Michael Mauboussin

Mauboussin: Frequency vs. Magnitude


Our last article on the uncontrollable nature of luck was just downright depressing. To lift spirits & morale, this article showcases more comforting content on factors that are within an investor’s control. The following excerpts are extracted from a piece by Michael Mauboussin written in 2002 titled The Babe Ruth Effect - Frequency versus Magnitude. Expected Return, Sizing

Quoting Buffett from the 1989 Berkshire Hathaway Annual Meeting: “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.”

“…coming up with likely outcomes and appropriate probabilities is not an easy task…the discipline of the process compels an investor to think through how various changes in expectations for value triggers—sales, costs, and investments—affect shareholder value, as well as the likelihood of various outcomes.”

“Building a portfolio that can deliver superior performance requires that you evaluate each investment using expected value analysis. What is striking is that the leading thinkers across varied fields—including horse betting, casino gambling, and investing—all emphasize the same point.”

“…a lesson inherent in any probabilistic exercise: the frequency of correctness does not matter; it is the magnitude of correctness that matters.

“Constantly thinking in expected value terms requires discipline and is somewhat unnatural. But the leading thinkers and practitioners from somewhat varied fields have converged on the same formula: focus not on the frequency of correctness, but on the magnitude of correctness.”

Bill Lipschutz, a currency trader featured in Jack Schwager’s book New Market Wizards advised readers that, “You have to figure out how to make money being right only 20 to 30 percent of the time.” 

Strange as this advice may seem, it is congruent with Mauboussin’s words above that “the frequency of correctness does not matter; it is the magnitude of correctness that matters.” Depending on how you translate expected return estimations into portfolio sizing decisions, it is possible to make $ profits by being “right” less than 50% of the time (by upsizing your winners), just as it is possible to lose $ capital by being “right” more than 50% of the time (by upsizing your losers).

Psychology, Expected Return, Sizing

“The reason that the lesson about expected value is universal is that all probabilistic exercises have similar features. Internalizing this lesson, on the other hand, is difficult because it runs against human nature in a very fundamental way.”

“…economic behaviors that are inconsistent with rational decision-making… people exhibit significant aversion to losses when making choices between risky outcomes, no matter how small the stakes…a loss has about two and a half times the impact of a gain of the same size. In other words, people feel a lot worse about losses of a given size than they feel good about a gain of a similar magnitude.”

“This behavioral fact means that people are a lot happier when they are right frequently. What’s interesting is that being right frequently is not necessarily consistent with an investment portfolio that outperforms its benchmark…The percentage of stocks that go up in a portfolio does not determine its performance, it is the dollar change in the portfolio. A few stocks going up or down dramatically will often have a much greater impact on portfolio performance than the batting average.”

“…we are risk adverse and avoid losses compounds the challenge for stock investors, because we shun situations where the probability of upside may be low but the expected value is attractive.”

Selectivity, When To Buy, Patience

“In the casino, you must bet every time to play. Ideally, you can bet a small amount when the odds are poor and a large sum when the odds are favorable, but you must ante to play the game. In investing, on the other hand, you need not participate when you perceive the expected value as unattractive, and you can bet aggressively when a situation appears attractive (within the constraints of an investment policy, naturally). In this way, investing is much more favorable than other games of probability.”

“Players of probabilistic games must examine lots of situations, because the “market” price is usually pretty accurate. Investors, too, must evaluate lots of situations and gather lots of information. For example, the very successful president and CEO of Geico’s capital operations, Lou Simpson, tries to read 5-8 hours a day, and trades very infrequently.”

In a June 2013 speech, Michael Price shared with an audience his approach to portfolio construction and sizing. His portfolio consists of as many as 30-70 positions (his latest 13F shows 89 positions).  Price then compares and contrasts across positions, giving him a more refined palette to discern the wheat from the chaff, and eventually sizes up the ones in which he has greater conviction. 

When To Sell, Psychology, Expected Return

“Investors must constantly look past frequencies and consider expected value. As it turns out, this is how the best performers think in all probabilistic fields. Yet in many ways it is unnatural: investors want their stocks to go up, not down. Indeed, the main practical result of prospect theory is that investors tend to sell their winners too early (satisfying the desire to be right) and hold their losers too long (in the hope that they don’t have to take a loss).

More Than You Know: Chapter 1


Below are numerous psychological gems extracted from Chapter 1 of More Than You Know by Michael Mauboussin. Also be sure to check out his thoughts on Process Over Outcome. Psychology, Sizing

“The behavioral issue of overconfidence comes into play here. Research suggests that people are too confident in their own abilities and predictions. As a result, they tend to project outcome ranges that are too narrow. Numerous crash-and-burn hedge fund stories boil down to committing too much capital to an investment that the manager overconfidently assessed. When allocating capital, portfolio managers need to consider that unexpected events do occur.”

“…we often believe more information provides a clearer picture of the future and improves our decision making. But in reality, additional information often only confuses the decision-making process. Researchers illustrated this point with a study of horse-race handicappers. They first asked the handicappers to make race predictions with five pieces of information. The researchers then asked the handicappers to make the same predictions with ten, twenty, and forty pieces of information for each horse in the race…even though the handicappers gained little accuracy by using the additional information, their confidence in their predictive ability rose with the supplementary data.”

Too much incremental information can lead to a false sense of comfort, overconfidence bias, and too narrow outcome ranges.

Given our psychological propensity for overconfidence and too narrow outcome predictions, does this mean portfolio sizing decisions should be based not only on what we know, but also on what we don’t know? As if investing wasn’t hard enough already…

Psychology, Expected Return

“Probabilities alone are insufficient when payoffs are skewed…another concept from behavioral finance: loss aversion. For good evolutionary reasons, humans are averse to loss when they make choices between risky outcomes. More specifically, a loss has about two and a half times the impact of a gain of the same size. So we like to be right and hence often seek high-probability events. A focus on probability is sound when outcomes are symmetrical, but completely inappropriate when payoffs are skewed…So some high-probability propositions are unattractive, and some low-probability propositions are very attractive on an expected-value basis.”

Certainty and being “right,” does not always equate to profits. Paraphrasing the great Stan Druckenmiller, being right or wrong doesn’t matter, it’s how much you make when you’re right and how much you lose when you’re wrong that ultimately matters in investing.

Team Management, Psychology

“…the way decisions are evaluated affects the way decisions are made.”

“One of my former students, a very successful hedge fund manager, called to tell me that he is abolishing the use of target prices in his firm for two reasons. First, he wants all of the analysts to express their opinions in expected value terms, an exercise that compels discussion about payoffs and probabilities. Entertaining various outcomes also mitigates the risk of excessive focus on a particular scenario -- a behavioral pitfall called “anchoring.”

Second, expected-value thinking provides the analysts with psychological cover when they are wrong. Say you’re an analyst who recommends purchase of a stock with a target price above today’s price. You’re likely to succumb to the confirmation trap, where you will seek confirming evidence and dismiss or discount disconfirming evidence.

If, in contrast, your recommendation is based on an expected-value analysis, it will include a downside scenario with an associated probability. You will go into the investment knowing that the outcome will be unfavorable some percentage of the time. This prior acknowledgement, if shared by the organization, allows analysts to be wrong periodically without the stigma of failure.”


“The only certainty is that there is no certainty. This principle is especially true for the investment industry, which deals largely with uncertainty…With both uncertainty and risk, outcomes are unknown. But with uncertainty, the underlying distribution of outcomes is undefined, while with risk we know what that distribution looks like. Corporate undulation is uncertain; roulette is risky…"

How interesting, some people associated risk with uncertainty, but Mauboussin highlights an interesting nuance between the two.



Mauboussin on Position Sizing


Below are excerpts from an article written by Michael Mauboussin in 2006 on the importance of position sizing (Size Matters). For fans of the Kelly formula, this is a must-read. Mauboussin highlights a few very important flaws of the Kelly formula when applied to our imperfect, non-normally distributed world of investing. Sizing, Diversification

“To suppose that safety-first consists in having a small gamble in a large number of different [companies] where I have no information to reach a good judgment, as compared with a substantial stake in a company where one’s information is adequate, strikes me as a travesty of investment policy. -- John Maynard Keynes, Letter to F.C. Scott, February 6, 1942”

“As an investor, maximizing wealth over time requires you to do two things: find situations where you have an analytical edge; and allocate the appropriate amount of capital when you do have an edge. While Wall Street dedicates a substantial percentage of time and effort trying to gain an edge, very few portfolio managers understand how to size their positions to maximize long-term wealth.”

“Position size is extremely important in determining equity portfolio returns. Two portfolio managers with the same list and number of stocks can generate meaningfully different results based on how they allocate the capital among the stocks. Great investors don’t stop with finding attractive investment opportunities; they know how to take maximum advantage of the opportunities. As Charlie Munger says, good investing combines patience and aggressive opportunism.”

This is consistent with my belief that investors can differentiate himself/herself from the pack by going beyond security selection, and applying superior portfolio management tactics.

Sizing, Expected Return, Fat Tails, Compounding, Correlation

“We can express the Kelly formula a number of ways. We’ll follow Poundstone’s exposition: Edge / Odds = F

Here, edge is the expected value of the financial proposition, odds reflect the market’s expectation for how much you win if you win, and F represents the percentage of your bankroll you should bet. Note that in an efficient market, there is no edge because the odds accurately represent the probabilities of success. Hence, bets based on the market’s information have zero expected value (this before the costs associated with betting) and an F of zero…if there is a probability of loss, even with a positive expected value economic proposition, betting too much reduces your expected wealth.”

"Though basic, this illustration draws out two crucial points for investors of all stripes: • An intelligent investor needs an edge (a view different than that of the market); and • An investor needs to properly allocate capital to maximize value when an investment idea does appear."

“In the stock market an investor faces many more outcomes than a gambler in a casino…Know the distribution. Long-term stock market investing differs from casino games, or even trading, because outcomes vary much more than a simple model suggests. Any practical money management system faces the challenge of correcting for more complicated real-world distributions. Substantial empirical evidence shows that stock price changes do not fall along a normal distribution. Actual distributions contain many more small change observations and many more large moves than the simple distribution predicts. These tails play a meaningful role in shaping total returns for assets, and can be a cause of substantial financial pain for investors who do not anticipate them.”

“…the central message for investors is that standard mean/variance analysis does not deal with the compounding of investments. If you seek to compound your wealth, then maximizing geometric returns should be front and center in your thinking…For a geometric mean maximization system to work, an investor has to participate in the markets over the long term. In addition, the portfolio manager must be able to systematically identify investment edges—points of view different than that of the market and with higher expected returns. Finally, since by definition not all market participants can have an edge, not all investors can use a Kelly system. In fact, most financial economists believe markets to be efficient. For them, a discussion of optimal betting strategy is moot because no one can systematically gain edges.”

Notice in order for the Kelly Formula to work effectively, the devil (as usual) lies in the details. Get the odds wrong, or get the edge wrong, the sizing allocation will be wrong, which can reduce your expected wealth.

Another question that I’ve been pondered is how the Kelly formula/criterion accounts for correlation between bets. Unlike casino gambling, probability outcomes in investing are often not independent events.

Psychology, Volatility

“The higher the percentage of your bankroll you bet (f from the Kelly formula) the larger your drawdowns.

Another important lesson from prospect theory—and a departure from standard utility theory—is individuals are loss averse. Specifically, people regret losses roughly two to two and a half times more than similar-sized gains. Naturally, the longer the holding period in the stock market the higher the probability of a positive return because stocks, in aggregate, have a positive expected value. Loss aversion can lead investors to suboptimal decisions, including the well-documented disposition effect.

Investors checking their portfolios frequently, especially volatile portfolios, are likely to suffer from myopic loss aversion. The key point is that a Kelly system, which requires a long-term perspective to be effective, is inherently very difficult for investors to deal with psychologically.”

“Applying the Kelly Criterion is hard psychologically. Assuming you do have an investment edge and a long-term horizon, applying the Kelly system is still hard because of loss aversion. Most investors face institutional and psychological constraints in applying a Kelly-type system.”


Montier & Mauboussin: Process Over Outcome


James Montier’s Value Investing: Tools and Techniques for Intelligent Investment is a book I often recommend to others - Montier does a wonderful job of pulling together a range of topics related value investing. Below are excerpts from Chapter 16 titled “Process not Outcomes: Gambling, Sport and Investment.” Montier derived much of the content below (story & matrix) from Michael Mauboussin's book More Than You Know - Chapter 1. Process Over Outcome, Mistakes, Psychology, Luck

“We have no control over outcomes, but we can control the process. Of course, outcomes matter, but by focusing our attention on process we maximize our chances of good outcomes.”

“Psychologists have long documented a tendency known as outcome bias. That is the habit of judging a decision differently depending upon its outcome.”

“Paul DePodesta of the San Diego Padres and Moneyball fame relates the following story on playing blackjack:

'On one particular hand the player was dealt 17 with his first two cards. The dealer was set to deal the next set of cards and passed right over the player until he stopped her, saying: ‘Dealer, I want to hit!’ She paused, almost feeling sorry for him, and said, ‘Sir, are you sure?’ He said yes, and the dealer dealt the card. Sure enough, it was a four.

The place went crazy, high fives all around, everybody hootin’ and hollerin’, and you know what the dealer said? The dealer looked at the player, and with total sincerity, said: ‘Nice hit.’ I thought, ‘Nice hit? Maybe it was a nice hit for the casino, but it was a horrible hit for the player! The decision isn’t justified just because it worked…’

The fact of the matter is that all casino games have a winning process – the odds are stacked in the favour of the house. That doesn’t mean they win every single hand or every roll of the dice, but they do win more often than not. Don’t misunderstand me – the casino is absolutely concerned about outcomes. However, their approach to securing a good outcome is a laser like focus on process…

Here’s the rub: it’s incredibly difficult to look in the mirror after a victory, any victory, and admit that you were lucky. If you fail to make that admission, however, the bad process will continue and the good outcome that occurred once will elude you in the future. Quite frankly, this is one of the things that makes Billy Beane as good as he is. He’s quick to notice good luck embedded in a good outcome, and he refuses to pat himself on the back for it…'

To me the similarities with investment are blindingly obvious. We are an industry that is obsessed with outcomes over which we have no direct control. However, we can and do control the process by which we invest. This is what we should focus upon. The management of return is impossible, the management of risk is illusory, but process is the one thing that we can exert influence over.”

“Outcomes are highly unstable in our world because they involve an integral of time. Effectively, it is perfectly possible to be ‘right’ over a five-year view and ‘wrong’ on a six-month view, and vice versa...During periods of poor performance, the pressure always builds to change your process. However, a sound process can generate poor results, just as a bad process can generate good results.”

Mauboussin on Portfolio Management


Michael Mauboussin, author & former Chief Investment Strategist at Legg Mason, recently joined Consuelo Mack for an interview on WealthTrack (one of my favorite resources for interesting conversations with interesting people; the transcripts are economically priced at $4.99 per episode). Their conversation touched upon a number of relevant portfolio management topics. For those of you with more time, I highly recommend listening/watching/reading the episode in its entirety. Luck, Process Over Outcome, Portfolio Management, Psychology

“MAUBOUSSIN: …luck is very important, especially for short-term results...everyone’s gotten better, and as everyone’s gotten better, skills become more uniform. There’s less variance or difference between the best and the worst. So even if luck plays the same role, lesser variance in skill means batting averages come down…So I call it the paradox of skill, because it says more skill actually leads to more luck in results…

MACK: So what are the kind of skills that we look at that would differentiate an investor from the pack, from the rest of the Street?

MAUBOUSSIN: …when you get to worlds that are probabilistic like money management where what you do, you don’t really know what the outcome is going to be, then it becomes a process and, to me, successful investing has three components to the process. The first would be analytical, and analytical to me means finding stocks for less than what they’re worth, or in the jargon means getting an investment edge, and second and related to that is putting them into the portfolio at the proper weight. So it’s not just finding good investment ideas, but it’s how you build a portfolio with those investment ideas. And by the way, a lot of people in the financial community focus on buying attractive stocks, but the structure is actually really important as well…the portfolio positioning, I think there’s room for improvement there.”           

When dealing with probabilistic predictions, such as in investing, one must focus on process, not outcome. (For more on this, be sure to check out Howard Marks’ discussion on “many futures are possible, but only one future occurs.”)

As our Readers know, PMJar seeks to emphasize the importance of portfolio management within the investment process. We are glad to see validation of this view from a premier investor such as Michael Mauboussin – that successful investing requires “not just finding good investment ideas, but how you build a portfolio with those investment ideas.”

One other corollary from the quote above – investing is a zero sum game. In order to make profits, you need to be better than the “average” market participant. But over time, ripe investment profits have lured the brightest talent from all corners of world professions and consequently, the “average” intelligence of investors has increased. This means that the qualifications necessary to reach “average” status has inconveniently increased as well.

Here’s an exercise in self-awareness: where do you fit in – below, at, or above average – versus other fellow investors?

Luck, Process Over Outcome, Sizing, Psychology

“MAUBOUSSIN: This is such an interesting question, because if you look into the future and say to people, “Hey, future outcomes are a combination of skill and luck,” everybody gets that. Right? Everybody sort of understands that’s the case, but when looking at past results, we have a much more difficult time, and I think the answer to this comes from actually neuroscience. Brain scientists have determined that there’s part of your left hemisphere in your brain which they call the interpreter, and the interpreter’s job is when it sees an effect, it makes up a cause and, by the way, the interpreter doesn’t know about skill and luck, so if it sees an effect that’s good, let’s say good results, it says, “Hey, that must be because of skill,” and then your mind puts the whole issue to rest. It just sets it aside. So we have a natural sort of module in our brain that associates good results with skill. We know it’s not always the case for the future, but once it’s done, our minds want to think about it that way.

MACK: Therefore, do we repeat, when we’ve had a success that we attribute to our skill, do we constantly repeat those same moves in order to get the same result?

MAUBOUSSIN: I think it kind of gets to one of the biggest mistakes you see in the world of investing…this is a pattern we’ve seen not only with individuals but also institutions: buying what’s hot and inversely often getting rid of what’s cold, and that ultimately is very poor for investor results. It’s about a percentage point per year reduction in long-term results for individual investors because of this effect of buying high and selling low.

…one would be over confidence. We tend to be very over confident in our own capabilities. You can show this with simple little tests, and the way that tends to show up in investing is people, when they’re projecting out into the future, they’re much more confident about the range of outcomes, so they make a very narrow range of outcomes rather than a much broader range of outcomes. So there would be one example, over confidence, and its manifestation...

...try to weave into your process tools and techniques to manage and mitigate them. I don’t think you can ever fully eradicate them, but just be aware of them and learning about them. So for example, in the over confidence, you can start to use tools to better calibrate the future, for example, using past data or making sure you’re pushing out your ranges appropriately. So there are, in every case, some tools to help you manage that."

An interesting observation on our brain’s inability to distinguish between luck vs. skill in a historical context, which explains our natural tendency to chase performance return trends.

In addition to projecting a narrow range of outcomes, overconfidence is deadly in another way – overconfidence in sizing. For example, after hitting a couple winners (mostly due to luck), an investor says “Hey, I’m really good at this. I really should have made those previous investments bigger bets. Next time.” And so, the overconfident investor sizes up the next few investments. But luck fails to appear, and the damage hurts far more because these bets were sized greater.

But worry not, salvation does exist. If investors are able to identify and become aware of their behavioral biases, they can work to control and counter the associated negative effect.


CONSUELO MACK: What’s interesting is we’ve just come through a period where we’ve heard over and over again that macro matters...I’ve had a lot of value investors come on who have very good long-term track records, saying, ‘You know what? I didn’t used to pay attention to the macro. Now I really have to pay attention. It really matters.’

MICHAEL MAUBOUSSIN: The first thing I would say about this, is this is an area of prediction that’s been very well studied, and my favorite scientist on this is a psychologist named Phil Tetlock at University of Pennsylvania who did an exhaustive study of predictions in social, political, and economic outcomes, and what he found, I think, beyond a shadow of a doubt is that experts are very poor at predicting the future. So while I know people are worries about getting whipsawed by macro events, the evidence that anybody can anticipate exactly what’s going to happen next is very, very weak. So that’s the first thing, is just to be very reserved about your belief in your ability to anticipate what’s going to happen next…Obviously, you want to be mindful of macro. I don’t want to say you be dismissive of it. I would say macro aware, but in some ways macro agnostic.

Risk Free Rate, Equity Risk Premium

“The most interesting anomaly that I see continues to be what is high equity risk premium. So in plain words, you think of a risk-free rate of return. In the United States, a 10-year Treasury note is a good proxy for that…about a 1.8% yield. An equity risk premium is the return above and beyond that you would expect for taking on additional risk on equities. Now, over the long haul, that equity risk premium has been about three or four percent, something like that, and today, by most reckoning, it’s a lot closer to six percent. It’s very, very high.”

Historically (depending on time period examined), equity risk premium is normally 3-4%, versus ~6% today. But does this mean that today’s equity risk premium is abnormally high? Or was the historical equity risk premium just abnormally low?

What is the qualitative explanation behind the figure for the “normal” equity risk premium? Must it hold true into perpetuity?