# Defensive Money Management Explained: It Pays Being Conservative

By Lawrence

Index Page

Basic Characteristics of a Trading Strategy

You maybe thinking of your trading methods in terms of entry, exit, target price, stop loss, trailing stop, etc. but all that is not required to understand the basic behaviour of a trading strategy.

In short, we can define any trading strategy using just a set of 4 statistics. Namely, the winning/losing percentage and the average winning/losing amount.

Many may challenge that such simplification is not doing justice to their super trading techniques. I am sorry to say, if your super trading method does not measure up with the basic statistics, it may not be that super after all.

Law of Large Numbers in Action

To find out how likely a strategy will make money, we can apply this basic formula to find out.

Expected Outcome per Trade = Winning % x Average Winning Amount – Losing % x Average Losing Amount

For example, looking up your own trading records, you find out that on average you make \$100 on a winner and losing \$80 on a loser, and overall 60% are winners, then you can tell from the formula,

60% x \$100 – 40% x \$80 = \$60 – \$32 = Netting \$28 a trade

Remember that this answer you get requires that,

• many trades happened already to make the statistics collected to be reliable
• going forward you are going to perform exactly the same way like before
• the market behaves the same way going forward
• you are going to make many trades to allow the law of large numbers to work in your favour

The Law of Large Numbers (LLN) is a theorem from Probability Theory. It states that if you repeat enough number of times from a statistically stable event, then the average of the outcomes will get closer and closer to the expected outcome. In other words, if the historical trades you have completed is a reflection of the expected outcome, then as long as you keep performing like what you have done before, you will achieve similar performance.

As many of you already know from real trading experience, the problem is that you will still not likely to be able to get similar performance based on your trading history (or historical backtesting results). To illustrate why that is the case, this is the time to use a Monte Carlo simulator.

Using a Monte Carlo Simulator

If you do not have one, then go to TickQuest website to download Equity Monaco. It is available for free. A Monte Carlo simulator will be very useful going forward as we get into more details about understanding money management. Thus, even if you do not like learning new software, it is a good idea to start doing that now with Equity Monaco because it may be one of those applications that you wish you knew about them yesterday.

What a Monte Carlo simulator does on historical trade records (or trading models) is that it reuses the historical trades you provided as a starting point, and then generate possible scenarios by drawing from those historical trades randomly. In a sense, the Monte Carlo simulator produces alternative views of your trading performance. As oppose to looking into just a few alternatives, a Monte Carlo simulator can generate thousands of possible outcomes from the historical trades in a very short time. The information collected from these simulation runs can be utilized visually and they can provide important clues that many traders are not aware of from their trading.

It can be very confusing if I keep talking about Monte Carlo simulation without actually showing an example. In next section, we will work on our first analysis based on a simple case.

A typical beginner learning to trade emini S&P who is using one of the larger brokerages for execution usually starts with about \$10,000. The minimal margin required at these firms for trading 1 lot Emini S&P is around \$5,000. Making about 4 trades a day, each year this trader would make 1,000 trades.

You cannot expect a beginner to be able to have a high winning percentage nor can you expect strong discipline in place to enforce good measures in protecting his/her capital.

Let’s start with 50% win rate, with average winner amount of \$150 and average losing amount of \$150. We will ignore commission for now.

Start up Equity Monaco and enter the win/lose info under Settings tab. The rest of the inputs are not needed because the default values already match what is needed.

Change the Settings>Settings>Trials from 1000 to 10. Enable the Settings>Options>Enable Equity Curves Plotting. Now press the Start button.

Switch to the Equity Curves page, you will see a graph similar to the one below.

Each color line represents one possible outcome of the equity changes for this particular trader.

Notice that although we know from the formula, that this trader is likely to make no money, but most people would not imagine how likely this typical beginner would lose the trading account. From the 10 random runs I have done, one of the cases (the red line) got terminated at 350 trades (roughly translated to 4 months) because when it has less than \$5,000 there is not enough margin to continue trading.

In fact, out of the 10 runs, 4 of them terminated at \$5,000 mark. Not a pretty scene.

Finding Useful Information to Improve the Odds

Now, let’s change the settings a bit to make Equity Monaco to get us some useful information.

Change the Settings>Settings>Trials back to 1000. Disable the Settings>Options>Enable Equity Curves Plotting. Now press the Start button.

This time we will focus on the Equity page.

This graph tell us how likely the typical beginner trader would end up with after 1000 trades are made.

Key findings,

• 30% of the time, this beginner can no longer trade due to lack of enough trading capital
• 50% of the time, this beginner is not making any money
• Less than 5% of the time, this beginner can double his money

The last point in our finding is a thought provoking one. At 50/50, these 5% individuals can definitely be branded as lucky, but can their luck overcome the odds against them?

Lesson 1: Increase in Initial Capital Only Improve the Survival Rate

The following graph shows the potential terminal equity at \$10,000 initial capital (the red line as in the previous graph), and adding \$5,000 per run up to \$30,000.

If you trade only 1 contract at a time, at \$30,000 initial capital, your probability of having \$25,000 or less left in the account is 12%. At the extreme 2% scenario, you are still likely to have more than \$20,000 in the account. Comparing this to the survival rate of having just \$10,000 initial capital, this experiment clearly shows that having more money backing your trading improves your survival rate significantly.

That is all initial capital can do. It can improves your odds in surviving the brutal fights in trading, but it cannot help you make more money from trading because your ability to win more frequently, to win more money per trade, and to lose less money per trade are more important factors that drive your success in trading. The odds of making \$10,000 from someone whose performance is 50/50 all the way is, politely speaking, very remote (less than 5% across all the initial capital settings).

Chinese Proverbs: Losing Comes of Winning Money

When someone mistaken that his/her luck in doubling the money (from \$10,000 to \$20,000) within a year is a sign of skill, I am quite sure the person would go for 2 contracts per trade quickly. At \$20,000 starting capital (the beginning of another year), the probability will catch up with this person easily because the survival rate will behave like the one with \$10,000 initial capital on 1 contract. That means, 25% of the time, this person will have a crash on the equity down to \$10,000 or worse. 50% of the time, this person will not make a dime in the following year.

What failed this person is the misuse of the trading experience from the first year combined with LLN catching up on his/her performance. The money-making trading record from the first year of trading is not a sign that the future performance will be as good as that year, instead it is a sign that it is more likely going to fail miserably going forward. The most important clue that this person has missed is that the results was not an indication of skill at all. We know, because I told you the true performance statistics beforehand. For this person, all he/she sees at the end of the first year is great performance with flying colors.

The effect on a person from such huge equity swing can be extremely damaging. For someone who has no idea that he/she was lucky in the first place, equity swing of this scale will either finish this person’s trading career for good, or, turn this person into another problem gambler.

What Separate Real Trading Progress from Dumb Luck?

Should this person be smart enough to understand that the performance in the first year is not statistically significant and stayed with 1 contract per trade over the second year, he/she would have a chance to find out if his/her performance is sustainable. If another \$10,000 is made, with comparable statistical characteristics on the trades between the first and the second year, the person can then be confident that he/she is progressing onto something good. On the other hand, if there is significantly less amount of money is made, or even a loss, this person will still have a survive chance to figure out what went wrong.

As you can see, the only thing that separate a surviving trader from those who cannot make it, is conservative money management. By doing so, the person is giving himself/herself a better chance to develop profitable trading skills before taking on more risk.

This concept of putting more capital behind each unit traded (e.g. contracts in Emini S&P, number of shares in stocks) as trading capital increased, until the point that most of the risks identifiable by the trader are no longer a threat to the continuation of the trading operation, is the foundation of defensive money management.

– end of part 2 –

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