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Are you trading or gambling?

Christopher J. Gan

Thanks to the r/wallstreetbets subreddit, we have all heard of infamous tales where retail traders have profited millions of dollars. Accompanying this is often a cult-like worship by individuals who wish to do the same, and are desperate in finding the secret to such success.

Greed afterall, is human nature.

When it comes to games of pure chance such as the roulette, we are quick to label it as gambling. For games of chance like poker where you possess some level of control, conventional wisdom tells us that it is a game of skill. Because there are elements of decision making and skill associated with trading, it is often not viewed as gambling.

But what actually is gambling? Gambling cannot simply be any games involving uncertainty, otherwise casinos would be out of business. Additionally just because a game involves skill, it doesn’t mean that it is not gambling, otherwise Lehman Brothers would never have collapsed.

Gambling occurs when you have a poor understanding of risk, resulting in either (1) negative expected value bets, or (2) poor bet sizing that leads to ruin.

Negative Expected Value Bets

All bets have the potential to make or lose you money when standalone. The expected value of your bets, is how much you make on average as the cumulation of all of your bets. Thus it follows, a negative EV bet is one where you will on average lose money - like the roulette table.

To help reinforce your intuition, let us imagine a game involving coin flipping. You will win $2 if the coin flips heads, or lose $1 if the coin flips tails. Do you take this bet?

It is pretty obvious that this is a good deal for you. This is because on average, you will gain $1 with every coinflip. For those interested in the maths, you have a 50% chance of winning $2, and a 50% chance of losing $1. 50% * (+2) + 50% * (-1) = +$0.50. Try to do the same thing yourself with roulette table odds.

A not so obvious result that follows from making successive negative expected value bets, is that in the long run you are guaranteed to lose all your money (or ruin). Intuitively this makes sense as with each bet, you are losing money on average.

It should be noted that you can still make money in the short run due to volatility, so the unintuitive optimal strategy for a night out at Vegas is to bet all your money in one go. If you win, cash out and walk; if you lose, go home - either way, it makes for an extremely short night.

Poor Bet Sizing

Bet sizing is simply how large your bets are - do you throw $100 or $100k at a particular stock? However, it is often more useful to think of bet sizing in terms of percentages, as opposed to numeric figures. In summary the larger the expected return, the larger your bet size.

The concept of bet sizing can be modelled mathematically through Kelly Criterion. It is worth pointing out that it is extremely common for poker players or hedge funds to run Kelly Criterion suboptimally, by betting less. This dramatically reduces the risk of ruin, and adds a margin of safety to often nebulous assumptions.

So why is bet sizing important? This is an often overlooked concept, but it is extremely important to prevent ruin (or losing all your money).

To reinforce your intuition, we will once again return to the coin flip game. Suppose you are in a situation where you win $200 for heads, but lose $100 for tails. But, you only have $100 - do you take this bet?

While this is a positive EV bet, remember that you are only making money on average in the long run. This does not safeguard you against the short term, where you can be making or losing money. Had you taken the bet and the coin landed tails, you would have lost all your money. This means that you are barred from participating in further potentially profitable bets.

Translating this to investing, if you over-leverage yourself, not only might you lose all your money, but you might miss out on partaking in potentially profitable situations.

Summary

A 101 on not gambling:

  1. Don’t make negative expected value bets - you are guaranteed to lose all your money in the long run.
  2. Scale your bets according to confidence in order to prevent ruin. Overextending yourself can make good bets go bad.

In my past life, I was a derivatives trader on Wall Street. My goal is to share everything I learnt about investing and decision making on Wall Street. Follow me on Twitter to not miss out.

This article is originally published on my personal website christopherjgan.com