There are lots of ways to invest. Holding cash, holding index funds, buying and turning around whole companies, and hedging stocks are all different ways to try to generate returns.

What do you have to believe about the world to invest in one versus the other?

I’ve been thinking about Judea Pearl’s Ladder of Causation, and what it can tell us about how different investment classes let investors buy into different abstractions of “cause and effect.” Pearl proposes three views of cause and effect: association, intervention, and counterfactuals. In this post, I speculate that this is a useful way to understand what investors have to believe about the world for their investment to make sense.

What does this mean? Here is Pearl’s Ladder:

The ladder exposes three levels of abstraction about cause and effect.

Association, or correlation, shows that two variables seem to move together. This abstraction might include, for instance, that rainbows are associated with rain. But correlations can be spurious, which is why everybody knows that “correlation isn’t causation.”

Intervention is “doing something” to measure or cause an effect. In drug trials, researchers will give a drug to one group of patients, and a placebo to another group of patients, to measure the effect that the drug caused.

Counterfactuals are understanding what would have happened if a cause was absent. For example, you can ask what would have happened to your headache if you hadn’t taken the aspirin. Based on lived experience and previous interventions of aspirin, you might conclude that your headache would have continued until it naturally subsided. But this depends on a model that you have about what effects aspirin causes with respect to headaches.

The higher you go on the ladder, the richer your model of the cause-and-effect has to be. Association requires that you observe and notice two or more things about the world, and that they may be connected. Intervention requires being able to create meaningful change in the environment and notice the impact. Counterfactual reasoning requires having a fully-fledged model of cause and effect, so you can imagine the world under different circumstances.

We can translate this framework to investing:

• Association investing: Investors invest based on their ability to notice associations in the market. They do not affect pricing or intervene in management decisions.
• Intervention investing: Investors invest based on their ability to affect price, management decisions, or events facing the market or firm. This can come through outright ownership. influence on management, or publicizing information as an activist investor.
• Counterfactual investing: These “alternative” asset classes involve writing contracts with contingent claims based on events, future prices, or by litigating. This includes insurance, options, and certain kinds of litigation.

Association: Passive and Active Investing

Passive investors are our first step onto the ladder. Buying an index fund requires no model of the world. Passive investors do not change their allocations based on anything besides the weighting of stocks in the market. They are completely indifferent to events, press releases, meteor strikes, or any other event besides a change of weighting in the stock market. They don’t intervene in anything, and since they are unable to use discretion to sell, the most the largest index funds can do is to try to improve governance.

As the base of the ladder, it is unsurprising that this is the performance benchmark other asset classes are judged against.

Retail active investors—ranging from stock pickers sitting at home to black-box quant funds—are the next step up. They have no practical ability or desire to affect management decisions or the price of the stock, so their entire source of profit is from associations that they don’t believe the market has noticed or priced into the stock.

Association investing is increasingly hard to be smart at. Quant funds that use sophisticated statistical techniques to mine these kinds of “unseen” associations are in secular decline as their job becomes harder and harder. Conventional wisdom also suggests that being persistently good at stock picking is very hard, if not indistinguishable from statistical noise.

Intervention: Activist Investors and Private Equity

With enough capital, some investors are able to affect the pricing of a stock or management decisions, and can actively intervene in the market to get a desired result.

Activist investors, like Bill Ackman’s Pershing Square Capital Management, are able to affect the stock price by owning a fraction of a company and demanding changes to management. With this intervention, activist investors are able to negotiate on some management decisions at the firm without (always) having to purchase a huge percentage.

LBO (leveraged buyout) firms, including private equity firms, raise debt to purchase firms outright, and then have full control over management and strategic decisions. While these firms can work to identify efficiencies and strategic opportunities, they are often subject to the winner’s curse: with no additional information, no synergies with other assets, and no other ability to cause market-moving events, the highest-bidding private equity firm is often the only firm optimistic enough to bid that much on that asset.

These firms also often charge large fees. One question is: can you automatically replicate private equity or hedge fund returns with an associative strategy, and not an interventionist strategy? Erik Stafford at Harvard Business School seems to think so, and articulated a scheme in which you could replicate private equity returns without needing to intervene in firms and pay these fees.

Counterfactuals: Derivatives, Insurance, and Lawsuits

Finally, we come to the top of the ladder: counterfactual investing. I see this as investing in contingent claims, or claims that only pay out when a specific event happens, or based on the price of assets at a specific time.

Options, futures, and other derivatives are our first counterfactual rung. An options writer has to price options using a model of the world like Black-Scholes, and understand their prospective risk based on the rest of their portfolio. Derivatives can be risky: the seller of a call option, for instance, can lose and unlimited amount of money. Unlike insurance, derivatives traders are only exposed to risk related to the pricing of the asset, not specific underlying events in the world that might change that price.

That makes options trading slightly different from insurance. Insurers get paid a fixed rate, and owe money if a specific event occurs in the future. These claims can be as small and frequent as broken bones, car accidents, or stolen property and as large as pandemic or terrorism insurance. In this instance, they know exactly what their counterfactual is: if the event hadn’t happened, they wouldn’t be subject to a payout, so insurers have to price the upfront stream of income based on the probability of an event happening, and the economic severity if it does happen.

Hedging and insurance strategies are products that can create value for buyers and sellers alike. I am better off for having health insurance, for instance, for reasons that are not purely financial, and a cattle trader may wish to hedge around their wealth being tied up in cattle. As a financial asset class, however, it is difficult for options traders to show that they are really doing something “smart” to deserve their exorbitant fees. Erik Stafford found that alternative investments, in aggregate, are often no better than a strategy of dumb put-writing, which suggests that this complex counterfactual reasoning is overpriced after fees.

Finally, we have certain kinds of lawsuits, especially those related to securities fraud. Matt Levine has a great description of these in his peerless financial newsletter, Money Stuff:

You know the basic idea. A company does something bad, or something bad happens to it. Its stock price goes down, because of the bad thing. Shareholders sue: Doing the bad thing and not immediately telling shareholders about it, the shareholders say, is securities fraud. Even if the company does immediately tell shareholders about the bad thing, which is not particularly common, the shareholders might sue, claiming that the company failed to disclose the conditions and vulnerabilities that allowed the bad thing to happen.

In this instance, shareholders don’t have a contingent claim against any specific event, but will claim that management has defrauded them when a “bad thing” happens. These lawsuits say that management “should have” acted differently, and if they had, things would be better. (Note that no sane attorney would quite craft it this way—they need to demonstrate acts of fraud, after all—but the point stands.) As described, this kind of litigation is counterfactual investing in its purest form.

The Investment Cause-and-Effect Test

Active investing is hard, and every non-passive investment product has an incentive to show that they are using some causal magic to create superior returns value.

To scrutinize this, a few questions to ask include:

• Is this investment capturing an association that isn’t accurately priced by the market?
• Is this investment causing an intervention that is going to create and capture value?
• Is this investment modeling the probability of contingent events in a way that isn’t captured by the market?
• Isn’t there a synthetic way to generate the same returns at this level of risk—for instance, via put-writing—without having to pay fees?

The answers to these questions is usually “no,” because again, active investing is hard. If it isn’t, however, it should say something interesting about what you have to believe about the world for a particular investment strategy to make sense.