Decision trees prevent swaying
‘In short, I panicked and sold many of the stocks I held for over 10 years … Over the past two years, I actually did the opposite to what 13 years of reading and research had told me—much to my financial pain.’ So confesses one of Intelligent Investor’s members in an email reliving the depths of the financial crisis.
Acting rationally is what we’d all like to do. In reality, our emotions and psychology play a big role. It’s our brain’s default option; an evolutionary trait that overrides rational (and slower) thinking during uncertainty. Imagine you encounter a lion; it’s better to bolt than assess.
Playing the odds
This instinctive, emotional reaction to threats helped us survive the savannah but it can be a hindrance in the financial landscape. The desire to act logically, however, is not enough; we need tools that help us do it.
Key Points
- Use decision trees to help make more rational decisions
- Expected outcomes matter, not probabilities
- Investing decision trees are uncertain; it requires judgement
Probability—the source of many a school student’s headaches—is one such tool. By thinking through the chances of a particular event occurring, rather than responding to the emotional panic the event may induce, rationality is reintroduced to our decision-making.
For a few lessons in probability, see this video. |
And we’re generally not too bad at assessing probabilities. If the Australian cricket team played Zimbabwe, you’d expect the green and gold to win. But what odds would you accept to bet on that outcome? That’s the question we all have to answer each time we buy or sell a stock. This lies at the heart of investing.
Expected outcomes matter
Probability of success (striking oil) = 1/3 | |||
P(failure) = 1 - P(success) = 1 - 1/3 = 2/3 |
In a recent podcast, we posed a little brainteaser. Assume an oil company is considering whether to drill two independent exploration holes, each with a one-third chance of success (see Table 1). It’ll cost $10m to drill both holes, and each hole that strikes oil is worth $20m. Should they go ahead with the drilling?
To figure it out, take a look at the decision tree in Diagram 1. Each ‘branch’ represents one hole drilled in our scenario, resulting in either success (S) or failure (F). The probability of each outcome is shown in fractions.
The ‘leaves’ on the right show each possible outcome, its probability and associated payoff from the $10m investment. From top to bottom, the possible outcomes are success at both holes; success at the first hole but not the second; success at the second hole but not the first; and failure at both holes.
Table 2 gives a useful representation of this information. After subtracting drilling costs, multiplying the net payoff by its probability gives the expected value of each outcome. Adding those up gives a total expected outcome of $3.3m. But what does that mean?
Outcome | Payoff ($m) | Drilling costs ($m) | Net payoff ($m) | Probability | Expected value ($m) |
---|---|---|---|---|---|
1: Both successful | 40 | -10 | 30 | 1/9 | 3.3 |
2: Hole 1 successful | 20 | -10 | 10 | 2/9 | 2.2 |
3: Hole 2 successful | 20 | -10 | 10 | 2/9 | 2.2 |
4: Both fail | 0 | -10 | -10 | 4/9 | -4.4 |
Total | 3.3 |
Well, it doesn’t mean our company will have an extra $3.3m in the bank after drilling; that actually can’t happen. It’ll end up with either $30m more, $10m more or $10m less than it had before.
But, if this exact scenario was repeated many times, the average of all those payoffs would tend towards the company being $3.3m better off. So it makes sense to drill.
Thinking in terms of decision trees isn’t intuitive, nor especially easy. Too often a carrot, or in the case of our aforementioned member, a stick, distracts us from thinking rationally. As former US Treasury Secretary Robert Rubin says in his biography (In an uncertain world), ‘while a great many people accept the concept of probabilistic decision making and even think of themselves as practitioners, very few have internalized the mindset.’
Which is of course why lotteries tend to make large sums of money for their operators and not their participants. A punter’s expected return is almost always negative; the yachts and fast cars they might be able to buy sits at the front of mind, rather than the probability of winning and the negative expected return.
Far from certain
Decision trees are useful but they require the assessment of the probability of something happening or not. Robert Rubin suggests you use ‘subjective judgements … but also instinct, experience and “feel”’. To paraphrase Buffett, ‘decision trees are imperfect but that’s what investing is all about.’
Let’s now use decision trees in a practical investing situation. In Dexion jumps into The Ideas Lab, we reviewed GUD’s 80 cent bid for Dexion, which was trading at 70 cents at the time. Considering the risks of the bid failing, was buying into this takeover arbitrage at 70 cents sensible?
Condition | Probability (%) | Payoff (cents) | Expected value (cents) |
---|---|---|---|
Bid succeeds | 85 | 80 | 68 |
Bid fails | 15 | 40 | 6 |
Total | 74 |
Before the bid, Dexion was trading at 40 cents a share, which is where we assumed it would fall if the bid collapsed. With the stock trading at 70 cents, the market as a whole believed that the bid was a 75% chance of succeeding (derived using a decision tree). We believed the market was being slightly pessimistic about the bid for reasons explained in the article. Our estimated probability for the deal occurring was 85% and, as Table 3 details, our expected return came to 74 cents; 4 cents above Dexion’s then trading price.
Simple but not easy
The bulk of our investing decisions are less clear than examples such as this. In late 2008, for example, we recommended Flight Centre at $7.29 in Flight Centre gloom is just the ticket. A global recession, lower Australian dollar and instabilities in several major tourist destinations had contributed to a price slump.
‘You’re looking for a mispriced gamble. That’s what investing is. And you have to know enough to know whether the gamble is mispriced. That’s value investing.’ Charlie Munger. |
It’s almost impossible to build a reliable decision tree under such circumstances; all the inputs are judgements rather than hard numbers. But the same guiding principles apply. The probability of Flight Centre’s longer term success, multiplied by the subsequent value (payoff) appeared much greater than the probability and payoff of long term failure. In other words, our expected return (intrinsic value) was far greater than Flight Centre’s price at that time. Of course, that didn’t stop the share price halving before it eventually turned around and proved our thesis right.
It’s easy to get lost with decision trees. It’s neither an easy nor precise tool and, like any model, it’s only as good as the soundness of your estimates. But they can help circumvent our instinctive, emotional reactions to tricky situations. Decision trees can help minimise investing mistakes, so it’s a tool well worth having.