Lessons from the world of gambling

Portfolio strategy

Betting your beliefs

We generally think of investing and gambling as quite different. But, there is something serious investors can learn from the world of professional gambling. It relates to money management and the weighting one gives to individual investment positions.

Let’s reflect on a comment made by Warren Buffett at the Berkshire Hathaway Annual Meeting in 1989: “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.”

Buying a stock and establishing a portfolio is all about return expectation. An investment with a high risk but high potential reward may have the same return expectation as a low risk low reward opportunity. What Buffett was talking about in 1989 was return expectation. While skilled common stock investors generally only invest in superb companies, not every investment has the same return expectation.

A question we frequently ask ourselves is how much to put into any particular position. Regardless of the odds in your favour you can lose money on any single investment. Over the long haul, with a carefully chosen and well managed portfolio, the law of large numbers plays out and a skilled investor will enjoy profitable investing.

The interesting question is whether investors can learn from gamblers about the optimum size of particular investments in a portfolio. Gamblers are familiar with the Kelly system or as it is sometimes called, the Kelly Criterion.

William Poundstone’s 2005 book Fortune’s Formula, The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street explains: “Professional gamblers, who have to have an advantage, speak of ‘money management.’ This refers to the tricky and all-important issue of how to achieve the greatest profit from a favorable betting opportunity. You can be the world’s greatest poker player, backgammon player, or handicapper, but if you can’t manage your money, you’ll end up broke.” (Poundstone, 2005)p.49.

The money and betting management system is also called ‘betting your beliefs.’ The system tells the gambler the optimum amount to wager on each bet. The magic sauce is the use of the geometric mean of the return expectations, as opposed to the arithmetic mean.

The math is calculated by taking the ‘ mathematical expectation of winnings’ on each bet, say ten bets in a ten horse race, multiplying them together and then taking the tenth root of the product. This gives the geometric mean of the ‘expectation of winnings’ of each bet. This has the same logic as the words of Warren Buffett quoted above.

The key insights from the Kelly system for common stock investors are as follows:

1. The optimum strategy is the one that gives the highest compound return over the long haul with no risk whatsoever of going broke.

2. A corollary to not going broke is that no position is ever so large that it imperils the portfolio; this is a significant constraint on concentration.

3. To take advantage of the Kelly system one has to be able to reinvest returns and control the amount invested in any particular position.

4. One apportions investment positions or portfolio weightings according to one’s informed estimate of each stock’s probable return; it is the weighting that provides the highest geometric mean of outcomes; betting your beliefs.

5. The amount to invest in any particular position is not fixed in absolute dollars but as a percent of the total portfolio.

6. As the portfolio grows the dollar amount of positions increases but the percent weighting remains the same or is rebalanced based on estimated probable returns. That is, subject to issues of liquidity, a ten million dollar portfolio can contain the same number of stocks and the same weightings as a one million dollar or a one hundred thousand dollar portfolio.

7. Rebalancing individual stock weightings is a constant activity through good times and bad and everything in between.

8. In a drawdown (after a bear market) individual positions will retain the same fixed percent of the total portfolio or be appropriately readjusted or rebalanced to reflect the then estimated probable return.

9. The investor has to accept volatility and have faith that over the long haul, the law of large numbers will ensure the best return.

The main message here is that there are dangers both from over-betting and under-betting. Betting your beliefs suggests a fairly concentrated portfolio of superb companies. My general rule of thumb is that I will not invest in any company that I am not confident putting 5% of my investing capital into. My preference is stocks with a weighting of 8 to 10% of the portfolio. If any position grows to more than 15% I will sell it down to 10% no matter how much I like the company and the stock.

Want to read more about the issues raised in this post take a look at Part 7: Building and managing a portfolio, in particular Chapter 36. Diversification, balance and strategy and specifically Sections 36.20 How many stocks to own – 1, 36.21 Lessons from the world of gambling – betting your beliefs (for deeper dive) and 36.22 How many stocks to own – 2.

Thinking about betting our beliefs, readers are cautioned that the strength of our conviction we are right has nothing to do with the validity of our judgement. The following blog post explores this subject.

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