How much of our portfolio should we invest in a high conviction stock?
This is an age-old question for any investor. In this article, I touch on two concepts – the absorbing barrier and Kelly criterion – and see how we can use them to structure the way we think about position sizing in investing.
Imagine playing a game of Texas Hold’em poker and being dealt the best starting hand of the game – a pair of aces. This hand has an approximately 80% chance of winning against any other starting-hand combination.
What would be the ideal bet to make here? In theory, the bigger your bet, the bigger your expected return is on the investment because the odds of winning are tilted heavily in your favour. But does this mean we should bet all our savings on this hand? Probably not.
“[A]bsorbing barrier is a point that you reach beyond which you can’t continue. You stop. So, for example, if you die, that’s an absorbing barrier. So, most people don’t realise, as Warren Buffett keeps saying, he says in order to make money, you must first survive. It’s not an option. It’s a condition. So once, you hit that point, you are done. You are finished. And that applies in the financial world of course to what we call ruin, financial ruin.”
The idea is that even if you have a big edge in a game, bet sizing matters. If you keep betting 100% of your net worth on a game of poker, even if you start off as an 80% favourite to win, in the long run, it will eventually result in financial ruin. This applies to any financial decision, even if the probability of the tail risk is extremely low.
In his Fat Tails Statistical Project, Taleb wrote,
“Every risk-taker who survived understands this. Warren Buffett understands this. Goldman Sachs understands this. They do not want small risks, they want zero risk because that is the difference between the firm surviving and not surviving over twenty, thirty, one hundred years.”
This brings us to the next topic, the Kelly criterion. The Kelly criterion is named after researcher J. L. Kelly who described a gambling formula for bet sizing that leads to the highest possible wealth compared to any other strategy if you have a slight edge in the game.
According to the Kelly criterion, the optimal size of an even-money bet is calculated by multiplying the percentage chance of winning by two and subtracting 100%. For a game that you have an 80% chance of winning, the optimal bet sizing is 60% of your available funds (80% x 2 – 100% = 60%). So if you lose your first bet, your next bet should be smaller, and vice versa.
By making the bet sizing a percentage of your available funds, the chances of complete financial ruin drop to zero as you will never bet all your available funds on a single bet.
However, as you may have guessed, in casinos and in gambling in general, you will probably never find a situation where you are a consistent favourite to win in an even-money bet. This is because casinos only offer games where the house has an advantage over the players.
Investment risk management
This is not the case in investing. Great stock pickers, with a proven approach, have higher odds of making winning bets by picking the right stocks to invest in.
Warren Buffett, for example, has been one of the investment greats of the past seven decades by consistently finding stock market winners to invest in. But even great stock pickers may not have a 100% track record. Despite his investing prowess, Buffett has admitted numerous investing mistakes, some of which has caused him or his firm to lose money.
And yet, Buffett is far from financial ruin. This is because of the position sizing for each of his investments and the diversification of his portfolio across a range of “bets”.
Calculating the ideal bet sizing using Kelly’s criterion may not be practical in real life investing, due to our inability to accurately calculate win rates and the fact that no investment is completely identical.
However, understanding the fundamentals behind absorbing barriers and the Kelly criterion can, at the very least, give us a framework to think about how to size our investments to reduce the risk of financial ruin over the long run.
Portfolio positioning is a complicated topic and absorbing barriers and Kelly’s criterion are just some of the topics to consider. For more thoughts on portfolio sizing, you can read some of our other articles here and here.
Note: An earlier version of this article was published at The Good Investors, a personal blog run by our friends.
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Disclosure: Jeremy Chia does not own shares in any of the companies mentioned.