follow. The problem is that we don?t know in advance which trial will benefit from increased size so increasing position size may leave us with large loss. Those trying to pick up tops and bottoms may sooner or later succeed, provided they still have capital left. Thus, we need to make an unrealistic assumption that we have unlimited capital when trading.

One of the ways to deal with risk and uncertainty of trading is to use some special software that makes risk strategies simple. The common feature of those pieces of software is that they use a technique called Monte Carlo simulation. Monte Carlo Simulation in general is distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner ? usually by using random numbers (in practice, pseudo-random numbers) ? as opposed to deterministic algorithms. Because of the repetition of algorithms and the large number of calculations involved, Monte Carlo is a method suited to calculation using a computer, utilizing many techniques of computer simulation. Monte Carlo applied to trading is about letting a computer select trades randomly and collecting the results in way that gives them meaning. It is quite useful to find strategies that maximize profits while limiting draw downs (the largest decline in equity below the previous high generally expressed in percent, but can also be measured in absolute amounts). Also some pieces of software go beyond the above in order to give meaningful comparisons of trading systems.

Expectancy is sometimes recommended as a predictor of profitability. It is the probable return or profit for the next trade. It applies to a single trade. For a series of trades expectance needs to be extended in ways that are not always obvious. They way expectancy is extended to a series of trades depends on the risk strategy being used for that series of trades. If fixed risk is used then the extension is quite simple and straightforward. At the same time, if a percent of equity is being used as a risk strategy then extending expectancy is quite difficult. It?s also noteworthy that all measures of expectancy have problems because they forecast only the average expected profit that might occur. Monte Carlo simulation shows the range of profit and drawdown that can expected from a series of trades.

When applying Monte Carlo Simulation, we have a series of past trade results and want to know the likely results this trading method will produce in the future if things go as they did in the past. The past two series of trades contain two important measures of success, the final profit and the draw downs that took place. In the future if the trading method produced identical returns in the same order, then ending profit and draw downs will be identical. However, this is quite unlikely, and with this degree of certainty some of the trades will be invested heavily, while others ? skipped. Even if the method produces results that are statistically similar to past returns, the future returns will not exactly be the same neither in magnitude nor in the order of occurrence of wins and losses. One way to get statistical results from historic data is to sample returns randomly. Basically, it boils down to tossing the historic returns into a hat and drawing one randomly, recording the result of that trade on equity, draw down, and anything else that is important. Then replace that sample in the hat and make another draw. A series of such draws make a trial. Even though the returns in the hat are the exact same as the historic values, the order in which they are drawn is different. There is no requirement that they are supposed to be in the same order. In fact, some returns may be drawn more than once while others ? not all. At the end of the trial we need to record the results for that trial. The above results may be similar to the values from the historic returns, but not exactly the same. There will always be some random variation from the historic values as it is the case in actual trading. Repeating a trial many times results in a range of values for profit, draw down, and other performance measures. Sorting these into an ordered list, we can see which results are most likely and which are less likely. Manual trials can be done repeatedly. For example, we make 100 trades, record maximum drawdown and ending equity. That is one trial. But then we need to repeat this trial 1,000 times in order to get statistical distributions. Finally, as the result of this exercise there are lists of results: maximum draw down during a trial, lowest equity during a trial, longest runs of wins and losses, and end of trial equity. Then we sort each of these into ascending order and inspect their percentile ranking. Obviously this process is quite tedious for a human to perform. This job is better left for a computer to do. With a good computing power it?s quite easy to test.

So using computer power we can take full advantage of simulation. It enables us to gain insight into statistical processes that might not be intuitive. At the same time, coupling the simulation with charts of results helps us make the latter more understandable and more intuitive rather than a mere collection of obscure numbers. Also, the power of simulation is in removing the need for laborious formulations and allowing quick and simple treatment of situations that are very difficult, even impossible to analyze with formulas. Simulation is a tool that has great analytical power. This power becomes clear in the ability to treat risk strategies and boundary conditions.

Given some trading method that has good profit potential, the next question is what risk strategy will maximize the profit. To simpler applications we can apply fixed risk strategy or percentage of equity strategy. However for something sophisticate like trading we need something that is more advanced. Some software applications dealing with Trading extend simulation to apply a user defined risk curve. It is useful for the case where there is a limited amount of capital, but as it grows additional risk is added in a defined manner. The ability to apply an arbitrary risk strategy would be difficult or impossible to do with any simple formula. The next powerful feature of simulation is the flexibility to restrict the path that equity can take at each trade to defined limits or boundary conditions. A starting equity can be chosen to examine the results at different equity levels. More importantly there is a minimum equity limit.

Thus, when we use the simulation for trading, we get answers to many questions such as:

- What is the range of profits expected for a method represented by a list of returns? (this list may be either historic returns or a simulation of a game.)

- What drawdown is expected for trading a method represented by a return list?

- How much capital is required to trade a method?

- What is the lowest equity expected?

- What are the longest runs of winning and losing trades?

The above questions can be explored in combination with various risk strategies such as fixed rate per trade, a percent of equity per trade, a user defined risk curve.

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