Decoding the CAPM Mystery

If we want to develop a global standard for ensuring that shareholder funds anywhere in the world are deployed prudently, we cannot allow subjective interpretations of the cost of capital. If there is one market in any economy where public companies raise funds, then every company operating in that market must ensure that it understands what returns that market as a whole expects and, at a minimum, deliver those returns. Chasing extra returns over and above this minimum can only be permitted if it is commensurate with the associated extra risk. This responsibility squarely falls on the financial professional because the goal of financial management is to enhance shareholder wealth.

The Capital Asset Pricing Model (CAPM) has failed thousands of validation tests since its development in the 1960s. Based on extensive research by the 2013 Nobel Laureates Eugene Fama, Lars Peter Hansen, and Robert Shiller, the Nobel Economic Sciences Prize Committee confirmed that the CAPM does not work and “currently no widely accepted ‘consensus model’ exists” Although CAPM applies to all risk-prone financial assets in general, this article analyses the model from the perspective of equities. However, the analysis equally applies to any financial asset which produces uncertain returns.

CAPM: Is the base return and deviations in returns rightly stated?

According to Modern Portfolio Theory, on which the CAPM was built, a rational investor eliminates unsystematic risk by constructing an optimum portfolio. Does a “rational investor” stop at this and thereby avoid only unsystematic risk? We know that professional wealth managers worldwide should deter investors from pursuing short-term returns, and encourage long-term financial planning. Clearly, holding portfolios over longer periods helps reduce the risk inherent in the entire portfolio, which is nothing but systematic risk! Typically, the long term in financial planning spans periods of 20-25 years, which therefore should be the basis of the investment goal as an average long-term portfolio return. This target return essentially is greater than mere compensation for inflation, that is the interest. This is equivalent to what the CAPM defines as “Rm” in its equation Rs = Rf + beta (Rm - Rf). Beta for the portfolio is 1 in any case.

Rational investor and opportunity cost of equity

If a rational investor were to invest their equity capital, wouldn’t the above stated target return be the relevant opportunity cost? We know that “opportunity cost of equity” is the return that a rational investor sacrifices by not investing in a portfolio of equivalent risk in the capital market. We need to understand two concepts clearly. First, who is a rational investor? Second, what is the equivalent portfolio whose return they are sacrificing?

We have already discussed that a rational investor does both—constructing a portfolio as well as holding the portfolio for the long term. This answers the first question. To answer the second question, even if different types of investors holding portfolios of disparate risk-return profile constitute the market, a public company is responsible for satisfying the expectations of the market as a whole and not any subclass of investors. Therefore, for a company the only relevant investor is the market as a whole, and the only relevant investor portfolio is the market index. It follows that for deciding proper deployment of shareholder funds, the only relevant opportunity cost of equity funds is the long-term index returns.

Measuring deviations in returns or “risk”

Annual portfolio returns as well as average returns over, for example, 2-3 years could swing unpredictably with respect to the long-term return defined above. That’s true for any financial asset. Let us consider the following example.

Can we say that all the three portfolios above are equal in risk return characteristics because their mean and standard deviations are same? Even if the probabilities of future returns are the same as historical returns, the order in which they occur may not be same as the past. Therefore, the next period’s return always remains unpredictable. If the investment horizon is strictly the next ten years, short-term risk—regardless of its severity—becomes irrelevant.

Yet, if project durations are shorter, they are impacted by short-term risk. Exactly how do we measure short term risk? If the short term was one year, what is the probability of earning less than mean returns in that period? “Portfolio I” would stand out as most risky on this count because 9 out of 10 periods in the past delivered less than mean returns. We can say that “Portfolio I” has a 0.90 probability of 9% periodic return and a 0.10 probability of 19% return for any future period. 

Let’s extend this argument by presuming that each of the periods above represents a couple of years—for example, 3 years corresponding to a typical capital expenditure project. In this scenario, we must be interested in understanding how much risk our project is exposed to during its lifetime vis-à-vis the long term average return of 10%. How do we estimate that?

One of the biggest criticisms of Modern Portfolio Theory, on which the Capital Asset Pricing Model is based, is that returns in equity and in other financial markets are not normally distributed. Large swings (3 to 6 standard deviations from the mean) occur in the market far more frequently than the normal distribution assumption would predict (see The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin, and Reward). The pattern of annual returns of risk prone assets is typically described as a “random walk”. Given that annual returns over the entire 30 years (3x10) in the above example could vary unpredictably, what could be the expected 3-year average returns for any future 3-year period? This is a relevant question because, while rational investors wouldn’t look at annual volatility, they would certainly be worried about whether deviations in 3-year average returns vis-à-vis the 30 year average is within normal limits. If annual portfolio returns do not follow normal distribution, how do we determine this deviation? The central limit theorem is the answer to this question. The theorem states that even if a population is not normally distributed, the sampling distribution of practically any population distribution approaches normal curve as the sample size increases.

The implication is that the appropriate measure of short-term risk corresponding to the lifetime of the project in question should be the “Standard Error” of market returns—i.e., deviations in “short-term average market returns” with respect to “long term average market returns”.

Proof of validity of Central Limit Theorem for asset pricing: Dow Jones Industrial Average

Two important characteristics are required for the Central Limit Theorem to be valid, a) randomness (unpredictability) and b) independence (preceding values do not influence subsequent values). While examining the question, “Are asset prices predictable?” the Nobel Economic Sciences Prize Committee commented as under in its 2013 background note:

“....the asset price may go up or down tomorrow, but any such movement is unpredictable: the price follows a martingale, which is a generalized form of a random walk.”

Year-end closing values of the Dow Jones Industrial Average since its inception in 1896, (the population) taking three year arithmetic mean as the sample statistic, were studied. A frequency distribution was plotted to produce the sampling distribution area graph. The resultant graph appeared to approximate a normal distribution as shown below.

The graph shows that even with a sample size as small as three years, the sampling distribution has closely approximated a normal distribution. The distribution could easily approach perfectly normal for a slightly larger sample size—perhaps 5 years. Then all we have to do is to invoke the Central Limit Theorem and determine the standard error.

In contrast to the above, the CAPM does not take into account any deviation in returns at all while it prescribes a Risk Adjusted Return as the output of its equation. On top of this, since opportunity cost of equity is based on portfolio returns and not individual security returns, as explained above, applying beta of the security to (Rm - Rf) conflicts with rational investor behavior.

My conclusion based on this evidence is that the best way to estimate risk adjusted Cost of Equity for a project is the long term market return + standard error of market return. This is because every project must necessarily deliver at least the long term market return. Once that is done, a subsequent evaluation of the project’s extra return must be made against its associated extra risk given by standard error.

I welcome your thoughts on using the long-term market return with a standard error of market return as the basis for discounting project cash flows.

Note:

The above article is an edited and significantly condensed extract from the author’s book The Timeless Essence of Financial Science. Due to constraints of space, more detailed explanations could not be provided here but are available in the book, supported by ample authoritative evidences.