When I was asked, “What do you believe, but know you can’t prove in investing?” the Donald Rumsfeld quote about knowns, known unknowns, and unknown unknowns came to mind. Where in that context do unprovable beliefs fit?

My first thought is that they’re known unknowns. If we have an unprovable belief, then we have a strong opinion that could be wrong, which would seem to place us squarely in the known unknowns.

Considering it further, though, I’ve come to the conclusion that unprovable beliefs actually fall more directly into the unknown unknowns category. After all, if we can’t prove something, the reason has to be either that we don’t understand the problem well enough, that we don’t have a sufficient data set, or perhaps that there are elements of the problem that are simply unknowable. Any unprovable belief has elements of all three.

Let’s look at the question of the equity risk premium. I think all of us believe that, over time, it has to be positive. I don’t want to get into the actual magnitude of it, as that’s a separate debate, but that it is positive over time seems to be simple common sense. How could any equity market thrive without a return over that of debt? Is this even an assumption? Surely it would be easy to prove?

Try it. Let’s start with history. Most arguments for the equity risk premium use U.S. data or data from other developed countries, covering several centuries at best. Many U.S. commentators use even smaller data sets; post-World War II U.S. data is common. Based on that limited data, it does appear that a positive equity risk premium exists.

I would argue, though, that this conclusion is dependent on the limited data set. Many out-of-sample examples would lead to different conclusions. Examining Tsarist Russia and Weimar Germany, among others, might result in the conclusion that the realized equity premium is zero. We can also find periods, including very recently in the United States, during which the actual achieved equity risk premium was negative. Finally, let’s look back to cultures with different value sets — Egypt with the pyramids, Native American cultures that used potlatch, Renaissance Italy and its massive cathedrals. Equity was actually considered most valuable when destroyed, in the case of potlatch, or devoted to noneconomic uses, in the case of the pyramids and cathedrals. The argument that now is different is meaningless. Now is simply now, no more relevant to history as a whole than any other period.

The reality is that we don’t really understand the problem. The interaction between social institutions, including political structures, resource availability, knowledge capital, and investor behavior, is not well understood at all. Anyone who doubts this has only to look at any number of financial crises and wars over the past centuries. The modern conceit that we are smarter than our ancestors, and understand things better, was most recently expressed in the Great Moderation, when we thought we had transcended the business cycle through prudent macroeconomic management. We were wrong.

You could argue that the reason we don’t understand the problem is that we don’t have a sufficient data set. That is certainly true—given the magnitude of the problem, a data set that would allow us to draw any conclusions would have to be immense. An example of the sort of data set that might allow real analysis is Reinhart and Rogoff’s “This Time Is Different.” As recent controversy over their conclusions has shown us, centuries of data spanning multiple countries and continents allows us to get a look at problem but perhaps not draw firm conclusions.

The final element — that some aspects of the problem are, in principle, unknowable — is undoubtedly part of the picture, but is also, by definition, unsolvable. This is something we simply have to live with.

Many of the assumptions we make are grounded in our experience, which we assume to be representative. I have two ways to illustrate this — one highbrow and the other less so. The highbrow one is to invoke the Copernican principle. Copernicus found that the Earth was not the center of the universe after all, and future discoveries revealed that the sun wasn’t either, nor the solar system, nor the Milky Way galaxy . . . up to the present time, when we find that everything we can see and perceive is actually only a very small part of everything there is.

The more down-to-earth example is the drunk looking under a streetlamp for his keys. When asked where he lost them, he points to a dark area down the street but explains he is looking under the streetlamp because the light is better there.

Judging future investment performance based on the past 50 years in the United States is assuming the Earth is the center of the universe. Analyzing market trends using U.S. data alone is looking under the streetlamp.

I do believe the equity risk premium is and has to be positive over time, at least in a capitalist system based on an economy of scarcity. I also believe that any analysis has to recognize this as an assumption, not a bedrock fact, which arises from human expectations as expressed in our current socioeconomic context. The Pharaohs and Medicis didn’t invest solely for results in this world, and the transformation of economic capital into social capital is arguably just another example of a premium. The problem is that our analyses are based on financial metrics.

So what to do? One approach is to simply expand the data sets used. Many great investors do exactly that. Jeremy Grantham and his team, for example, write regularly about the large data sets they use in their analyses. (The other extreme is Long-Term Capital Management, which reportedly used only a very short-term data set to develop its models.)

Another approach is to be very aware that current conditions can and will change. In Russia, for example, capital market investors have regularly been expropriated, including very recently. This happens in the United States as well, with GM bondholders being a recent example. As Mark Twain told us, “It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”

For our purposes today, it is appropriate to act as though the equity risk premium is, at least potentially, positive. We can’t prove it, though, and should be mindful that, as conditions and societal values change, the magnitude — and even the sign — of that premium may change as well.

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