The Monty Hall Problem

The Monty Hall Problem is a probability puzzle based on a game show scenario. You’re given three doors to choose from — behind one is a car (the prize), and behind the other two are goats. After you pick a door, the host, who knows what’s behind each door, opens one of the remaining doors to reveal a goat. Now, you’re given the option to stick with your original choice or switch to the other unopened door. The counterintuitive solution is that you should always switch, as it increases your chances of winning from 1/3 to 2/3.

Stay or Switch?

This is the critical question when considering an exit strategy in long-term investing. Warren Buffett once said that selling is harder than buying — specifically, knowing when to sell is more challenging than knowing what to buy.

Imagine you have a diversified portfolio of stocks. Suddenly, one or more of those stocks drop significantly in value. Should you sell the underperformers and reallocate that capital to the better-performing stocks?

If we draw inspiration from the Monty Hall Problem, the optimal strategy would be to switch, or in this case, sell the “bad” stocks and buy more of the “good” ones. However, this strategy rests on two crucial assumptions:

  1. The poor performance is not temporary. The underperforming stocks are truly beyond recovery in the long run.
  2. The great compounders are already in your portfolio, meaning you’ve correctly identified the rising stars.

Neither of these assumptions is easy to verify. This is the realm of “super investors,” a league that most of us are not in. To make the Monty Hall strategy work in investing, you’d need absolute certainty about which stocks (or “doors”) are the “goats” and which ones hold the grand prize. In other words, no hidden information and no unexpected developments.

A More Practical Approach

  1. Never sell a slow performer unless it’s clear the company is failing or the stock has completely collapsed.
  2. Hold a broad portfolio that certainly includes many potential winners. By having a wide selection, you’re more likely to have a few big winners (the “rising stars”).

This strategy may seem overly simplistic, but it can often outperform more complicated methods over the long run. It may not lead to spectacular short-term gains, but it can deliver consistent success over time.

Why Simplicity Works

Here’s why a seemingly “dumb” strategy can outpace a “smart” one:

  1. The sheer size of the candidate pool: There are tens of thousands of listed companies to study. A mortal simply does not have the bandwidth or time to cover them all. This correlates to Buffett’s ‘circle of competence’ concept.
  2. It cannot be hacked by brute force using machines either. Algorithms can work well for data-driven quantitative analysis, but not as effectively for qualitative analysis. Especially when it needs to combine art and science, the investor has to decide what data to feed and what questions to ask. This is not an easy task for long-term and cultural analysis.

It takes a lot of knowledge and experience to embrace simplicity. This is not an easy process, as it requires changing your mindset and aligning your overall life approach to fit a simpler strategy. Paradoxically, knowing that you’re “not smart enough” can make you the wisest person in the investment field.

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