Trading and probability

Embrace the odds in your trading

“Probability is not a mere
computation of odds on the dice or more complicated variants; it is the
acceptance of the lack of certainty in our knowledge and the development of
methods for dealing with our ignorance.”

Nassim Nicholas Taleb,
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

Trading is all about choosing a trade idea with the highest
probability of success. However, human intuition and common wisdom can be
rather deceitful and lead to poor judgments. In this article, we will revisit
the main laws of probability that can be applied to trading and learn from

The flaws of intuition

The problem is that many times
when we go with our intuition without giving it a deep thought, we make a poor
estimate of probability. Let’s resort to the prospect theory developed by
Daniel Kahneman and Amos Tversky. This theory explores the ways we make
decisions which are associated with risks.

Imagine that you face a

1. A 75% chance to win $100
with a 25% chance of getting nothing.

2. A sure profit of $70.

There’s one more test. This time
necessary to choose between:

1. A 75% chance of losing $100
with a 25% chance of losing nothing.

2. A sure loss of $70. 

Logic would say that a
risk-averse person would choose option 2 in both cases (limited profit plus
limited risk). However, in reality, the majority chooses 2 in the first choice
and 1 in the second choice.

The prospect theory shows that
people overestimate the probability of getting no gain but overestimate the
chance of losing nothing. They seek to reduce their risks and in doing so they
may get a smaller profit and a bigger loss. 

In other words, losses
psychologically affect people more than gains. If the probability of success is
low, people tend to risk more, while if the probability of success is high,
they, on the contrary, are reluctant to take risks. It’s clear, that to
maximize utility, one should do everything the other way round. The same bad
tendencies are observed with losses. The higher the probability of loss, the
more people tend to risk.

When emotions are ruling your
trading decisions, you are not really trading, you are gambling. You are
tempted to limit your profit and let your losses run. The solution that can
help improve the situation self-control, a decent trading system (we’ll return
to this later) and the respect of risk management.

Amanda Cox, the editor of the
New York Times’ The Upshot, provides a nice visual of the human fallacy in
judging probabilities:

The problem arises when we
move from probability to predictions and actions based on these predictions. If
we estimate the chance of profit by 80%, we may be carried away and disregard a
protective stop. Even though it’s hard to think probabilistically, traders
should make this effort.

The gambler’s fallacy

Let’s make sure that the
concept of probability started to sink in. Imagine that you toss a coin. The
outcome is random, so the probability of either heads or tails equals to 50%.
For example, you are betting on heads. Will the probability of your success
decline after 5 heads in a row? The answer if no, it will still be equal to
50%. The reason is that we don’t count the probability of several events at
once, but start anew with an independent event, so the possibility of success
is 50% each time. 

This is called the gambler’s
fallacy (the mistaken belief that, if something happens more frequently than
normal during a given period, it will happen less frequently in the future) and
was witnesses in Monte Carlo often enough. 

Traders should also remember
it when chilling after a set of gains or brooding over a series of losses.

Befriending mathematical expectation

Of course, a trading decision
is more complicated than a coin flip. And yet, it all comes to probability.

The goal of a trader is to
build a trading system with a positive expectation and combine it with sound
risk management. Regrettably, the maths doesn’t allow us to predict the future
performance of a trading system. All we can do is to study historical data
gathered during the period when you backtested your strategy. The formula of
positive mathematical expectation will be something like:

[1 + (W/L)]xP – 1, where W is
the amount of average winning trade, L is the amount of average losing trade
and P is the probability of winning.

Remember that mathematical
expectation is not predictive in nature, but a system with a positive
expectation is your basis for successful trading. The other crucial element is
proper risk management. Incidentally, risk exposure is the one thing we can
actually control in trading with tools like position sizing, risk-reward ratio,
and stop loss orders.

Risk management allows
maximizing the gains provided by the trading system with a positive expectation
while limiting risks. It’s wise to use your power when it can be used and make
it yield you the benefits. It’s a way for a trader to stop looking for a “holy
grail” (a 100% success system) and start actually making profits ― thinking
probabilistically as he/she is doing so.  

This article was submitted by FBS.

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