The Ellsberg Paradox: Can Uncertain Investments Be Your Safest Bet?

How a famous investor 4x'ed his money by leveraging our fear of the unknown

Daniel Ellsberg (…) next to his wife, Patricia. (AP Photo)

How did one of the most famous value investors from recent years manage to 4x his money investing in one really boring business? I'm always surprised how sometimes the most successful strategies are the most simple. You just have to connect the dots, in this case taking advantage of The Ellsberg Paradox. So, what am I talking about? Let's dig in!

Although most well-known for his role as a political activist and his role in helping to end the Vietnam War, Daniel Ellsberg was also the author of a groundbreaking work in decision theory.

In his paper "Risk, Ambiguity, and the Savage Axioms," Ellsberg proposed a thought experiment involving urns filled with coloured balls. The experiment went like this:

1. Imagine an urn containing 90 balls. 30 of these balls are known to be red, and the remaining 60 are either black or yellow, you don’t know in which proportion.

2. Participants are asked to choose between two bets: Bet A: Win $100 if a red ball is drawn Bet B: Win $100 if a black ball is drawn.

3. Then, participants are asked to choose between two more bets: Bet C: Win $100 if a red or yellow ball is drawn Bet D: Win $100 if a black or yellow ball is drawn.

A bowl containing 90 balls. 30 of these balls are known to be red, and the remaining 60 are either black or yellow, in an unknown proportion.

Ellsberg found that most people prefer Bet A to Bet B, and Bet D to Bet C. This preference pattern violates the sure-thing principle of expected utility theory, because it implies that people simultaneously believe that there are more red balls than black balls (preferring A to B) and more black balls than red balls (preferring D to C).

This paradox demonstrates that people tend to prefer known probabilities (the 30 red balls) over unknown probabilities (the unknown split between black and yellow), even when this preference leads to inconsistent choices.

Could this really be true? Well, the Ellsberg Paradox has been replicated numerous times and has also spawned a vast literature in economics, psychology, and decision theory. It's a cornerstone study in understanding how people make decisions under uncertainty and has significant implications for us in the investing world.

In this post, I’ll explore the concept of ambiguity aversion—its origins, relation to other biases, impact on financial markets—and, to finalize, I’ll analyze a famous investor's approach to uncertainty.

The Psychology of Risk: Understanding Ambiguity Aversion in Investing

To fully understand ambiguity aversion, we need to asses its psychological roots. It’s fascinating to look at other cognitive biases and see how the Ellsberg Paradox is related to them (note that throughout the article, I'll be using ambiguity aversion and Ellsberg Paradox interchangeably).

Now let’s take a look on the most common biases in the finance world and who they relate to our paradox:

1. Loss aversion: People tend to prefer avoiding losses over acquiring equivalent gains. This bias can amplify ambiguity aversion, as unknown probabilities may be perceived as potentially leading to greater losses.

2. Status quo bias: The tendency to prefer the current state of affairs. This can manifest as a preference for familiar investments with known risks over unfamiliar ones with ambiguous risks.

3. Illusion of control: People often overestimate their ability to control outcomes. Known probabilities may provide a false sense of control, making them more appealing than ambiguous situations.

4. Availability heuristic: We tend to overestimate the probability of events that are easily recalled. Known risks are often more easily imagined and thus may seem more likely than ambiguous ones.

5. Confirmation bias: The tendency to seek out information that confirms pre-existing beliefs. This can lead investors to avoid ambiguous situations that challenge their current understanding.

6. Anchoring: People tend to rely heavily on the first piece of information offered when making decisions. In financial contexts, this can lead to an over-reliance on historical data or familiar metrics, avoiding more ambiguous indicators.

As you can see, all these biases tend to generate a reinforcing loop that may strengthen ambiguity aversion once it is in play.

Hardwired for Certainty: Did Evolution Shaped Our Fear of the Unknown?

Now, how did all this psychological scaffolding come to be? If you allow me, from an evolutionary standpoint, ambiguity aversion may be seen as an adaptive trait that enhanced survival chances:

1. Resource conservation: In prehistoric environments, resources were often scarce. Opting for known risks over unknown ones could have helped conserve energy and resources, critical for survival.

2. Predator avoidance: Known dangers (like familiar predators) could be more easily avoided or managed compared to unknown threats. This preference for the "devil you know" may have translated into a general aversion to ambiguity.

3. Learning and pattern recognition: The human brain evolved to recognize patterns and make quick decisions based on past experiences. Known risks fit more easily into this framework than ambiguous ones.

4. Short-term focus: Evolutionary pressures often favored short-term survival over long-term gains. Known risks provide immediate feedback, whereas ambiguous situations might require longer-term evaluation.

5. Emotional regulation: Ambiguity can trigger anxiety and stress. Avoiding such situations could have helped maintain emotional stability and provide comfort, which was important for survival and social functioning.

In prehistoric environments, resources were often scarce. Opting for known risks over unknown ones could have helped conserve energy and resources, critical for survival.

Certainly, I'm no anthropologist, and the points above are purely speculative. Nevertheless, it seems that ambiguity aversion is deeply ingrained in our brains and continually reinforced by other psychological biases. So, if this is prevalent in human nature, we should be able to identify behaviors in financial markets that are a result of this aversion, right? Well, there's some truth to that.

How Ambiguity Shapes Market Behavior

Ambiguity aversion plays a significant role in shaping investor behavior and market dynamics, let’s see some of the most common examples:

1. Volatility clustering: Ambiguous information can lead to divergent interpretations, which can exacerbate market volatility during periods of uncertainty. I remember watching a video of a hedge fund manager who had studied Amazon's volatility before it was clear that it was going to consolidate its moat and its marketplace. While uncertainty lasted, the stock price was all over the place. When there is uncertainty, ambiguity aversion can exacerbate volatility.

2. Underreaction to ambiguous information: You also have the opposite reaction: markets may be slower to incorporate ambiguous information into prices, potentially creating opportunities for investors who can better tolerate or resolve ambiguity.

3. Overreaction to ambiguous information: I think you can see a set of effects in the presence of uncertainty: increased volatility, a stickiness bias towards underreaction, and also a stickiness bias towards overreaction where a stock is absurdly underpriced in the presence of uncertainty and ambiguity. As we will see below, sometimes uncertainty can create opportunities to find bargains.

4. Overvaluation of "safe" assets: During periods of high market ambiguity, investors may flock to perceived safe havens, leading to overvaluation of these assets.

By recognizing areas where ambiguity aversion may be leading to market inefficiencies, great investors can position themselves to capitalize on these behavioral patterns.

Let’s see how Mohnish Pabrai did exactly that in the case study below.

Low-Risk, High-Uncertainty: Mohnish Pabrai's Approach to Ambiguity

This is a fascinating strategy. Below, I've included an interview where Pabrai explains which type of business has the lowest rate of failure and how he leveraged ambiguity aversion to invest in it.

Let's break this down further:

1. Defining the Concept:

   • Low-risk: The potential for permanent loss of capital is minimal.

   • High-uncertainty: The range of possible outcomes is wide and not easily predictable.

2. The Paradox: Most investors conflate risk and uncertainty, avoiding both. Pabrai separates them, seeing opportunity where others see danger.

3. The Rationale:

   • Asymmetric Payoff: If the downside is limited but the upside is potentially large, the investment becomes attractive even if the probability of success is uncertain.

   • Misspricing Opportunity: High uncertainty often leads to misspricing as ambiguity-averse investors avoid these situations.

4. Managing Risk:

   • Extensive Due Diligence: You have to understand the business and industry deeply to assess the true worst-case scenario.

5. Long-Term Perspective:

   • Patience: You have to be willing to hold the investments for extended periods as uncertainty resolves and the thesis plays out.

   • Optionality: You may have high-uncertainty situations that often come with embedded options that can become valuable over time as well.

As you can see, Pabrai’s approach essentially turns ambiguity aversion on its head. While most investors avoid ambiguous situations, Pabrai sees them as potential opportunities, provided the downside is protected.

By focusing on the risk of permanent capital loss rather than short-term volatility or uncertainty, Pabrai is able to enter situations that others avoid, of course with this leading to outsized returns.

Bring home my whole thesis here: ambiguity, when properly understood and managed, can be a source of opportunity rather than something to be universally avoided.

The Adaptive Investor: Thriving in a World of Ambiguity

In conclusion, let's recap the key takeaways from our discussion:

1. Enhanced Decision-Making: Awareness of ambiguity aversion empowers us to make more rational, well-informed decisions, especially when faced with market uncertainty.

2. Refined Risk Management: Distinguishing ambiguity from risk allows for more comprehensive and nuanced risk assessment and mitigation strategies.

3. Unlocking Opportunities: By managing this bias, we can tap into "behavioral alpha," capitalizing on market inefficiencies arising from others' aversion to ambiguity.

4. Long-Term Focus: Recognizing and managing ambiguity aversion encourages a focus on long-term fundamentals rather than being swayed by short-term market fluctuations.

If you've read this far, I hope I've shown that as we navigate an uncertain future, embracing ambiguity is a required mindset to thrive and generate alpha.

If you have any comments or contributions, I'd love to hear them below!