People talk about stocks a lot. Individual equities, the market as a whole, etc. But there’s wide disagreement on exactly what we mean. This is not an accident. If we all agreed on the fundamentals, there would be less to talk about: one of the persistent aberrations academics struggle to explain is why, exactly, people trade so much.

This question is a challenge both for believers in efficient markets and for skeptics: if markets are efficient, trading introduces a cost, but switching from one stock to another doesn’t produce any real advantage. It just costs you commissions and taxes.

If the market is inefficient, frequent trading either implies that a) inefficiencies are tiny, such that someone who bought a stock at $10 and sold at $10.10 got what they expected, or b) inefficiencies are huge but variable, such that you bought at $10 with a $12 price target, and when the stock hit $10.10 you updated your model and lowered your price target to $8.

But it’s possible that one reason most models predict lower trading volume is that they imply that every investor uses the same model. A diversity of models gives diverse motivations: a gambler sells to a market-maker who sells to a passive asset allocator who sells to a cap-structure arbitrageur who sells to a value investor. More models means more uncorrelated assessments of the asset’s value, which makes it more and more likely that the price target of a buyer will exceed the price target of an owner, which is the necessary precondition for them to do business together.

To different people, a stock is…

… A Trading Sardine

Old joke, from the classic Margin of Safety:

There is an old story about the market craze in sardine trading when the sardines disappeared from their traditional waters in Monterey, California. The commodity traders bid them up and the price of a can of sardines soared. One day a buyer decided to treat himself to an expensive meal and actually opened a can and started eating. He immediately became ill and told the seller the sardines were no good. The seller said, “You don’t understand. These are not eating sardines, they are trading sardines.”

A trading sardine is an asset whose price is a number you can bet on. To a cynic, that’s all a financial asset is: it’s worth what you can buy it or sell it for. If you think of a stock as a trading sardine, the entire game is to figure out what other traders are thinking, and out-think them. When they care about fundamentals, you try to figure out the fundamentals. When they’re just slaves to hype, you buy, and you don’t sell until you see the stock on the cover of The Economist.

This is an enticing view because it’s internally consistent, and because it’s flattering; if you’re the only person who understands the nature of the game, you’re the smart money by definition. But it’s limiting. Anyone can come up with a mental model of the world in which everything they don’t understand is irrational, but that’s a model that has equivalent explanatory power regardless of how much of the real world you can explain.

At best, the sardine trader is a liquidity-providing gambler. At worst, if enough traders are sardine traders, the market explodes into a nonlinear Keynesian Beauty Contest, where everyone models everyone else as a slightly dumber version of themselves.

… Wholesale Merchandise

An equally nihilistic, but more socially-useful version of sardine trading is the idea that a stock is just merchandise that can be moved from one owner to another at a small, predictable profit. Market-makers implicitly think of stocks this way. Like sardine traders, they believe a stock is worth what a buyer pays or what a seller accepts, but they intend to fit their trading into the gap between those numbers.

To the wholesale merchant, stock picking is really counterparty-picking: they want to take the other side of uninformative trades. The two kinds of information that matter here are:

1. Smart orders
2. More orders

A smart order is a trade from someone who has credible information that an asset is mispriced. You don’t want to trade with that person. But to a market-maker, that’s only a theoretical risk. If market-makers held stocks for weeks or months, they’d worry that they were buying from smart sellers and selling to smart buyers. But on the sub-second scale, that doesn’t matter.

However, being frequently in the possession of good trading ideas correlates with being in the possession of lots of assets under management, which leads to the second problem: on a short time-scale, the directional move of an asset is a coin-toss. If a market-maker buys at $10.00, they have good odds of selling at $10.01. But if the person who sells at $10.00 is happy to sell again at $9.99, and $9.98, and so on, all the way down, the market-maker gets an increasingly large position in a stock that someone has high conviction is a loser.

This is bad for business, to put it mildly.

From the wholesale-merchandise perspective, the game is to avoid being run over like this. There are some simple tricks, like quoting a wider spread if positions keep moving against you, or getting preferential access to order flow from small investors (for more on this business, and why it’s not as scary as it sounds, definitely read Patrick McKenzie’s breakdown of the discount brokerage business.) This leads to an arms race, in which informed traders carefully minimize the market impact of their trades.

(I haven’t heard of anyone using the RobinHood API to execute large trades for institutions, but it’s only a matter of time.)

The Wholesale Merchandise approach is basically nihilistic because it’s directly working against one of the social purposes of markets, which is to pay people to create informative asset prices. On the other hand, a) it makes markets a more efficient vehicle for savings, and b) the market-makers don’t dodge every bullet.

… An Asset Earning RFR + Risk Premium * Beta + Risk Factors + Random Error

This is the capital asset pricing model view. You can run a series of linear regressions that decompose a given stock’s performance into a) the risk-free rate, b) the risks that stock’s owners are paid to take, and c) random noise. In the simplest model, you just compare performance to volatility: higher-volatility stocks should “pay” holders higher returns. If you want to get more clever, you add other factors, like the size of the company, and how statistically cheap it is.

But why stop there? Stocks are affected by all kinds of variables! Some companies sell oil, which has a market price and a liquid futures market, so you could throw in oil as a factor. Other companies consume oil. Some companies are theoretically short oil (because they consume it) but effectively long oil (because they hedge their exposure and their competitors don’t, so the market price of what they’re selling is set by oil even though their cost structure isn’t).

This reaches its apotheosis in the “alpha assembly-line” approach, which works like this:

1. Make a list of every factor that impacts lots of stocks: interest rates, exchange rates, commodity prices, investors’ preference for risk.
2. Hire the world’s leading experts in predicting each of those variables.
3. To control your company-specific risk, hire analysts to track every single company, measure its fundamental sensitivity to these variables, and also perform old-fashioned fundamental analysis on its business.

This model works extremely well; you don’t have an edge on every factor every month, but over time those experts come to smarter-than-average conclusions, and by modeling with more variables than your competitors, you can better measure your risk and thus lever up. One downside is the usual Black Swan risk: if your signals all tell you tech is doing well, and then an asteroid annihilates San Francisco, you’re going to have to adjust your portfolio.

This model leads to a weird Marxist alienation from labor. If every decision is filtered through ten layers — asset class, size, value factors, momentum, rates, oil sensitivity, company-specific factors — then everyone involved in a given trade had only incremental impact. That’s fine for quants, who are used to a paradigm where they the signals but not the companies. But it’s alien to stock pickers, who are sometimes surprised to find that, after all the factors are accounted for, their long idea turns out to be a short.

You can model your decisions as: I did research, and made a trade. You can even model them as: I did research, and submitted my results to a committee. But it’s hard to get in the mindset of: I did research, and it was an input into a regression that, for obvious competitive reasons, can never be disclosed to me.

In addition to providing a good architecture for maximum theoretical efficiency in asset management, the CAPM view is mostly helpful as a tool for dismissing people who smugly point to their personal portfolio’s outperformance compared to famous hedge funds. It is entirely possible to outperform by dint of better stock picking, but the top 1% of RobinHood users will outperform the top 1% of hedge funds in any given year mostly by taking absolutely bonkers risks.

(The polite dismissal is “Yeah, it’s great that individual investors can get an edge against the pros since they’re not subject to the same institutional constraints. The mean dismissal is “If you’re so smart, why are they so rich?”)[1]

Large funds market risk-adjusted returns to risk-sensitive investors, so to a stock picker who mostly believes in CAPM, the goal is diversify up to the point where the marginal risk reduction from more ideas is smaller than the marginal return loss from worse ideas.

… A Call Option on Cash Flow Struck at the Value of the Firm’s Net Debt

This is another theoretical model, from the opposite direction. Instead of asking what a stock appears to be when we observe the price, it asks: what does a stock seem to be when we observe the underlying inputs into that price?

In the 1930s, an academic named John Burr Williams decided to ask what a stock is really worth. It was a good time to wonder that. Either stocks had been much too expensive in 1929 or they were much too cheap a few years later. What Burr concluded was that the value of a stock, or of any stream of cash flows, is the sum of the present values of all futures cash flows, discounted back to the present.

This is a very elegant theory. If you buy a stock, you’re committing money upfront for money in the future in order to get some expected return, and the DCF model just asks what amount of money at what expected return would justify a certain price.

A further refinement on this takes advantage of work in the 1970s on how to value an option.

Think of a deeply-indebted company, whose debts exceed the value of its assets. The stock isn’t worth much, but it isn’t worthless, because if the company’s situation improves it might be able to pay down debt, whereas the lowest it can go is zero. Under this framework, the optimal capital structure is the one that produces the most option value. (I wrote much more about this here.)

This approach is surprisingly powerful, because many changes at a company can be modeled in option terms. When the company enters a new country, makes an expensive hire, launches a new product, or unionizes, this affects both the level of future cash flows and their expected variance.

This is also a convenient model because it lets you compare a given stock to any other financial asset: private companies, real estate, bonds, cash — they all produce streams of cash flows, and the DCF approach makes them all commensurable.

On the other hand, anyone who has spent enough time with DCF models to make a mistake in one knows how crazy sensitive they are to assumptions. If you really want to hit a certain price target, but the earnings growth doesn’t justify it, you can tweak your discount rate until you get the preferred outcome.

DCF models are sometimes less about coming up with a bold new valuation, and more about coming up with an explicit set of assumptions that justify the current valuation. If you need heroic growth assumptions to achieve a reasonable discount rate, or an arbitrarily low discount rate on sensible growth assumptions to justify the current price, then maybe it’s not very cheap.

Yet another way to use a discounted cash flow analysis is to give yourself more situational awareness: once you know what growth rate a company has to hit to justify the current price, every quarterly report gives you more information on whether or not that’s achievable.

… A Share of a Business

The traditional value approach is to deemphasize price and theory, and emphasize the fact that a shareholder is, in effect, a partner in a business. Yes, you’r’e buying a stream of cash flows; yes, the price bounces up and down; and, sure, those bounces correlate with measurable quantities. But that’s all a distraction. A stock is a piece of a business.

This is easy to forget, because publicly-traded companies are amenable to so many sophisticated analyses. You could become part-owner of a local restaurant, but you couldn’t day-trade your restaurant on your phone when you’re bored, or see if your restaurant partnership’s value was more sensitive to changes in the price calamari or red wine. Those quantities exist in some Platonic sense, but they’re not accessible without lots of liquidity.

The share-of-a-business framework is popular among people who either have access to permanent capital or are feeling the ill effects of using impermanent capital. You wouldn’t sell out of your restaurant partnership because the hardware store down the street went up for sale, so why dump a given stock just because the broader market is down?

Of course, that highlights the limitation of this model: on an infinite timeframe, it’s right — over the next twenty years, the performance of a given stock is a function of the quality of the business and the trustworthiness of management. But if shareholders are not using their own money, and they’re being judged on a shorter timeframe, gaps between the share-of-a-business value of a company and other valuation metrics can persist.

But, unlike some other valuation metrics, they can’t quite be quantified. How do you measure how trustworthy management is? What do you plug into your model to represent the fact that this CEO is a humble manager, not a maniacal empire-builder who will waste earnings on overpriced acquisitions? Those aren’t impossible questions to answer, they’re just not questions you can win an argument about.

The share-of-a-business model accepts some things that matter, but can’t be truly measured. When “things that matter” are important, this is good; when “things that can be measured” are the judgment criterion, it’s a distraction.

Which Model Matters When?

Of all of these models, the sardine-trading and DCF models are the two that are the most intellectually pure. They’re both deductive; they ask about what we know for sure (the market price, the fact that financial assets generate future cash flows), rather than inductive (determined by making atheoretical observations about history, and then biasing a portfolio away from any situation that requires theory). Interestingly, they both apply during extremes, but opposite extremes. If you’re a forced buyer or seller, you are by definition a sardine-trader. You may have some idea of what a stock is worth, but if you get a margin call, what it’s worth is what you can sell it for. At the other extreme, if the stock market shut down for ten years, the only tool you could use to decide what your assets was worth would be a discounted cash flow analysis, probably leaning a lot on the share-of-a-business framework for modeling and choosing a discount rate.

At any given time, these models are all being used by different investors, often by the same investor in different contexts.

For example, one conception of active investors is that they’re bulk market-makers who use fundamental analysis to control risk. When a valuation-insensitive trader makes a big trade, the traditional market-makers get out of the way — a succession of ticks in the same direction tells the market-maker there’s someone more opinionated than them on the other side of the trade, so they back away. But the active investors step in, because they know that the valuation gap compensates them for the short-term risk of being run over. They’re sort of catchers in the rye for the rest of the market.

The model you use depends on your skills and your constraints. On the skills side, you should model a stock as whatever it is that you’re best at modeling. In the aggregate, all opinions sum to average, and it’s hard for skills to translate across investing styles. The usual ideal is mediocrity in all approaches and excellence in one. You need to rise to the level of mediocrity to have enough situational awareness not to get run over. And then you go all-in on whatever approach best suits your strengths.

All of these models tell you something, but none of them tell you everything. You can’t treat any one of them as a single source of truth, but ignoring them is perilous, too. At different times, different views become more or less fashionable and more or less necessary; sometimes one version of reality wildly disagrees with another. And that’s what makes a market.