Investing Isn’t About Being Mostly Right 

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Investing isn’t about being mostly right. In fact, you can be mostly wrong and beat portfolios that were mostly right!

Today, we’ll explore how investors can potentially improve portfolio outcomes by targeting two seemingly contradictory but deeply complementary systems as outlined in the latest Mauboussin-Callahan paper, Probabilities & Payoffs: The Practicality and Psychology of Expected Value.

But understanding this counterintuitive reality requires a shift in mindset—one that embraces uncertainty and focuses on the power of diversification.

Let’s dig in!

The Babe Ruth Effect: Why Being Wrong Often Can Still Make You Rich

The baseball legend Babe Ruth hit 714 home runs, a record that stood for nearly 40 years. But here’s another fun fact—he also retired as the all-time leader in strikeouts. Still, nobody remembers his strikeouts. They remember the home runs!

The same is true in investing: it’s not about how often you win, but how much you make when you do. In fact, you can be wrong most of the time and still come out on top if your winners more than make up for your losers. 

In their paper, Callahan and Mauboussin examine the Babe Ruth Effect by contrasting two return distributions. One that charts human height, and the other city population dispersion. 

Obviously, there isn’t a single human towering 500 miles tall to throw off the average height calculation, so we can safely assume that human height follows a simple normal distribution. 

But when it comes to city populations, things aren’t so neat. Just one metro area holds a staggering 6% of the entire U.S. population. According to the paper, New York City is 205 times larger than the country’s 1,000th largest city, making averages and standard deviations poor measuring tools.

Author Nassim Taleb famously uses two quirky terms to describe different types of distribution domains:

Mediocristan – Where things follow a normal distribution and no single data point has an outsized impact. Human height, for example, falls into this category—one exceptionally tall person won’t skew the average.

Extremistan – A world of power-law distributions, where a small number of extreme events dominate. City populations are a classic case—just a handful of massive metros, like New York City, dramatically skew averages.

But how does this apply to portfolio construction?

Simply put, being wrong often doesn’t necessarily mean you won’t come out ahead. Returns from Extremistan can not only match or exceed average returns but also serve as powerful tools to help smooth the path to and in retirement.

Here’s how.

Expected Value: The Real Measure of Investment Success

In the paper, Callahan and Mauboussin simplify this idea with an elegant formula.

Expected Value = Probability x Payoff

What an investor expects to gain is a function of the probability of gain times the payoff for such gain less the probability of loss times the payoff for such loss.

According to the authors, expected value is a moving target shaped by uncertainty, human behavior, and unpredictable external forces. The best investors understand that maximizing expected value sometimes means taking bets that don’t always pay off. That’s why this formula does not imply anything about the frequency and magnitude of wins investors should pursue.

Going back to our seemingly contradictory but deeply complementary systems, here are two broad types of expected value distributions investors are able to target:

Negative skewness  – These are high probability, moderately gaining assets. Think stocks and corporate bonds. You can usually count on these asset classes for steady returns—but every now and then, they jump off a cliff.

Positive skewness – These are low probability, highly gaining assets. Think long-volatility strategies like trend following and tail hedging. Most of the time, these positions will make you second-guess whether the noise and bleed are worth it… until they don’t.

Notice how both are polar opposites in probability and payoff structures, and are therefore natural diversifiers to each other. More on that later.

First, let’s explore why market returns are skewed in the first place.

External Shocks and the Limits of Prediction

Financial models, no matter how sophisticated, often fail due to exogenous risks—external shocks that disrupt markets without warning. According to Callahan and Mauboussin, a study of the biggest stock price moves from 1941 to 2012 found that many were driven by geopolitical or macroeconomic surprises. But here’s the kicker: a large percentage of market swings had no clear external cause—they emerged from within the system itself.¹

Clearly, there are deeply ingrained behavioral forces that steer humans into making prediction errors, and the gap between expectation and reality opens up opportunities for investors to seize.

But before diving into portfolio sizing, it’s crucial to recognize that not all positive expected value strategies are created equal. Some can still lead to financial disaster if they expose investors to excessive downside risk.

The Kelly Criterion: Sizing Bets for Long-Term Success

In the paper, Callahan and Mauboussin flesh out some major holes in mean-variance optimization systems and offer a more robust alternative: the Kelly Criterion. In short, investors should seek to optimize for geometric mean returns instead of focusing on expected value from a single period as “some strategies with positive expected value can still result in financial disaster.” (16)

You can feed a mean-variance optimizer assets that you know are going to zero. Guess what? The mean-variance optimizer will still tell you to invest. 

Therefore, expected value only matters if path dependency doesn’t destroy you first.

To illustrate this concept, the authors present an example from Ole Peters² of two similar systems that experience wildly different results. Imagine a coin that increases wealth 50 percent when it comes up heads and decreases it 40 percent when it comes up tails. If you start with 1 dollar, the expected return is 5 cents. But let’s run this experiment twice with a bit of nuance.

First, you have 100 friends flip the coin all at once. Your realized return will likely not deviate too far from 5 cents.

But let’s say you don’t have 100 friends that could help you out with this experiment, so you’re constrained to flipping the coin yourself 100 times. If you were to compound this series over time starting with $100, it’s much more likely that you run out of money well before the end of the experiment!

This concept, known as ergodicity, perfectly relates the danger of utilizing arithmetic averages instead of geometric returns as portfolio construction tools. Unlike subjective risk tolerance inputs in MVO systems, Kelly provides a mathematical framework for determining the optimal bet size, balancing risk and reward to prevent overexposure.

Investor Takeaways

Let’s bring this all home and present three practical tips investors can use in their portfolios.

1. Diversify your bets: Of course, most investors understand the importance of eliminating idiosyncratic risk by diversifying within asset classes. But few apply the same thought process across asset classes. By combining negatively skewed assets (stocks, bonds) and positively skewed strategies (trend following, tail hedging), investors may minimize the randomness introduced by path dependency. While younger investors can afford to ride out volatility, those in retirement face the risk of significant drawdowns with little time to recover. Failing to diversify properly doesn’t just limit potential gains—it exposes retirees to losses they may not be able to recover from.
   
2. Target the winners: While those in the decumulation phase benefit most from asset and strategy diversification, both accumulators and retirees can gain from targeting momentum exposures within and across asset classes. In short, momentum has not only enhanced returns but has also, at times, improved drawdown profiles.
   
3. Cut your losses short: While trend following has struggled recently, the underlying math remains too powerful to dismiss. Much like the power laws behind the Babe Ruth Effect, trend-following strategies reinforce the principle that investing isn’t about being right most of the time—it’s about making the most when you are.

Final Thoughts: Expected Value vs. Path Dependency

Investing is a game of survival. 

All good strategies can fail if they expose investors to catastrophic downside risk; therefore, investors must implement portfolios that increase the chance for success, both economically and behaviorally, while being mindful of the pitfalls that could wipe them out.

The goal isn’t just to win—it’s to stay in the game long enough for the odds to work in your favor. Play smart, stay in the game, and let compounding do its work.

Sources:

Mauboussin, Michael J., and Callahan Dan. “Probabilities and Payoffs: The Practicalities and Psychology of Expected Value.” Counterpoint Global Insights by Morgan Stanley Investment Management, February 19, 2025. 

1 David M. Cutler, James M. Poterba, and Lawrence H. Summers, “What Moves Stock Prices?” Journal of Portfolio Management, Vol. 15, No. 3, Spring 1989, 4-12 and Bradford Cornell, “What Moves Stock Prices: Another Look,” Journal of Portfolio Management, Vol. 39, No. 3, Spring 2013, 32-38.

2 Ole Peters, “The Ergodicity Problem in Economics,” Nature Physics, Vol. 15, December 2019, 1216-1221