Inversion

Sacha Meyers
9 min readNov 7, 2022

or why avoiding losers can be more valuable than selecting winners

New York City. Photo by Elsa Gonzalez on Unsplash.

“He wins his battles by making no mistakes” Sun Tzu

Investors look for winners. Implicitly, investors also avoid losers, but it isn’t how they structure research. They do not aim to write reports on companies they believe are poor investments. That would be silly, right?

Developing an edge

Let’s explore this question with two new investors: Peter and Nancy. They aim to invest in companies that successfully beat a benchmark like the stock market or an absolute return. Such companies we call ‘outliers,’ ‘winners,’ or ‘success.’ We then adopt a heuristic for successful investing: we want a higher proportion of outliers in our portfolio than in its benchmark.

We’ll arbitrarily define outliers as top quintile performers. Peter and Nancy start with a 20:80 chance of identifying success (top quintile) and failure (not top quintile). In other words, they begin with no edge. These are their conditional probability trees and table as new investors:

Conditional probability trees and table for a new investor with no edge

Contrasting approaches

From this starting point, Peter and Nancy take different approaches to improve their investment skills and develop an edge.

Peter focuses on ensuring that he never misses a success. His ability to do so will eventually reach 100%. Thus, if a company is an outlier, he will correctly identify it as an outlier 100% of the time. However, his hit rate on failures remains at the base rate of 80%. If a company is a failure, he will think it is an outlier 20% of the time.

Nancy decides to focus on ensuring that she never misses a failure. Her ability to do so will eventually reach 100%. Thus, if a company is a failure, she will correctly identify it as such 100% of the time. However, her hit rate on outliers remains at the base rate of 20%. If a company is an outlier, she will think it is a failure 80% of the time.

After some time, Peter and Nancy achieved the perfect hit rate they each targeted without developing an edge in those they did not. Each starts a portfolio. What is the share of outliers in Peter’s and Nancy’s respective portfolios? Let’s work it out by looking at conditional probability trees and tables.

The top tree gives the probability of Peter and Nancy thinking an investment will be a success or not, given it is a success or not. The bottom tree inverts this conditional, telling us the probability that an investment will succeed or not, given that Peter or Nancy thinks it’s a success or not. The tables give the overall outcomes split between all four permutations for a sample of 100.

Notice that Peter’s right column in the table and Nancy’s left column are unchanged from the “new investor” table above: Peter has focused on perfecting the identification of winners, and Nancy of losers, so Peter’s identification of losers and Nancy’s of winners is unchanged from the base rate.

Peter’s and Nancy’s conditional probability trees and tables

The bottom of the two trees shows how Peter and Nancy implement their approach if they invest in companies they think will succeed. The top ‘thinks success’ branch tells us what proportion of the companies Peter and Nancy will invest in. The sub-branches show the ratio of successes to failures in their portfolios.

Peter thinks 9/25, or 36%, of the companies he researches are successes, even though we know from the base rate that only 20% of them will be. Five-ninths of Peter’s portfolio will succeed, or 20 out of 36. Four-ninths, or 16 out of 36, will be false positives or companies Peter thinks will succeed, hence invests in, but which fail.

In contrast, every company in Nancy’s portfolio will succeed. She only invests in 4% of those she researches. All are successes.

Yes, Peter will always recognize an outlier, but often he’ll think failures are outliers. Nancy, on the other hand, will always identify failures. She won’t ever let one get in her portfolio. Therefore, even though she will miss 80% of the outliers, which she thinks are losers, her fund will only have outliers.

Nancy will outperform Peter by inverting her task from ‘find outliers’ to ‘avoid losers.’ We can see why on the probability trees. By ensuring she thinks a company is a failure when it is a failure, Nancy indirectly ensures that it is an outlier when she believes it is an outlier.

This duality makes for an interesting observation in the relationships between the numbers in the regular and inverted trees above: by moving away from the base rates and towards a perfect hit rate on ‘thinks successful given is successful,’ Peter also achieves a perfect hit rate on ‘is a failure given thinks is a failure.’ Likewise, by moving away from base rates and towards a perfect hit rate on ‘thinks a failure given a failure,’ Nancy also achieves a perfect hit rate on ‘is a success given thinks is a success.’

The difference between what is the case and what we think is the case is crucial. Yet, these conditional probabilities may seem counterintuitive or outright confusing. One way to grapple with it is to focus on how we act in this ‘game’ and the relationship between the treatment of false positives and negatives.

How we act is simple: we only act if we want to. We don’t need to invest in anything. Not investing is not the same as shorting; hence, we aren’t punished if we misclassify a great success — a false negative. However, all investments we choose to make will affect us, so we are punished if we misclassify a failure — a false positive.

The positions of Peter and Nancy can be thought of this way: by targeting positives, Peter also gets false positives, for which he is punished. By targeting negatives, Nancy gets false negatives, for which she is not punished.

In this game, we act based on what we think is the case, and we are rewarded or punished based on what is the case. Therefore, false positives are costly and within our power to avoid, while false negatives are irrelevant. Since Nancy only focuses on failures, she gets a far higher share of successes.

Some potential objections

We see three objections to this conclusion. First, being downside-aware, Nancy may inadvertently lower her hit rate on outliers. Technically that doesn’t matter. She will miss more outliers, but her fund will still have 100% outliers. What matters is if the distribution of outliers, which we defined as the top quintile, is different for Nancy than for Peter. If Nancy discounts extreme outliers, say top decile, at a higher rate than Peter, Peter may have better results. Such is the power of the asymmetry of returns.

Second, because Nancy is pickier, she will need to review more companies than Peter to fill a fund with the same number of investments. After researching 100 companies, Peter invested in 36. Nancy invested only in four. Still, for any given number of companies researched, Nancy will create a better, albeit more concentrated, portfolio than Peter.

Peter can outperform Nancy if we change the ‘game’ so each must construct a 36-stock portfolio while keeping their research limit to 100 companies. Under such constraints, Nancy cannot cherry-pick her investments, and her edge will necessarily be diluted. After reviewing 100 opportunities, Peter will have identified what he thinks are 36 outliers. His work is done. After 100 companies, Nancy will only have identified four outliers. She will thus be forced to fill the remaining 32 slots with random companies.

Let’s now see how each did. Twenty of Peter’s 36 investments are outliers. Nancy will have correctly identified four outliers before running out of time and adding 32 random companies. Of those 32, we can expect 20%, or 6.4 on average, to be outliers since that is the base rate in the population sampled. Her fund will therefore have 10.4 outliers, on average, compared to Peter’s 20. Nancy loses.

As it turns out, the tipping point is at nine companies: if both must construct a 9-stock portfolio, having looked at 100 companies, Nancy’s five extra random choices, on top of her four sure successes, will lead to one success on average, bringing her total five. The ratio of outliers in the portfolio is, therefore, five-ninths. As the chart below shows, Peter’s performance only starts to decay above 36 stocks.

In a subsequent article we will explain the formulae used to derive these figures and vary the outlier cutoff, currently (arbitrarily) set to the top 20%.

Concentration benefits Nancy. It may seem counterintuitive, but Peter’s strategy of looking for winners is better suited to diversified funds. Nancy will beat Peter if she can choose her investments. Nancy is the ideal high-conviction growth investor. She achieves that by doing precisely the opposite of what’s expected. She understood that if you are going to have a perfect hit rate, it’s better to be right when you think you’re right than it is to think you’re right when you’re right. Call it the Meyers-Farrington law. It implies that correctly identifying losers finds proportionally more winners than correctly identifying winners.

The third objection may be that achieving a 100% hit rate in the real world is impossible, as is being sure what your hit rate is. The future is uncertain. This is true, of course. But it doesn’t invalidate the core insight that avoiding failures is more valuable. Let’s look at how the rate of outliers in their portfolios increases as they improve their respective skills.

To make the comparison fair, we broke down their goal into four proportional steps to 100%. So, Peter’s hit rate on success will increase from his initial 20% to 40%, 60%, 80%, and finally, 100%. Nancy’s hit rate on failure will increase from 80% to 85%, 90%, 95%, and then 100%. The results may explain why few people follow Nancy’s strategy. She only matches Peter’s rate of outliers in her fund when both are one step away from their goal — Peter at 80% and Nancy at 95%. We might interpret this as the development of Nancy’s skill taking longer to pay off and her result being more sensitive to overconfidence in this skill.

Ratio of outliers in fund as skills progress for 20% outlier cutoff

It is also worth noting that Nancy’s skills pay off faster for less extreme outliers. The table below shows a similar skill progression for outliers that occur 40% of the time instead of 20%. If the objective is to exclude the bottom 20% of investments, Nancy becomes significantly better than Peter at most skill levels.

Ratio of outliers in fund as skills progress for 40% outlier cutoff

Portrait of an old man

Nancy rejects most companies and only invests in the few she knows won’t fail. She runs a concentrated portfolio of high-conviction ideas. She misses plenty of winners, but that does not bother her.

A picture emerges, that of an older man, an oracle, the Oracle. As Warren Buffett said, there are only two rules to investing:

Rule #1: Never lose money

Rule #2: Never forget rule #1

That is precisely Nancy’s strategy. Nancy shows why so much of Buffett’s advice works. Take his ‘20-slot rule,’ which asks that you view your investment career as a 20-slot punch card. You may only invest in 20 companies. It is a call to be selective, to pass far more often than you invest. Nancy approves.

And finally, this method works because investing is a particular game. In investing, unlike baseball, you do not strike out. That is another of Warren’s gems. It doesn’t matter how many times you pass on opportunities. They will keep coming. Nancy can let 96 balls fly by her. She need only hit the four she knows for sure are home runs.

Sacha Meyers & Allen Farrington

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