A few weeks ago, I wrote an article titled, “Cultivating an Expected Return Mindset.” This article is an updated version of the aforementioned article. The reason I devote another article to this subject is because I really think probabilistic thinking is a mental model that is enormously important yet often ignored by the general investing public. It is my hope that after reading this article, a few readers can adopt this probabilistic mentality.

Let’s start by reviewing a quote from Robert Rubin.

“Any individual decisions can be badly thought through, and yet be successful, or exceedingly well thought through, but be unsuccessful, because the recognized possibility of failure in fact occurs. But over time, more thoughtful decision-making will lead to better overall results, and more thoughtful decision-making can be encouraged by evaluating decisions on how well they were made rather than on outcome.”

Rubin’s wise words imply that a flawed decision making process can yield satisfactory, or even superior outcome, compared to that of a better and well thought-out decision making process. In order to deserve a superior return, an investor ought to have a thinking system that is superior to the linear and one-dimensional thinking that is naturally preferred by the human brain. And when it comes to investing, it is hard to have a superior thinking system without incorporating the mental model of probabilistic thinking. As Charlie Munger (Trades, Portfolio) put it: "If you don’t get elementary probability into your repertoire you go through a long life life a one-legged man in an ass-kicking contest. "

Anyone who wants to seriously understand probabilistic thinking should read Robert Rubin’s book called "In an Uncertain World." For those of you who are interested in the big idea, here is how Rubin describes the probabilistic mindset:

“Sound decisions are based on identifying relevant variables and attaching probabilities to each of them. That’s an analytic process but also involves subjective judgements. The ultimate decision then reflects all of this input, but also instinct, experience, and ‘feel’. All the time bearing in mind that reality is always more complex than concepts and models.

A true probabilistic view of life quickly leads to the recognition that almost all significant issues are enormously complex and demand that one delve into those complexities to identify the relevant considerations and the inevitable trade-offs. With an enormous number of competing considerations, the key to reaching the best possible decision is to identify all of them and decide what odds and import to attach to each."

Now that we have learned the mental model, how can we apply it to our investment process?

Well, I think incorporating the probabilistic thinking into the intrinsic value calculation is a good start. The calculation of intrinsic value, which is of utmost importance, is often carried out inappropriately. This could mean failure to include all scenarios, failure to assign probabilities to each scenario, and overly optimistically assigning probabilities to favorable outcomes. If we cross reference to another mental model, human psychology, we can easily tell that the overconfidence tendency often results in a narrow outcome range, and the confirmation bias certainly pushes us to seek information that will enhance the probabilities of more favorable outcomes. When applying probabilistic thinking, we need to be keenly aware of the psychological biases that may come in play at the subconscious level. Rather to err on the side of conservatism, I suggest that one should automatically assign at least a 20% probability for worst case scenario. One way to quelch your enthusiasm is to look at objective statistic data. For instance, if you are considering investing in an turnaround situation, you should find out the historic success rate of corporate turnaround, which is about only 33%. I think you would be wildly optimistic if you assign a 70% success rate.

Let’s use BlackBerry (BBRY) as an example. There’s been a lot of buzz since CEO John Chen took over and we’ve witnessed a period of investor enthusiasm earlier this year. Since then BlackBerry has dropped considerably. At this level, should you invest in BlackBerry?

Applying probabilistic thinking, we should first think of all the possible scenarios and assign a probability and value to each scenario.

Scenario 1: The turnaround is successful and let’s say BlackBerry can be worth $20 a share under this scenario.

Scenario 2: The turnaround is not successful and BlackBerry is acquired by another company, or by a combination of companies. Let’s say BlackBerry is worth $8 under this scenario.

Scenario 3: The turnaround is not successful and BlackBerry has to be liquidated. Let’s say you can get probably $3 to $4 per share out of liquidation.

Scenario 4: The success of the turnaround cannot be assessed but due to BlackBerry’s recent financial engineering and Foxconn deal, the company actually achieves nominal profitability and positive cash flow. Let’s say under this scenario, investors cheer for John Chen’s leadership and bid up BlackBerry to $12 per share.

This is how a conservative investor may assign probabilities and calculate expected value:

Scenario Probability Outcome Weighted Value 1 15% $20 $3 2 30% $8 $2.4 3 30% $3 $0.9 4 25% $12 $3 Expected Value 100% $9.3

This is how an optimistic investor may assign probabilities and calculate expected value:

Scenario Probability Outcome Weighted Value 1 50% $20 $10 2 20% $8 $4 3 10% $3 $0.3 4 20% $12 $2.4 Expected Value 100% $16.7

You can see that changing probabilities alone can have a profound impact on valuation, not to mention change both probabilities and the the outcomes. No wonder value investing is as much as art as it is science.

Again from my observation, most investors don’t use the probabilistic thinking approach when calculating intrinsic value. As I pointed out in my previous article, “Our brain is wired to take shortcut when it comes to complex decision making process such as making multiple assessment of both the probabilities and outcomes of an investment. So we have to overcome this biological hurdle before we can even move on. Secondly, both estimating the probabilities and outcomes involve a great deal of judgment and better judgment comes from knowledge compounding and experience accumulation. Unfortunately (and fortunately for those who are more determined), there is no shortcut to knowledge and experience accumulation.”

Therefore, to successfully apply probabilistic thinking, one has to overcome the human nature of relying too much on System 1 and to work diligently towards relentless knowledge and experience accumulation.

Next time you analyze an investment opportunity, I hope you apply this powerful probabilistic thinking model.

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