MarketFox Investment Commentary – Investment Innovation Institute

MarketFox Investment Commentary

In Search of Temperament V

Probabilistic Thinking

Our exploration of the ideal investor temperament continues with our fifth post in this series. We’ve considered curiosity and flexibility, contrarianism, patience, self-awareness and self-control. Now we’ll focus on the reasons why investors need to think probabilistically and how to do it.

This leads into a discussion on how successful investors update their beliefs and change their minds. Mistakes are an unavoidable part of probabilistic thinking. We finish off the post by considering the attitude that successful investors have about their inevitable mistakes. 

Define Investing

If someone asked you to define what investing is how would you reply? The Oxford Dictionary defines invest as follows:

Put (money) into financial schemes, shares, property, or a commercial venture with the expectation of achieving a profit.

This is fine as a linguistic definition that can be applied broadly. The word ‘expectation’ implies that results can differ from expectations. But aside from this, the Oxford Dictionary definition doesn’t really capture the challenges that people face when they invest.

Such a definition might read like this:

Making decisions in the face of uncertainty on the basis of incomplete information where the consequences of those decisions may not be known or understood for a long time.

This is how I think about investing. I came to this definition not through any brilliance on my part, but by studying the work of successful investors.

For example, a fund manager who I consider to be one of the best investors I’ve ever met told me a long time ago that he’d learned ‘to work with uncertainty’. All of the successful investors I know share their own individual twist on this sentiment.

Why Probability?

Probability is the mathematics of uncertainty. It gives us a set of tools that we can use to work with uncertainty.  Michael Mauboussin is one of the best writers on how to apply probabilistic thinking to investment problems. In his paper 30 Years – Reflections on the Ten Attributes of Great Investors, Mauboussin lists Thinking Probabilistically at number five on his list of successful investor attributes.

Winning in any competitive activity requires having an edge. Mauboussin explains that an investor’s competitive edge is being able to identify mismatches between the price of an investment and the probability (uncertainty) or magnitude of an outcome. In other words, successful investors look for opportunities where their assessment of the future outcome is either more likely and/or more profitable than the current price suggests.

Of course, this is a highly uncertain exercise. Mauboussin points out that this fact leads successful investors to two important realisations. The first realisation is the importance of focusing on the decision-making process, rather than the outcome.

When probability plays a large role in outcomes, it makes sense to focus on the process of making decisions rather than the outcome alone. The reason is that a particular outcome may not be indicative of the quality of the decision. Good decisions sometimes result in bad outcomes and bad decisions lead to good outcomes. Over the long haul, however, good decisions portend favourable outcomes even if you will be wrong from time to time. Time horizon and sample size are also vital considerations. Learning to focus on process and accept the periodic and inevitable bad outcomes is crucial.

The second important realisation is that it doesn’t matter how often you’re right or wrong. What really matters is what happens when you’re right or wrong.

Great investors recognize another uncomfortable reality about probability: the frequency of correctness does not really matter (batting average), what matters is how much money you make when you are right versus how much money you lose when you are wrong (slugging percentage). This concept is very difficult to put into operation because of loss aversion, the idea that we suffer losses roughly twice as much as we enjoy comparably sized gains. In other words, we like to be right a lot more than to be wrong. But if the goal is to grow the value of a portfolio, slugging percentage is what matters.

Most successful investors realise this, which is why they focus on minimising – not avoiding – losses. Avoiding losses is impossible because the future is unknowable. But while we may not be able to avoid being ‘wrong’ we can control the consequences of our mistakes. We’ll return to this idea later in the post.

This is different to most investors, who find frequent losses, even if they are small, uncomfortable. Even a small loss hurts disproportionally more than it should. Nobody likes being ‘wrong’.

Jim Paul’s experience highlights the danger of this kind of thinking. Successful investors learn to identify the signs of a switch in their thinking form a ‘profit’ motive to a ‘prophet’ motive. They develop a process to help them avoid personalising and internalising investment outcomes. Great investors also use risk management to prevent their mistakes from wiping them out.

The Types of Probability and Their Uses

Mauboussin suggests three types of probability that investors can use:

  • Subjective – translating your knowledge and beliefs into a figure representing your level of uncertainty.
  • Propensity – measuring the physical properties of a system. For example, most dice have six sides, so the chance of rolling a given number is one in six.
  • Frequency – Identifying a suitable reference class (i.e. a group of events with similar attributes and circumstances) for the outcome you’re interested in and measuring how often a given outcome has happened in the past.

Subjective probabilities help investors to make implicit assumptions explicit. They facilitate comparisons and create the feedback necessary to learn. Subjective probability estimates also require frequent updating. This requires curiosity, flexibility and sometimes contrarianism. It’s interesting that many of the traits great investors share often work in concert. 

Frequency-based probabilities are a great reality check. For example, we may subjectively believe that a certain outcome is possible. But we would do well to first check how often an outcome has occurred across a group of similar situations.

There’s a time and place for probabilistic thinking. It should never be used when catastrophic failure is a possible, no matter how remote that possibility may seem. As Nassim Taleb reminds us, if someone offered you $1 million to play Russian Roulette, standard cost-benefit analysis suggests that you should play as your expected “gain” from playing is $833,333. Yet we all know that this is absurd, given a one in six chance of death!

The right setting to apply probabilistic thinking is when there’s:

  1. No chance of catastrophic loss
  2. Asymmetric payoff if things turn out as you expect
  3. You can create a portfolio of unique (i.e. lowly correlated) opportunities that satisfy points 1 and 2


Becoming a Good Loser

Mistakes happen all of the time in investing. It’s impossible to avoid them as the future is uncertain. If that’s true, then the mission of all successful investors is to find ways to survive and thrive despite their mistakes.

How do great investors do this? They learn how to become good losers. This involves:

  • Understanding the difference between a good and a bad loss
  • Limiting losses before they get out of control
  • Focusing on the downside

Every investment strategy known to humankind carries the risk of loss. If there was no risk, there would be no reward. Good investors differentiate between business as usual losses which are a sign that their investment process is working and large, unexpected losses that may be a sign that something is wrong.

This is exactly what mathematician, gambler and legendary hedge fund manager Ed Thorp did when he figured out how to Beat the Dealer in blackjack. Thorp experienced some large losses when he first applied his strategy at the blackjack table. Understandably this shook his confidence.

How did Thorp respond? He went back and recalculated the expected probability of his blackjack strategy. Thorp found that his earlier calculations were correct and that the run of short-term bad luck that he’d experienced was entirely consistent with a successful long-term strategy. He stuck with his strategy and became so successful that he kept getting banned from casinos and resorted to using disguises to evade security. Finally, Thorp gave up gambling when he discovered that the brakes on his car had been tampered with! Evidently, the casinos weren’t good losers.

Probabilistic thinking helps great investors to identify unanticipated extraordinary losses. It also helps them reinterpret losses that are consistent with their strategy. Instead of evidence that we were ‘wrong’, a loss becomes just cost of doing business. They become normalised because the great investors expect them as part of a long-term strategy. Also, they have a plan in place for limiting the impact of these losses, so they’re not such a big deal.

 No Pain No Gain

Most people HATE parking fines. I know that I certainly do. When I was studying at university, I lived at home and drove to the campus each day. I had two parking options:

  • 2-hour parking which was free
  • All-day parking which was $5

A parking fine was $50. You can tell from the dollar amounts in this story that I’m getting old.

Despite my dislike of parking tickets, I soon figured out that it was cheaper to park in the 2-hour on street parking; just as long as I received a ticket less than once every two weeks. This is a simple expected value calculation, a $50 fine multiplied by a 1/10 probability of a parking fine = $5 or the cost of all-day parking.

I decided to take my chances with the 2-hour parking. I received many tickets, but they were usually weeks apart. Sometimes I’d experience a bad run of tickets. But I’d also experience long stretches without a fine.

I discovered that parking could become even cheaper if I applied some basic risk management by moving my car between lectures. Eventually, I was getting fined once every 2-3 months. This meant that my daily parking expense worked out to be roughly $0.80 – $1.20.

Back then there was no online payment option. I remember walking into the Melbourne City Council parking office and happily paying my fines. Instead of resenting the loss, the fines were proof that my strategy was working and that I was actually saving money!

Limiting the Damage

If mistakes are unavoidable, then it’s important to keep them as small as possible. This involves striking the right balance between taking enough, but not too much, risk. This goes against our nature. For example the disposition effect predisposes us to sell our winners and stick with our losers.

Most great investors don’t rely on themselves to manage losses. Rather, they use pre-defined rules. This was Jim Paul’s advice. It would have saved him from losing everything.

What’s the Downside?

The best investors focus far more on what they stand to lose rather than what they may gain. Joel Greenblatt sums the idea up in his conversation with Howard Marks.

My largest positions are not the ones I think I’m going to make the most money from. My largest positions are the ones I don’t think I’m going to lose money in.

Great investors use probabilistic thinking to work with uncertainty. It helps them to focus on their investment process rather than outcomes. Thinking probabilistically prompts them to consider the impact of their decisions. It helps them to put losses into perspective. And it motivates great investors to limit the damage that their inevitable mistakes will have on performance.

My next post is the final part of this series where we’ll consider how great investors measure success and how great investors treat others.


[i3] Insights is the official educational bulletin of the Investment Innovation Institute [i3]. It covers major trends and innovations in institutional investing, providing independent and thought-provoking content about pension funds, insurance companies and sovereign wealth funds across the globe.