Position sizing
If you’ve ever played blackjack at the casino you’d be familiar with the concept of bet sizing.
You don’t bet the same amount regardless of your hand; instead you aim to place larger bets on high probability events.
Here’s a very simple formula where ‘p’ is the probability of winning, expressed as a percentage, and ‘x’ is the position size:
2p – 1 = x
It’s very logical: if you’re less than 50% certain of an outcome then that’s no better than a coin flip and you shouldn’t bet, whereas if you’re 100% certain of success then you go all in!
Of course, in the real world few things are 100% certain, and when it comes to investing you’ll need to adopt a different and more conservative stance.
Capital Growth Theory
If you want to maximise your long-term wealth from investing then you can think of your strategy as a series of repeated similar bets.
The Kelly Optimization model can help you to determine what fraction of your available capital should be allocated to a new investment.
The advantage of the Kelly model is that it maximises your long-term gains, and can help you to minimise losses.
As a general rule, where there’s a reasonable margin of safety, you can maximise returns by increasing your exposure, but this only works up to a certain point.
For one thing, no outcome is certain, and you also shouldn’t over-bet as there will always be other great investment opportunities in the future.
For this reason, many investors choose to use a fractional Kelly strategy to manage risk.
The traditional view
Capital Growth Theory differs from the traditional Modern Portfolio Theory (MPT) taught in business schools.
In the real world we don’t have to invest all of our money today, or indeed in any given market.
Unlike a fund manager, an individual is not bound by a mandated asset allocation, the demands of nervous investors, or the need to benchmark against an arbitrary index or other measure of returns each year.
And since some markets are much cheaper than others, we can use this information to our advantage.
Most investors aren’t very good at stock picking – it’s surprisingly challenging to get right over time – but these days you can buy country or sector ETFs, so you don’t necessarily need to be.
What we’re really interested in is maximising our wealth for the long term, and there will be numerous wonderful investment opportunities in the future to help us achieve that goal.
The Kelly capital growth strategy is the approach that’s mathematically proven through simulations to maximise long-term expected wealth.
Variations of Kelly strategies are used by some of the wealthiest and most successful investors of all time, including Jim Simons, Bill Gross and others.
Thinking in bets
When you contribute to your superannuation fund a portion is invested in the markets regardless of the environment, according to the fund’s allocation.
It’s often noted that super funds don’t beat the market, but when you think about it that’s not really what they’re setting themselves to do.
Super funds generally track the fortunes of the market, and the name of the game is maximising assets under management (and their fees), not your long-term wealth.
To a certain extent institutional investors are the market these days, so in aggregate fund manager returns lag the market due to the fees and transaction costs.
But those of us managing our own money strategically as a series of bets know that the odds of success are considerably higher when markets are attractively priced.
Impressive and substantial gains are achievable, provided you practise careful risk management, although there may be more volatility in your portfolio from month to month.
Indeed, using a Kelly capital growth strategy can see your wealth exceed that of any other strategy, and by more and more as the horizon becomes more distant.
Next we’ll take a look at the Kelly Optimization model in action.
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