Of course, we may have mitigated the risk of a remote, extreme loss that never happened. And yet, such a remote loss could happen suddenly at any time, and our risk mitigation could thus raise our CAGR (relative to our position had we not used that mitigation). This is the problem of induction, where the arrival of just one black swan falsifies any claim that all swans are white. But when I say that cost‐effective risk mitigation raises a portfolio's CAGR over time, this also means over a sufficiently broad range of observable outcomes, which largely resolves these epistemological problems. (We will address this with what is known as a bootstrap in later chapters.)
Amusingly, this principle that risk mitigation, done well, should raise our CAGR over time is actually quite controversial. In fact, most practitioners and academics would probably call it a crackpot idea. Lower risk comes at a cost, they believe, so risk mitigation is incompatible with higher returns.
To wit, one of the historic commodities trading houses had the German motto: “Besser gut schlafen, als gut essen.” (“It is better to sleep well than to eat well.”) And academics claim that lower returns actually accompany lower risk or volatility as a consequence, ipso facto. Their story goes, as you hedge and diversify away all of your correlated and uncorrelated risks, respectively, your returns will approach the lowly risk‐free rate. Or going the other way, the academics argue that in order to induce an investor to hold an asset that is relatively volatile, its price drops until its expected return becomes high enough to justify the additional risk. In their world, it sounds reasonable, and it's a comfortable story, asserted but not proved: You've got to take more risk to make higher returns; sleeping well comes at a cost. No guts, no glory.
To make matters worse, academics furthered this idea by positing that investing and risk mitigation are about lowering or calibrating a portfolio's volatility relative to its average return—the risk‐adjusted return or dreaded Sharpe ratio—unwittingly at the expense of the growth rate of wealth. They thus claim an intellectually dishonest victory based on their own theoretical scoreboard. It is a solution in search of a problem, and a bad idea. (It's even a big reason for our great dilemma.) I don't really believe that most investors even have this bad idea. Rather, to paraphrase Carl Jung, the idea has them.
We need to measure our success as investors by the practical scoreboard that counts, rather than the theoretical ones that don't. And there is just one scoreboard that counts, just one bullseye.
But we are often lured away from such practical objectives by gratuitous mathematical formulas. Modern quantitative finance suffers from a certain science or physics envy. After all, according to the American physicist Richard Feynman, “Physics is like sex: sure, it may give some practical results, but that's not why we do it.”
Well, practical results are precisely why we do what we do in investing and risk mitigation: to maximize the growth rate of wealth by lowering risk. And the best practices of the scientific method can actually help us with this.
MODUS TOLLENS
Aristotle is generally considered to be the earliest and foremost developer of the idea of deductive reasoning, or sullogismos. Deduction is “top‐down” logic, whereby general rules or premises are applied to particular cases or conclusions. This contrasts with induction, which is “bottom‐up” logic and goes in the opposite direction, whereby particular cases or premises are applied to reach a general rule or conclusion. Examining the geometry of a die to estimate the frequency that any side will come up over repeated rolls is deductive reasoning. Reasoning in the other direction, by repeatedly rolling a die and using those results to estimate the geometry of the die, is inductive reasoning. (We will be rolling the dice in both directions in this book.)
A syllogism applies deductive reasoning to draw a valid conclusion from assumed premises. One example is the syllogism called modus tollens or “denying the consequent.” It is the main logical method to avoid mistakes of reason in science—what Feynman has described as “what we do to keep from lying to ourselves.” It is an ideal BS filter (so don't be too surprised if you haven't encountered it in the context of investing).
A modus tollens takes the form of “If H, then O. Not O. Therefore, not H” (with H for hypothesis and O for observable). There are two premises—an explanatory hypothesis, made up of an antecedent and consequent, paired with an observable; brought together, they yield a conclusion, which follows logically from the premises. The logic goes, if a statement is true, then so is its contrapositive.
Think of this example of modus tollens involving my dog Nana:
If Nana is good at catching groundhogs, then I won't have a groundhog problem.
I have a groundhog problem.
Therefore, Nana isn't good at catching groundhogs.
We can see that a modus tollens serves the specific role of falsifying or eliminating a hypothesis. But neither it, nor anything else for that matter, can ever be used to verify a hypothesis as true. When we pair our proposed hypothesis with a minor premise that is an observable fact, we have a well‐constructed test of that hypothesis. Modus tollens, then, is the logical principle of the empirical sciences, and the scientific method itself; it allows us to clarify our ideas and move them away from mere metaphysics. Scientific rigor demands that we be able to pose, experimentally test, and ultimately falsify theories or conjectures in this way. When, like sleuths, we disqualify false theories whenever we can, then step by step we approach the truth. It's all very Sherlock Holmesian: “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”
Most significantly, the twentieth‐century Austrian philosopher of science Karl Popper constructed his whole falsification principle around it—as the fundamental demarcation between science and pseudoscience. “Universal statements are never derivable from singular statements, but can be contradicted by singular statements,” as Popper wrote in The Logic of Scientific Discovery. “Consequently, it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to universal statements.”
So far, we have been discussing cost‐effective risk mitigation as if it were something worthy of our attention—something that exists. Even uttering the phrase presupposes it. (And this is why no one ever really utters the phrase “cost‐effective” in the context of risk mitigation in investing. Have you noticed?) Taking such a conclusion for granted is begging the question.
It might even appear that we did this in our principle number three. However, the principle only claimed what risk mitigation should be, not necessarily what it always is. Cost‐effective risk mitigation could still be only theoretical, and not actually possible.
So, instead, we need to treat this principle as a conditional premise. It is an explanatory hypothesis, and this conveniently suggests our own modus tollens syllogism for safe havens, which we will be testing and investigating over and over:
If a strategy cost‐effectively mitigates a portfolio's risk, then adding that strategy raises the portfolio's CAGR over time.
Adding that strategy doesn't raise the portfolio's CAGR over time.
Therefore, it does not cost‐effectively mitigate the portfolio's risk.
What we have here is a natural, testable conjecture about safe haven investing.