## The Gambler’s Fallacy

The gambler’s fallacy applies to a common misconception connected with statistics and probability. Traders use a lot of math, but probability is very useful when evaluating your portfolio risk. Basically, you are trying to figure out the probability of something happening (in trading, the market going up) or not happening.

In this respect, gamblers have it easy: the possibilities of what can happen are relatively limited. In poker, for example, there are a limited number of cards, which makes probability calculations easier. But when trading with currencies, or even stocks for that matter, there are virtually infinite possibilities for what might disrupt the markets. This is why putting backstops in place to protect your portfolio against risk is even more important.

### The Science of Coin Flipping

But to make things simple to explain the general concept, let’s say there is a 50-50 chance of the market going in either direction. Like, say, flipping a coin, for example. If you flipped the coin 10 times, you might think you could expect the coin to land five times heads, and five times tails, right? 50-50 odds?

No.

That’s the gambler’s fallacy: in assuming that there is any connection between the chances of the coin tosses. If you tossed a coin three times, and all three times it landed heads up –you might think the next toss would be more likely to land heads down. But the reality is that each toss has the same chance of landing heads up or down, regardless of how many times the coin has landed on each side previously.

### How Does This Affect my Trading?

The chance of the market going in one direction or the other depends on the economic factors of the moment, and is not necessarily related to what has happened previously. That might get technical analysts a bit peeved, but the important concept to understand here is that past performance has no effect on the chances of the market doing something.

Consequently, when you are analyzing your risk management strategy, don’t let what the market is doing affect how you make risk decisions. No matter how sure you are of where the market is going to go, there is always a chance that it will go in the opposite direction.

### Calculating Exposure Through Probability

Good risk management is divorced from how likely it is that an investment will pay off. It’s the annoying pessimist in the room, always thinking of the worst-case scenario. But it is possible to turn that into a profit.

Using coin flipping as an example again can make this simpler. Coins are great for these kinds of examples, because they are money and have equal chances of landing heads or tails. Well, actually, it’s closer to 51% heads, because that side of the coin has more mass – yes, someone actually studied this. But sticking with a 50-50 chance makes the math easier.

For this example, assume that you are betting on heads. If you win, you double your money; but if you lose, you lose all of the money you bet. If you bet on one flip of the coin, then you have a 50% chance of winning, and a 50% chance of losing.

But, if you flip the coin twice, how many chances do you have the coin will land heads? Remember the gambler’s fallacy. The chances are still 50-50 for each toss, but not overall.

If it lands on tails in the first toss, you still have another toss and there is still a 50-50 chance that it will land heads or tails. That means that the chance of the coin landing tails both times is 50% of 50%, or 25%. In other words, your chance of losing all your money is only 25%.

Your chance of winning is also 25%, but your chance of breaking even is 50%. The amount of money hasn’t changed and nor have the chances, but by splitting your money into smaller amounts and making several bets, you are statistically reducing your chances of losing money.

### What About Forex?

(Bear in mind that while the markets do sometimes spike dramatically, these numbers are excessive and are purely to help you understand the workings.)

If you put all your money into one investment, you could either make 10 or lose 10. If, however, you split your money into two investments, one after the other, your chances are:

Notice that by splitting your investments, you now have a 75% chance of making some profit and only a 25% chance of losing. Significantly, this is without changing any of the variables that made you choose the investment in the first place: simply by managing your risk through probability, you can make your portfolio more profitable in the long run.

Of course, there are a lot of other factors that influence these outcomes in the real world, but the basic concept is to spread risk through smaller investments. There are ways to calculate the ideal exposure, which will be covered later.

### Variance

An often-ignored factor in investment that’s particularly relevant to overall portfolio management, and also touches on how to deal with risk, is variance.

The term is borrowed from game theory, which studies how to optimize different winning and losing scenarios. Variance is also a very common concept among professional gamblers – and although there is a clear and definite difference between gambling and investing, some of the risk mitigation tools from gambling can be useful while trading with currencies.

Basically, variance deals with how money is made and lost during investing. Understanding variance requires accepting an important concept of trading: no one, ever, finishes in the money all the time. Eventually, everyone is going to have losing trades; this is completely normal. Sometimes they will be individual trades, sometimes they will be part of a series. But, ultimately, a successful trader realizes this and takes steps to avoid it.

Understanding how those gains and losses cause a portfolio to “vary” in size is the basics of variance study. A study by a major retail trading company found that, on average, traders were right around 64% of the time. The normal distribution was between 60 and 70% of winning trades.

This means that the normal, average trader is going to lose money on 30 to 40% of their trades, depending on the situation. It’s important to understand how likely it will be that you will have losing trades.

But the really important part of the study was the difference between profitable traders and non-profitable traders: they both had, statistically speaking, the same winning ratio. The difference was that profitable traders made more money on their winning trades than they lost on their losing ones; while unsuccessful traders lost more money on their losing trades than they made on their profitable ones.

This is a very important fact in understanding trading psychology and success: the difference between a successful trader and a non-successful one is not necessarily better prediction of where the market is going, but to have better risk management to ensure that losing trades don’t take too much out of the portfolio.

Once you understand that you will have losing trades, the question is: how will that impact your portfolio? Losses have a bigger impact on your profitability than equivalent gains. Therefore, it’s important to build a certain amount of “cushion” into any trading strategy in order to absorb normal trading variance.

This is why traders are constantly studying past performance to understand how likely and frequent their losses are. This allows them to more accurately measure their capital margin to account for variance.

The “cushion” allows a trader to absorb losses without changing their trading method. It’s also important to understand that losses can come in “runs”, where there is a series of trades ending in the red, one after the other. This can be quite stressful, and besides being able to manage the money aspect, you need to be aware of the psychological part as well.

Variance is determined by calculating how much is made and lost over time. For example, you could have two trades post gains, and one loss (this would be a 66% gain ratio). This concept should not be confused with statistical variance; statistical variance assumes data at a single time point, but in trading, variance occurs over time. In this case, your variance would be 50% of your profitability. In other words, for $1 that you make, you are likely to lose 50 cents. So, if you are expecting to make $1,000 over the course of your investment cycle, you will need to consider having a $500 “cushion” to account for variance.

Unfortunately, there is no way to predict a person’s variance. Not only does it vary from person to person, but from strategy to strategy, and from risk profile to risk profile. All traders can do is keep a meticulous record of your trades, and figure out for themselves how much their strategy can afford to “lose” in pursuit of profit objectives.

### Determining the Right Risk Ratio

Luckily, there is an ideal risk to portfolio size that traders can use to maximize profits.

Ultimately, each individual’s risk ratio will depend on their particular investment goals and style, but there are some rules of thumb that can applied for a good starting place. Basically, you need to balance two risk factors: individual investment risk against portfolio risk.

The previous section showed how investments with more risk were offset by higher profit. That’s why –as a general rule– it’s best to take on as much risk as possible within a safety range, in order to maximize profit. On the other hand, portfolios can be managed in a way that allows traders to reduce overall exposure, making a risky investment less “risky”, because the risk management strategy helps mitigate the effects of an adverse outcome in the markets.

Portfolio value = money – risk.

By reducing the level of risk, you are essentially creating more portfolio value. This allows traders to either take on more profitable investments (higher risk) and make more money, or to have more security with the portfolio and invest more in it.

### The Liquidity Problem

If you start out with $100, and the market goes up; you’ve made $10, and your portfolio is worth $110. But on the other hand, if the market goes south, you lose $10, and your portfolio is only worth $90. That’s too bad, but maybe you can make 10% profit next time, right?

Let’s say that you do. 10% of $90 is $9, which means that after losing one and winning one, you now have $99. That’s $1 less than you started out with.

This is how losing has a bigger impact on a portfolio than winning. Your portfolio has lost value, there is less money to invest, which means it is not possible to recover as much as you lost with an equivalent return percentage.

If a trader can either win or lose 10% and has 50-50 odds on winning, he will lose $1 on average with each two investments, and eventually, his portfolio will reach zero.

This is why taking a 50:50 risk on an investment that will only double (100%) your money is not a good idea. You need to have more than a 1:1 risk to reward ratio, either by having more than 50-50 odds or by investing in something that pays out more than 100%.

### Determining investment size

The smaller the percentage of the portfolio, the less risk; but on the other hand, the less profit made. You could use complex computer models to find the exact ratio, but fortunately someone has already saved you the work. FXCM, a leading retail trading company, did a survey of all their investors’ trading habits, and after analyzing millions of traders and billions of trades, they found that the most profitable risk percentage is just under 3%.

If you risk less than 3% of your portfolio per investment, then you don’t have as much profitability. But if you invest more than 3%, the liquidity problem where losses have a bigger impact than gains asserts itself.

This doesn’t mean that you should invest only 3% of your portfolio, and leave the rest untouched in your account. It means that for each risk scenario, you should only risk 3% of your portfolio to ensure maximum profitability. This could mean that you risk 3% in one stock you are expecting to hear news about, while another 3% could be invested in long-term bonds, and a further 3% could be in gold, etc.

Eventually, you want to have as much of your money as possible “working”, but you need to diversify your portfolio’s risk profiles in such a way that you are not subject to losing more than 3% in any given risk scenario.

### Risk Capital

Trading should only be done with risk capital - money that you can afford to lose. Of course, no-one is ever happy about losing money, but at least they are not losing the cash needed to pay the bills.

**No-one should be trading with their life savings**. Obviously, they won’t want to lose the savings, but it is also important to realise that from a trading perspective, the high-risk element of using this money to trade will have an undoubted impact on ability to make objective trading decisions.

Fortunately, FX trading has progressed to a point where demo and small accounts are available and easy to set up. This is very beneficial to new traders, allowing them to play and practice systems and plans until they are truly ready.

One word of advice though: as soon as you are familiar with the trading platform, open up a small account instead of staying too long on a demo account. Trading real money is a lot different to trading demo money, and you can get a lot of false hopes trading demo accounts.

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