Causal Insight into CAPM Class Models (Part I)

This is the first of a series of posts on the Capital Asset Pricing Model, or CAPM. It was originally intended as a single post, but grew lengthy and so I broke it into parts. The goal of this series of CAPM posts is to discuss CAPM in terms of systematic (paid) and unsystematic (unpaid) risks, present several ways of viewing the model, and to help interpret the meaning of CAPM from a causal modeling perspective. This final interpretation helps to understand not only CAPM, but alternate models of return that include a “market factor” such as the Arbitrage Pricing Theory (APT) and the Fama-French three factor variant.

One of the centerpieces of contemporary financial theory is CAPM, or Capital Asset Pricing Model. Although few people these days truly *believe* in CAPM hook, line, and sinker, it is still a cornerstone on which many other asset pricing models are built and compared. The mathematical formulation of CAPM is fairly simple, but the interpretation of CAPM and its implications for investment strategy are sometimes lost in the rush to apply CAPM to examples.

CAPM basically says that, under certain conditions, the “market portfolio,” consisting of a piece of every investible asset in the world (and in proportion to its contribution to all world assets), is the most efficient portfolio one can possibly invest in, because it is the only “fully diversified” portfolio. Any other portfolio takes on some degree of “idiosyncratic” or “non-systematic risk,” because either some assets are left out, or they are not held in proportion to the world market values. Since the non-systematic risks are supposedly not compensated by higher returns over time, any portfolio that deviates from a mirror image of the market will, in effect, have “watered down” performance because it contains exposure to extra bits risk that do not add anything to expected portfolio return. These portfolios are inefficient because portfolios based on the market proportions can give the same level of returns but without taking on these extra bits of uncompensated risk. One might think of this “market portfolio,” so to speak, as if it were a refined metal, after all the “non-systematic” bits of metalic ore (representing uncompensated risk) have been burned away and eliminated by sensible, diversified asset allocation.

What is “systematic” vs. “nonsystematic” risk? Quite simply, systematic risk is exposure to the variability in the total performance of all world assets (i.e. the world market, or system) over a specific time period. The system “factor” represents how much total world assets grew in any one period; systematic “risk” is a measure how much this factor tends to vary from period to period. Sometimes the world will grow rapidly, sometimes it will grow slowly, and sometimes world assets actually contract (such as during wars, depressions, or ecological devastation).

It is notoriously difficult to predict how much the world will grow in any short time frame, but one can note two things: 1) the rates of growth tend to vary within a roughly definable range over time; and 2) on average, the world tends to grow because of improved knowledge, technologies, productive processes, and a fuller understanding of what brings value to businesses and consumers. There is risk in the short term variability of world production, but over the long term, there is an investment benefit to being exposed to this risk. This is systematic risk: being exposed to the unknown variability of average world asset returns, and it earns a reward because overall productivity has tended to improve over time.

[Note that this is different from the standard description that risk has a premium because otherwise no one would take on any. Since we cannot truly foretell the future, I believe it is logically flawed to say that taking risk must return a premium simply because we expect it to and that we wouldn’t accept risk if we thought otherwise. There are plenty of people who accept uncompensated risks (think Casino gamblers); and placing a bet because you expect a return does not guarantee that you were right to expect a return in the first place. I think it is much more defensible to suggest that market risk brings a premium because, on average, the market is becoming more productive through the application of knowledge and technologies, and that people who do not expose themselves to this risk will not benefit directly from the profitability of these productive improvements, even if they might benefit indirectly in the form of consumer surpluses.]

Non-systematic risk is basically all risk other than returns correlated to this general world market factor. This includes the risk of specific accidents, news events that are highly localized or firm specific, a CEO being hit by a truck or divorce, positive or negative regulatory rulings on a product, etc.. Now it’s true that, technically, all of these things do filter back to the average world productivity, because if something firm-specific affects company that composes 0.1% of all world assets, then 0.1% of the world market factor will be adversely affected in the same way, but in practice, those contributions are so small with any but the very largest firms as to be negligible.

More importantly, since world return is the average productivity of all returns in the world, all these other idiosyncratic risks cancel out, by definition! That tiny tiny part that filters back to world returns goes into the world average, and everything else idiosyncratic averages out to zero. What this means in practice is that idiosyncratic risks are 1) inherently unpredictable, and 2) average out to zero, whereas systematic risks are A) inherently unpredictable, and B) average out (over time) to something positive. These are important distinctions, in both cases, one has exposure to unpredictable factors, but the reason systematic risk is good, is that on average you get something positive (a “risk premium”) out of it.

Idiosyncratic risk, on the other hand, is bad because, on average, you get nothing out of it. Worse still, variability without a sufficient average return will tend to erode a portfolio over time. An easy example of this is that a portfolio that rises 10%, then falls 10% doesn’t end up exactly where it started: it ends up with 99% of its original assets, 1% less than before. Over time, uncompensated risk will eat away a portfolio, which is why one tries to eliminate it as much as possible. In fact, the corrosive effect of this volatility does place a lower limit on what the market risk premium should be, since returns below this amount will tend to eliminate the incentive to invest.

In the next post, I will go over the CAPM equation and discuss how it fits into a more causally oriented view of asset returns.