Ever since I devoured “The Success Equation” on a sun-drenched beach in Malaysia, I’ve eagerly anticipated every new piece from Michael Mauboussin. There’s something about his work that push the intellect, perhaps tinged with the nostalgia of that Malaysian coastline.
Michael’s latest release, “Probabilities and Payoffs” delves into the nuanced complexities of expected value calculations. It dissects the landscape of payoffs in investment, the perils of volatility drag, and the intricate psychology of navigating probabilities and payoffs. These insights are pivotal for anyone invested in diverse asset classes.
While the report zeroes in a bit too narrowly on individual securities at the expense of broader asset classes, it brims with invaluable insights, particularly for investors not steeped in high finance. Below, I’ve curated some excerpts and interwoven my reflections.
“value is really “expected value,” which represents a range of potential payoffs with associated probabilities.“
This is the paper’s key message, so simple yet easily misunderstood. We can expect to extract a premium by taking (certain) risks but there is no certainty on when and how much.
“One of the most challenging aspects of understanding expected value is that excess returns can be the product of high probability events with relatively low payoffs, or low probability events with
relatively high payoffs. In other words, how often you are right is not all that matters. What is vital is how much money you make when you are right versus how much you lose when you are wrong.“
In the era of social media, this reality doesn’t fly to the average content consumer.
Rare big gains accompanied by many small losses will attract less public than a cricket game in Rome. Remember how many people you know who allocate to trend following: this is the reason. Death by a thousand cuts is painful and not glamorous.
The high frequency – low payoff works better…as long as you hide the truth: there is a big loss waiting around the corner. Better if you run this strategy with someone else’s money, so when the tsunami comes, you already collected your gains as fees. Investors Clients suffer from amnesia, so the show-runner can hide for a couple of years after the bust and wait for memories to fade or for a fresh herd to milk.
Here you can listen to Benn Eifert explaining why that option trading strategy sucks.
“Some markets have seen a shift in appetite from high probability, low payoff opportunities to low probability, high payoff ones. In betting on horse races, there has been a rise in “exotic” wagers, which can include several horses and multiple races, versus simple win, place, and show bets. In sports betting, parlay bets, also wagers on multiple outcomes, have grown relative to simple point spread or over/under bets. And there has been a surge in the trading of short-dated options in equity options markets.“
I had to read the part about short-dated options three times to understand that the author is correct. Despite the number of lads I see selling options, an even higher number buy them in the hope of a home run.
“The key to financial success when dealing with unknowns and ignorance, a good description of most investing, is the ability to assess probabilities and payoffs. Decision theory becomes more important than optimization.“
Risk and uncertainty are two different things. With “risk”, the distribution of outcomes is known; in a risky environment, we try to solve an optimisation problem. The issue is that most investing is characterised by uncertainty, not risk: we have to assess probabilities.
Having to assess probabilities doesn’t mean that this is an impossible exercise. One thing is to say that modelling the equity risk premium is hard, another that it doesn’t exist.
As in every other field, even here we have the uncertainty fundamentalist: people who, despite their strong “we know nothing” opinion, still invest in stocks. Which means they actually believe in the equity risk premium.
If you have a process to assess probabilities, it is not that farfetched to build something resembling an optimisation on top of it. The guilt is not in thinking that a smart decision can be taken in an uncertain world but it is to take those models as “certain” and therefore push the optimisation process to the limit.
If the Sharpe World, as David Dredge calls it, becomes a religion, then yes, it is wrong. Correlations are not static, probabilities are not normally distributed, bla bla bla. But if a Central Bank cuts rates, bond prices go up. If stocks crash, implied volatility (option prices) go up. From here, we can build some scenarios: they will not fit 100% the future but they are still useful.
Instead of acting partisanship, can we meet in the middle?
“Phase transitions, where small changes in a cause lead to large effects, are pervasive in complex systems such as businesses and markets. Think of cooling water that starts at a temperature just above freezing. As the temperature drops below the point of freezing—ah whoom—the liquid turns into a solid. A modest change has a large impact.“
This describes beautifully why creating a model is a hard task. 99 times a small change brings a small effect and then, boom, here is the proverbial straw that broke the camel’s back.
“Research shows that investors commonly overprice stocks with lottery characteristics because they
overweight the probability of a high payoff. Some financial economists have concluded that it is better to sell, rather than buy, investments with lottery- and insurance-type payoffs. This thinking can be expanded from individual opportunities to investment strategies. Selling investments with lottery or insurance payoffs means making a little money most days and losing lots of money from time to time (blowup). Buying investments with lottery payoffs means losing a little money most days and making lots of money every now and then (bleed). Nassim Taleb believes in the bleed strategy and argues that extreme outcomes are underpriced.“
Any investor’s journey is a constant swing between these two camps: seek extreme outcomes and then revert back to small gains. Rinse and repeat.
Am I fooling myself by holding SVIX and CAOS in the same portfolio? I do not know if the best way to put it is that there is a season for each investment: my portfolio has convex instruments (TAIL, CAOS, Trend/MF) and small-gains one (bonds, L/S factors (?), carry, Nat Cat, SVIX). Would passive rebalancing be enough to make the strategy work?
Is it a matter of asset-mix or rebalancing? Neither? I get the allure of going all-in on a mix of convex strategies, but it’s easier said than done. Choosing the right assets is hard, and to avoid dilution, you have to limit diversification. Matter of fact, Taleb is rich but not that rich: is he rich because he’s selling you the right story or is he rich because of his skin in the game?
“Philosophers, statisticians, and mathematicians have debated the meaning of probability for centuries. Some have argued that probability is a subjective assessment that fails to reflect a real quantity, and hence does not really exist.”
Is there a meaning in assigning probabilities to an election?
The main issue with probabilities in the real world is that we do not know the distribution. Even if we knew that, we have to focus on the process and not on the outcome. It is difficult to assess how good our process is because we will rarely have a definitive answer on what the probability distribution related to that specific situation was.
Annie Duke suggests some tricks to at least diminish this problem:
- Embrace Uncertainty and Acknowledge the Limits of Knowledge: Acknowledging that uncertainty is inherent in most decisions helps you be more open to evaluating your choices based on available evidence, rather than pretending to know more than you actually do.
- Make Use of Available Information: an informed estimate is better than a finger in the air. or worse, just your own experience. sure, the definitive answer is not out there but using more information is better than nothing. Also, try to put yourself ‘outside’ of the decision, to be more objective.
- Apply Calibration: test and track your estimates to see how well you predicted outcomes. Keep an investing journal the more ‘active investing’ you go; record what was your thinking at the time. This helps improve your future decision-making and increases the accuracy of your estimations.
The fact that we are mostly driving in the dark doesn’t mean we should not use the few tools we have.
“One essential point is that probabilities and payoffs are dynamic. That means that new information will justify a revision in prior probabilities. The formal way to do this is with Bayes’ Theorem, which tells you the probability that a prior belief is true conditional on some event happening. While the math is useful, what is more important is an openness to updating your views.”
This is really hard, do not feel alone here 😉 Often, when I discover a more efficient method of accomplishing a task, I feel a sense of regret over my past inefficiencies. This feeling can be so overwhelming that I am tempted to revert to my old habits, simply to avoid confronting a flaw that, in reality, holds no shame—especially since I am the only one aware of it.
“Probability and confidence are distinct concepts that often get combined, unwittingly, in investment analysis. You can think of probability as an estimate of the chances of a payoff and confidence as “the degree to which an analyst believes that he or she possesses a sound basis for assessing uncertainty.” Psychologists call the probability assigned to a payoff “first order uncertainty.” A reasonable range of probabilities for first order uncertainty is called “second order uncertainty.” It reflects uncertainty about an uncertain payoff.”
Confidence in the probability assigned to an event/investment is important, as Michael says: if two investments have the same expected value, you want to go with the one you have the highest confidence. Put it this way, it is obvious but reality is never so clear cut. We are keen to look at payoffs more than probability and less so to confidence.
“Being well-calibrated does not mean knowing the answer to each question. It is about being as close as possible to the 45-degree angle line between confidence and being correct. Excellent calibration comes from knowing what you know and knowing what you do not know. The question is whether feedback helps improve calibration. The answer is yes.
We noted that feedback in investing and business is impeded by noise and lag time between forecast and outcome. The way to deal with noise is to keep score using probabilities instead of words. The way to deal with the lag time is to break down a thesis into subcomponents that are relevant over shorter time horizons.”
This passage is so important: how do we improve our process? With feedback.
Check your prediction against what happened. More subcomponents means more frequent events, which translate into more feedback.
“we are much more drawn to stories than we are to statistics. Experiments show that the impact on beliefs fades much slower for stories than it does for statistics. We are more likely to remember and believe a story than a statistic.“
Personal finance is plagued by stories and lacks a deep belief in statistics. This is the crime of content creators: stories stick and therefore are used, but they often miss the necessary nuances. Half a lie is not better than a full one (but it sells equally well).
“One way to think about this is that mean/variance optimization (Markowitz) focuses on diversification at a point in time and geometric mean maximization (Kelly) considers diversification over time. Markowitz was fully aware of Kelly and related research and wrote favorably about it.”
“Capital accumulation is a multiplicative process, which means that understanding geometric averages, risk management, and portfolio construction are all essential for compounding wealth.“
Nothing new here, at least to the readers of this blog. Michael summarises it so elegantly <3
“That life outcomes are non-ergodic also helps explain the value of buying insurance. A personal setback such as losing a home to a fire or a costly medical treatment can substantially damage an individual’s wealth and wealth trajectory. Insurance improves the time average growth rate for the insured because the reduction in wealth from paying premiums is more than offset by the prevention of financial disaster. Insurance is attractive from the insurer’s point of view because spreading risk among a population makes ensemble averages relevant.”
Cannot find a better ending than ergodicity 😉
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