Investing Is Not Gambling But It Sure Can Look Like It

I often meet people who conflate investing and gambling. Their confusion is understandable. There are many similarities between gambling and investing, but also important differences. As with most complex topics the devil is in the details.


How Investing And Gambling Are Similar

Both investing and gambling are exercises in decision-making under uncertainty. In both activities one places bets (takes positions) based on one’s appraisal of future expected value. Critically, both gambling and investing outcomes are subject to randomness. These are probabilistic activities. And therefore in both investing and gambling, it is difficult to disentangle luck and skill.

Professionals: let’s not kid ourselves. It is better to be lucky than skilled.

Another reason investing resembles gambling is that many people exhibit a preference for lottery ticket-like “investments.” Penny stocks and cryptocurrencies are excellent examples. People like to buy lottery tickets because the downside is small and well-defined, while the theoretical upside is very large. They say: “I’m just going to put $100 in BTC or this marijuana penny stock and maybe it goes up 100x.”

However, these individuals do not realize that many lottery ticket-like investments are, like lotteries themselves, negative expectation propositions. For example, some penny stocks and cryptocurrency ICOs are in fact fraud schemes with zero probability of success over the long run. Which brings us to…


How Investing And Gambling Are Different

Almost all casino games and lotteries are negative expectation games. That is, the odds are rigged against the players (in mathematical terms: the probability-weighted value of the payouts is less than zero). Were this not the case, neither lotteries nor casinos would last very long!

A casino underwrites risk in a similar way to an insurance company. Broadly speaking, the goal is to price risk in such a way that the insurance losses (gambler wins) will be more than offset by the insurance premium income (gambler losses) over long time periods.

In casino games, risk is priced such that if you play for an arbitrarily long period of time (let’s call it 1,000 years) you are all but certain to lose everything you bet. In other words, casino payouts are set so they do not adequately compensate gamblers for the riskiness of their bets. This is “the house edge.” In the United States, we actually use these negative expectation games as a regressive tax on the poor and uneducated, in order to fund certain social programs. You read a lot about social justice these days but one idea you don’t hear much is to outlaw lotteries!

Below is a table showing the house edge for various craps bets from the Wizard of Odds. As you can see, the best advice you can give to any craps player is to limit her bets to pass/don’t pass, taking the odds when the point is set (one of the best bets in the casino!), and maybe a place bet on the 6 or 8 to keep things interesting.

Source: Wizard of Odds; Second column is House Edge; Third column is standard deviation or “bankroll volatility”; Note that expected value and standard deviation (volatility) are also building blocks of Modern Portfolio Theory!

Investing, on the other hand, may or may not be a negative expectation game. Historical data leads us to believe investing is a positive expectation game (at least in the aggregate). If you have ever worked with a financial advisor, you have probably been told something to the effect that “in the long run the market always goes up” before being shown a chart like this one as “proof:”

Source: J.P. Morgan Asset Management

However, by naively extrapolating from historical data we are subject to the problem of induction. To make the issue more concrete, consider Nassim Taleb’s graph of a Thanksgiving turkey’s happiness:

Source: Attain Capital via ValueWalk

The turkey doesn’t realize it until it’s too late, but she is playing a negative expectation game. So are volatility shorts…

Source: Google

…and certain hedge fund managers…

Source: Wikipedia

Small wonder so many people believe investing, like gambling, is a negative expectation game. Indeed, it is entirely possible the long-run expected value of all our 401(k)s is $0.00. Try arguing to a Russian government bond holder circa 1917 that markets always go up over the long run!

So like the turkey, we will have to wait and see.

The Notion Of The US Total Market Portfolio Is Redundant And Really Kind Of Silly

Today I am going to channel my inner Cliff Asness and demonstrate why it is more or less irrelevant whether you own a Total US Market index fund or an S&P 500 index fund. Intuitively, the reason for this is straightforward:

Since a Total US Market index fund is market capitalization weighted, it is dominated by the largest companies. The largest US companies are all included in the S&P 500. Hence, S&P 500 stocks drive the overwhelming majority of the return of the total market portfolio.

If you trust me, you can stop reading here. If you would prefer to see some supporting data, read on. Fair warning: it gets wonkish rather quickly.

Statistical Evidence

I used Portfolio Visualizer to run regressions on two widely held index funds using the Fama-French Three Factor Model. The model fits the index funds extremely well as evidenced by the respective R^2 values of 99.7% and 99.99% (this means the model explains over 99% of the variation in returns over the time time period analyzed). One regression was for VTSMX and the other for VFIAX. Below is the output:

Source: Portfolio Visualizer
Source: Portfolio Visualizer

The key numbers are in the Loading column. Do a quick visual compare/contrast. See how they are almost identical? That is because at the end of the day, when you own the market portfolio, most of your money is invested in S&P 500 stocks (you can verify this using the actual portfolio holdings if you want).

This is further underscored by Portfolio Visualizer’s performance attribution analysis:

Source: Portfolio Visualizer

In the attribution table, SMB means “the return you got from investing in smaller companies” and HML means “the return you got from investing in “cheap” (value) stocks versus “expensive” (growth) stocks. The total market fund earned basically no return from exposure to small companies over this time period, while the value/growth stock exposures are so similar as to be irrelevant.


The market cap weighted total US market portfolio does not provide a meaningful exposure to small company stock returns (or a meaningful tilt to value or growth stocks–a non-issue for the purposes of this post).

Put another way, in statistical terms, the total US market index behaves nearly identically to an S&P 500 index fund.

For people who are knowingly overweight US large cap stocks in the form of the S&P 500, I’ve got nothing to argue with you over. This bet has worked out pretty well over the last couple of decades. Maybe it will keep working (there are a lot of great businesses in the S&P 500). Maybe it won’t keep working (a lot of those companies are richly valued). Anyone who claims he can handicap future market returns with any degree of accuracy is an idiot or a liar (possibly both).

For people who are naively overweight US large cap stocks in the form of the S&P 500, I have this to say: like it or not you have made a bet on a particular market segment. Admittedly, these are high quality companies and the underlying revenue sources are globally diversified. However, the valuation risk is not necessarily very well diversified. Something like 20% of the portfolio is invested in FANG stocks (that’s an off-the-cuff number).

My point here is not to say definitively that the S&P 500 is a bad place to be invested. No one knows what the next 30 years will look like.

Rather, I am making a philosophical point about asset allocation. Namely, when you “passively” allocate assets predominantly to a market cap weighted US total market portfolio, you have implicitly made an active decision to concentrate your risk exposure in US large cap stocks. Only about 50% of global equity market capitalization is located in the US. If you truly believed in the logic behind a capitalization weighted total market portfolio, you would obtain all your equity exposure via something like ACWI.

However, I have yet to meet anyone who does this. Or any financial advisor who recommends it.


(a good subject for another post)

“The Last, Best Order”

There is a neat post on Redfin’s blog. It is the CEO’s “IPO diary.” Read the whole thing for a fascinating look at the process from the inside. A couple of sections really resonated with me:

Masters of the Universe
In other ways too, the roadshow had the feel of a bygone era. For example, almost everyone on the buy-side we met that week was a man: in one group lunch, all 24 of the portfolio managers in attendance were male. We may have met more portfolio managers who were Israeli special forces veterans than women. I asked our bankers how long it would take the first one to kill me with his bare hands.

Almost all of them took notes on tablets. Some of them tried to look up as you spoke, but with their eyes focused on nothing except the numbers in their head. They weren’t just capturing the highlights of a meeting; it was a nearly verbatim transcription of what we’d said, so we could be held accountable for it later. Information in every form is the currency of Wall Street, and drops of it never seem to fall on the floor.

Chess with Bobby Fischer
Most of the fund managers were exotically, obviously smart. Except for one person who fell asleep in a meeting, none of the fund managers we met was anyone I’d want to be on the other side of a trade with, buying what he sold, or selling what he bought. This is what I realized I had been doing my whole life as an E-Trade stock-picker; it had been like challenging Bobby Fischer to a game of chess. I spent a long time that first week trying to judge whether it made sense to have so many brilliant people decide where our society allocates capital, as opposed to making cars or software or hospitals.

The Last Ideology-Free Realm
What impressed me most about these people was their willingness to change their minds. No one in our society seems to change her mind about Donald Trump or Hillary Clinton based on a new fact, but a fund manager on the wrong side of a bad trade has to change her mind in a moment or lose her job. This is why investing is the world’s last ideology-free realm. It would be easier to accept the premise that our society can’t agree on one version of the truth anymore, about whether temperatures are rising or the economy is growing, except that’s exactly what happens when every public company reports its earnings every quarter. You can believe what you want to believe, but not with a million dollars on the line.

And, perhaps most interesting to me:

The Last, Best Order
One of my favorite meetings was with a Scottish fund manager in San Francisco. His firm was known for buying only a few stocks, and holding each for as long as a decade. In a hotel meeting room with enough prospectuses, pitchbooks, cookies, fruit, cheeses, crackers and popcorn for 30 people, he came in alone. And rather than rattling through twenty or thirty questions about our metrics, he just asked me why I ran the company.

I found myself talking about my older brother, who had died just before I became Redfin’s CEO, and the feeling I had then that my life so far hadn’t made the world a much better place. He asked me about whether Redfin’s sense of mission would survive our public offering. He didn’t write much down. His order was one of the last, and the best, to come in.

My aspiration as an investor is to be that “last, best order.” There’s a reason I classified this post under Finance, Investing, Learning and Values. There is some real insight here.

Practicing Objectivity

They say there is nothing new under the sun and so when I started thinking more deeply about philosophy, The Meaning of Life, etc. a few years ago I should not have been surprised to find myself drawn to a philosophy developed over 2000 years ago!

I am of course talking about stoicism. I encourage everyone to at least read up on stoicism. The Daily Stoic is a good starting point. The site provides quite a bit of content that is useful for introspection or reflection.

Today I encountered this quote from the philosopher Epictetus:

Don’t let the force of an impression when it first hit you knock you off your feet; just say to it: hold on a moment; let me see who you are and what you represent. Let me put you to the test.

This is something to meditate on as an investor as well as an individual. As you go about your day, think of all the people and ideas you dismiss out of hand.

Are you dismissive about these people and ideas based on reasoned thinking? Or are you just making snap decisions for convenience?

How many people and ideas do you write off each day for no reason other than that they offend your preconceived notions of how the world works?

When you think about things this way, you will quickly discover surprisingly little of what you believe is reasoned from first principles. This isn’t something to be ashamed of! In fact it is intensely liberating. It means that life is not a test you pass or fail. Rather it is unknown territory for exploration. Life is an adventure, and you are the hero! What is more exciting than that?

A Comment on Cuba’s Biotech Sector

I was fascinated by this naked capitalism post on Cuba’s biotechnology sector:

This is not something we hear about in the US (you could probably write a whole book about that–may I suggest the title Ad Hominem: A Fallacy of Irrelevance?). I do not know very much about Cuba, and I know virtually nothing about the Cuban healthcare system. I do, however, have a close friend who has:

(1) worked as a practicing surgeon

(2) worked in healthcare policy here in the US

(3) visited Cuba and observed the Cuban healthcare system in action (though not the biotech sector)

I reached out to him for an opinion, and he replied with the following:

Cuba has an inexpensive system that delivers reasonably good outcomes. I thought the article was a little light on examples for exactly how the government’s control of pharmaceutical R&D delivers better outcomes. Costs are lower, in part, because they have a more favorable regulatory environment. They are also lower because the government probably maintains a single, narrow drug formulary for the entire country. With one formulary, they are able to regulate the number of drugs in each class. After all, do we really need 9 options for a medicine that gives old guys an erection? Less choice, but lower costs. You see examples of this here with Medicare Part D formularies preferred drugs.

The other question is whether they incentivize and reimburse drugs based on value. Many economists here have called for a more explicit determination of value when determining drug prices. Pharma companies can charge whatever they want for a medicine that may be no better or more effective than one that already exists, but may be within a lucrative class of medicines. Certain really important drug classes, like antibiotics, are underdeveloped in the U.S. because they are not likely to make much money, even during their exclusive patent rights period. If Cuba funded drug classes based on need and anticipated value, that would be quite smart. Some left-leaning folks have called for government to take this role here. Unclear how that would work in practice.

I am not trying to put a stake in the ground here. However, I was intrigued by both the original article and the comment and thought others might feel the same.

A Tangent

Just because some aspect(s) of the Cuban healthcare system may work well or promote decent outcomes does not imply:

  • Communism or socialism are superior economic systems to capitalist, market-based systems
  • The Cuban economy as a whole functions efficiently (or even “decently well”)
  • The economic deprivation and restricted personal freedoms of the Cuban system are acceptable tradeoffs for a healthcare system that produces some decent outcomes

(you get the idea)

A Mental Model For Politics

Politics is the process by which tribal groups negotiate the distribution of power and resources in a society. A tribal group may identify strongly with a particular philosophy. However, conflating politics with philosophy (“values”) is a muddy way of viewing the underlying drivers of political conflict. It took me a long time (about 15 years) to realize this.

I now realize there are two dimensions to tribal politics:

  • The competitive dimension (the political process itself). This is essentially a strategy game. Because it is a strategy game, effective political operatives (Lee Atwater) needn’t actually concern themselves with “correct” policy or philosophy. Their role is simply to “win”–that is, secure power and resources for the tribal group they serve.
  • The philosophical dimension (the inner lives of tribal group members). This is the process by which tribal group members construct their identities, bond with one another and develop a shared vision of how power and resources should be allocated across society. Tribal group members may or may not develop their identities through a rigorous process of reasoning from first principles. That depends largely on the mental complexity of each individual.

Thus, mental complexity is a key input to this model:

  • Socialized minds simply adopt an identity consistent with their surroundings.
  • Self-authoring minds go a step further and build their own identity.
  • Self-transforming minds go a step even further and work to develop a meta-understanding of tribal group dynamics, in order to integrate that into a more “complete” mental model of how the world works.

To make that more concrete:

  • The socialized mind says: “Everyone in my town and my workplace supports Political Party A. Political Party A is the place to be. I am A.”
  • The self-authoring mind says: “I identify with aspects of Political Party A, but also Political Party B. Furthermore, I believe in X, Y and Z based on my education, life experience and vision for what I want to achieve in life. I combine these inputs to formulate my own identity, views and goals. I am a C.”
  • The self-transforming mind says: “I am a C, but it is possible (in fact likely) that my views as a C are incomplete, inaccurate, or oversimplified. I must leave room to modify these views over time. Over the years I will likely transform from a C to a D, to an E, and so on as I constantly integrate new learnings into my mental model of the world.”

Morgan Housel provides a good example of how a self-transforming mind views tribal politics:

Everyone belongs to a tribe and underestimates how influential that tribe is on their thinking. There is little correlation between climate change denial and scientific literacy. But there is a strong correlation between climate change denial and political affiliation. That’s an extreme example, but everyone has views persuaded by identity over pure analysis. There’s four parts to this:

  • Tribes are everywhere: Countries, states, parties, companies, industries, departments, investment styles, economic philosophies, religions, families, schools, majors, credentials, Twitter communities.
  • People are drawn to tribes because there’s comfort in knowing others understand your background and goals.
  • Tribes reduce the ability to challenge ideas or diversify your views because no one wants to lose support of the tribe.
  • Tribes are as self-interested as people, encouraging ideas and narratives that promote their survival. But they’re exponentially more influential than any single person. So tribes are very effective at promoting views that aren’t analytical or rational, and people loyal to their tribes are very poor at realizing it.

Psychologist Geoffrey Cohen once showed Democratic voters supported Republican proposals when they were attributed to fellow Democrats more than they supported Democratic proposals attributed to Republicans (and the opposite for Republican voters). This kind of stuff happens everywhere, in every field, if you look for it.

It should be obvious by now why most political debates among individuals go nowhere:

  • Most individuals debating politics do not clearly distinguish between the strategy game dimension and the philosophical dimension. This is important. A genuine philosophical debate is a complex and mentally taxing endeavor requiring concentration and a high level of openness. The goal of a philosophical debate is to pursue Truth, not to “win.” What we call political “debate” is almost always strategy and tactics masquerading as philosophy.
  • Socialized minds are simply not capable of engaging in genuine philosophical debate. They do not possess the requisite level of mental complexity (though they certainly can develop it). You will never change a socialized mind with evidence and argument. You need look no further than the comments section of a website for evidence of this.
  • Self-authoring minds are more than capable of engaging in lively philosophical debate. However, they tend to grasp their mental models rather tightly (after all, these are intelligent, highly motivated individuals we are talking about). This can be perceived as either stubborn, obnoxious or even courageous, depending on the observer. As mentioned above, genuine philosophical debate is exhausting. Most people do not want to put the energy into engaging in genuine philosophical debate. Don’t waste your time trying to debate political philosophy with people who aren’t interested in working hard at the process!
  • From a distance, self-transforming minds can seem devoid of logical consistency. This is especially true from the perspective of a socialized mind, for which maintaining an identity consistent with the tribal group is of paramount importance. This is because self-transforming minds are explicitly aware not only of the need to develop mental models, but of the need to adjust them. This can make it difficult for them to relate to the more static worldviews of self-authoring and socialized minds (and vice versa). Others may view a self-transforming mind as an untrustworthy waffler.

To conclude, here is a little checklist for thinking about politics:

  • Be explicit about the dimension you are analyzing:
    • Strategic Dimension?
    • Philosophical Dimension?
  • When analyzing the strategic dimension, do not conflate “values” with strategy and tactics. This will allow you to reason more clearly.
  • If you are analyzing the philosophical dimension, account for mental complexity.
  • If you are involved in a political discussion, try to understand the level of mental complexity the other part(ies) are operating at. This will lead to richer, more fulfilling conversations. On the other end of the spectrum, it will clue you in on when it might make sense to simply disengage.
  • If you want to do deep, truthful, political analysis, you need to integrate both the strategic and philosophical dimensions.

First Principles

I have three great posts I would like to share. All deal with the subject of mental models and reasoning from first principles:

“Speculation In A Truth Chamber” (Philosophical Economics)

First, the idea behind the exercise is not for you to literally walk through it, in full detail, every time you are confronted with a question that you want to think more truthfully about. Rather, the idea is simply for you to use it to get a sense of what it feels like to be genuinely truthful about something, to genuinely try to describe something correctly, as it is, without pretenses or ulterior motivations. If you know what that state of mind feels like, if you are familiar with it, then you will be able to stop and return yourself to it as needed in your trading and investment deliberations and in your everyday life, without having to actually step through the details of the scenario.

Second, the exercise is intended to be used in situations where you actually want to get yourself to think more truthfully about a topic and where you would stand to actually benefit from doing so. Crucially, that situation does not describe all situations in life, or even most situations. There are many situations in life where extreme truthfulness can be counterproductive, creating unnecessary problems both for you and for others.

Third, all that the exercise can tell you is what you believe the most likely answer to a question is, along with your level of confidence in that belief. It cannot tell you whether you are actually correct in having that belief. You might believe that the answer to a question is X when it’s in fact Y; you might have a lot of confidence in your belief when you should only have a little. Your understanding of the subject matter could be mistaken. You could lack the needed familiarity or experience with it to have a reliable opinion. Your judgment could be distorted by cognitive biases. These are always possibilities, and the exercise cannot protect you from them. However, what it can do is make you more careful and humble as a thinker, more open to looking inward and assessing the strength and reliability of your evidence and your reasoning processes, more willing to update your priors in the face of new information–all of which will increase your odds of getting things right.

Thinking From First Principles” (Safal Niveshak)

Practicing first principles thinking is not as easy as explaining it. As Musk said, it’s mentally taxing. Thinking from first principles is devilishly hard to practice.

The first part, i.e., deconstruction, demands asking intelligent questions and having a deep understanding of the fundamental principles from various fields. And that’s why building a latticework of mental models is so important. These mental models are the fundamental principles, the big ideas, from different fields of human knowledge.

The best way to achieve wisdom, said Charlie Munger, “is to learn the big ideas that underlie reality.”

The second step is the recombination of the pieces which were identified in the first step. This is again a skill which can only be developed by deliberate practice. Any idea as an isolated piece of information doesn’t stay in the human brain for long. To be sticky, it needs to be connected with other ideas. A latticework is essentially a grid of ideas connected to each other. These connections are the glue which holds those ideas together.

If the new knowledge doesn’t find any connection or relevance to the old knowledge, it will soon be forgotten. New ideas can’t just be “stored” like files in a cabinet. They have to connect with what’s already there like pieces of a jigsaw puzzle. As you become better in finding connections between seemingly disconnected ideas, your recombination-muscle becomes stronger. Someone with a strong recombination-muscle will find it easy to practice the second step of first principles thinking.

“Playing Socratic Solitaire” (Fundoo Professor)

I am going to play a game based on ideas derived from Socrates and Charlie Munger. We will start with “Socratic Questioning” which is described as

disciplined questioning that can be used to pursue thought in many directions and for many purposes, including: to explore complex ideas, to get to the truth of things, to open up issues and problems, to uncover assumptions, to analyze concepts, to distinguish what we know from what we don’t know, to follow out logical implications of thought, or to control the discussion.

Socratic Questioning relates to “Socratic Method,” which is:

a form of inquiry and debate between individuals with opposing viewpoints based on asking and answering questions to stimulate critical thinking and to illuminate ideas.

Charlie Munger started using these two Socratic devices in a variation he called Socratic Solitaire, because, instead of a dialogue with someone else, his method involves solitary play.

Munger used to display Socratic Solitaire at shareholder meetings of Wesco Corporation. He would start by asking a series of questions. Then he would answer them himself. Back and forth. Question and Answer. He would do this for a while. And he would enthral the audience by displaying the breadth and the depth of his multidisciplinary mind.

I am going to play this game. Or at least, I am going to try. Watch me play.

If you are seriously interested in finance and investing, there is nothing more important to your development than accumulating a robust inventory of mental models. What mental models and reasoning from first principles allow you to do is see through to the true drivers of a situation, where it is often easy to get bogged down in unimportant details.

For example, if you are viewing a business through the lens of discounted cash flow valuation, here are the drivers of intrinsic value:

  • Operating margin
  • Asset turnover
  • Maintenance capex needs
  • Growth capex/reinvestment opportunities
  • Discount rate

Operating margin and asset turnover are quantitative measures reflecting the strength of your competitive advantage and, perhaps more importantly, the source of your competitive advantage.

Maintenance capex tells you how much cash the business needs to spend to keep running.

Growth capex/reinvestment opportunities give you an idea of growth potential over time.

When you combine operating margins and asset turnover (technically NOPAT x Sales/Invested Capital) you get a figure for return on capital. Return on capital is an excellent quantitative proxy for management’s skill allocating capital. Thus, it is also an excellent proxy for quality of management (though it is certainly not a be-all, end-all measure). When you combine return on capital with reinvestment opportunities you get an idea of what sustainable growth in operating income might look like.

There are lots of ways to handle the discount rate. Over time I have come to prefer an implied IRR method, where you simply “solve for” the discount rate that sets your cash flow model equal to the current stock price. You can then compare this to your hurdle rate for new investments.

DCF is one of the most important models in finance because it works with any investment that produces (or is expected to produce) cash flows in the future. At the end of the day, even an exercise as complicated as valuing a mortgage-backed security is just a variation on discounting cash flows.

All great mental models have two defining characteristics:

(1) They are robust. That is, they are applicable to a broad set of opportunities.

(2) They are parsimonious. That is, that is they demonstrate “economy of explanation.”

In my humble opinion, the most important mental models you need to understand in investing are:

  • Time Value of Money/Discounted Cash Flows
  • Capital Structure
  • Expected Value/Probabilistic Thinking
  • Optionality
  • Convexity/Linear Vs. Non-Linear Rates Of Change (e.g. compounding)
  • Investor Psychology

Conceptually that is really what it all boils down to (though the permutations are endless–for instance, a mortgage can be viewed as the combination of discounted cash flows and a call option). Now, you could of course write dozens of volumes on the nuances and applications of each of these models. That is part of what makes them robust. They are adaptable to an almost inconceivable range of circumstances.

This is something I don’t think most candidates in the CFA Program think about (they are too preoccupied with passing the exams!). The curriculum is designed to comprehensively introduce you to the most robust mental models in finance, and then to test your ability to apply those models to specific cases. Level I tests whether you understand the basic “tools” you have available to you; Level II tests more advanced uses of those tools (in exhausting detail, one might add); Level III tests your ability to apply all your tools to “real world” situations.

Maybe some day I will write up how I think about these super important mental models. In the meantime, enjoy the above linked posts!