Decoding the CAPM Mystery
Rajesh D. Mudholkar, ACMA (India), Author and Visiting Faculty, Pune University Dept. of Management | July 23, 2014 | 10
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.
| Portfolio I | Portfolio II | Portfolio III | ||||||
Period | X | Deviation | Variance | X | Deviation | Variance | X | Deviation | Variance |
1 | 9 | -1 | 1 | 13 | 3 | 9 | 11 | 1 | 1 |
2 | 9 | -1 | 1 | 7 | -3 | 9 | 11 | 1 | 1 |
3 | 9 | -1 | 1 | 13 | 3 | 9 | 11 | 1 | 1 |
4 | 9 | -1 | 1 | 7 | -3 | 9 | 11 | 1 | 1 |
5 | 9 | -1 | 1 | 13 | 3 | 9 | 11 | 1 | 1 |
6 | 9 | -1 | 1 | 7 | -3 | 9 | 11 | 1 | 1 |
7 | 9 | -1 | 1 | 13 | 3 | 9 | 11 | 1 | 1 |
8 | 9 | -1 | 1 | 7 | -3 | 9 | 11 | 1 | 1 |
9 | 9 | -1 | 1 | 13 | 3 | 9 | 11 | 1 | 1 |
10 | 19 | 9 | 81 | 7 | -3 | 9 | 1 | -9 | 81 |
Sum | 100 |
| 90 | 100 |
| 90 | 100 |
| 90 |
Mean | 10 |
| 9 | 10 |
| 9 | 10 |
| 9 |
Standard Deviation | 3 |
| 3 |
| 3 |
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.
Sampling distribution of 3-year mean annual returns
Dow Jones Industrial Average (DJIA) Index (1896 – 2012)
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.
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Rajesh Mudholkar September 5, 2014
Stefan Dunatov's paper on defining true risk points out precisely how financial practitioners, and consequently investors in risky assets such as equities, have been misled by wrong tools. For serious long term investors, what really matters is the potential stream of future earnings (cash flows), and how those earnings are likely to be adversely impacted by a various forecasted scenarios, regardless of short-term price volatility. The explanations provided by behavioural finance theories clearly invalidate the fallacious efficient market hypothesis, and therefore implicitly also invalidate all financial tools that are based on short-term irrational market behaviour, and which are then used for rational decision making to fulfill long-term investor expectations, a prima facie absurd logic! Good debate going on. Hope to see more.
Stathis Gould September 5, 2014
The short paper on Defining true risk by Stefan Dunatov, Chief Investment Officer, Coal Pension Trustees Investment Limited might be of interest. He suggests that using volatility as a measure of risk has potentially dangerous implications for long- term investors. The focus should be on forecasting returns rather than looking specifically at a short-term metric of volatility to forecast risk. http://www.the300club.org/Portals/0/Stefan-Dunatov-defining-true-risk-09-06-14.pdf
Prafula Joshi September 3, 2014
Really interesting article, and comments below are educational too. Thank you.
Rajesh Mudholkar August 19, 2014
'Outliers', 'tipping point' and 'chance events' that Mr Bijoy Guha mentions, are all valid phenomena that characterise short term price movements in financial markets driven by behavioural factors, and would be a matter of concern for typical traders. Extensive work has been done to demonstrate the effect of irrational behaviour on short term market prices by 2013 Nobel Laureate Robert Shiller, building on the earlier work done by Nobel Laureate Daniel Kanheman, well known for his 'Prospect Theory'. Shiller's book 'Irrational Exuberance' is a well known treatise on this subject. As mentioned in this article, even Harry Markowitz's 'Theory of Portfolio Choice' faced the criticism that market prices are subject to wide variations. There's no dispute that markets are unpredictable in the short term. In fact this has been amply proven and clearly reported in the 2013 Nobel Prize Committee's background note (http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/advanced.html). The key issue being discussed here is not how to predict short term market prices, or what factors contribute to unpredictability, but rather about how project investment decisions should be made. Clearly, rational decision making about deployment of shareholders' funds must not be influenced by short term unpredictable irrational market behaviour. The various theories of understanding financial markets, where 'outliers' 'tipping point' and 'chance events' come into picture have been discussed in detail in my captioned book 'The Timeless Essence of Financial Science'. The fact remains that there is a need to transform corporate finance from a cultivated art to an objective science, as stated emphatically by the Association for Financial Professionals (AFP) in its 'cost of capital survey report'. The present article, as already mentioned is a brief summary of only one of the key issues discussed in my book, which covers a much wider spectrum of ideas towards achieving what the AFP notes.
Bijoy Guha August 15, 2014
In continuation to my previous comment, I would like to hear the author's views on the role of 'outliers', 'tipping point' and 'chance events' that Nassim Nicholas Taleb writes about in his books 'The Black Swan' and 'Fooled by randomness'.
Rajesh Mudholkar August 2, 2014
According to a World Economic Forum report, (http://www.weforum.org/issues/long-term-investing) long-term investing helps to stablise financial markets, yet the capacity of investors for long-term investing has diminished in recent years, mainly because the lack of meaningful measurements for performance and risk over long time horizons. This paper directly addresses this concern and offers a scienctific solution. It's important to note that the entire chain of Plan-Do-Check-Act is involved here. Any flaw in investment appraisal directly hurts performance appraisal and corrective action. For example CAPM affects WACC, and WACC affects EVA which most companies use. Is WACC consistent with how project returns are actually shared between different sources of capital? Is EVA (which uses WACC) consistent with the long term investing and value creation goals? These are critical questions which need serious consideration and the prevailing practices must be reviewed in this light. I have analysed in great detail, all of these issues in my book referred here.
Bijoy Guha August 1, 2014
Good synopsis. However the alternative to CAPM proposed, would have been better understood if the article would have elaborated the Central Limit Theorem.
sumit roy August 1, 2014
Rajesh Mudholkar';s explanation of opportunity cost of equity, and measurement of short term risk using standard error, carries an undisputable logic which shows his deep understanding of economic principles and statistical application. His simple yet well explained and empirically supported answer to the criticism levelled against Modern Portfolio Theory - that returns in equity and other risky financial assets are not normally distributed and therefore unpredictable - shows his remarkable insight into understanding financial markets. This paper as well as his book deserves serious thought by the global finance community
Paritosh Basu August 1, 2014
I feel that the author has provided several points, which deserve to be pondered over and considered in the context of the main model under debate. One simple point is that the model, theories, views, etc., that have been commented upon are of such huge volume spread over such vast expanse of market and related dynamics, risk exposures and volatilities, etc. that there can always be a debatable argument against the conclusion of any author, irrespective of the enormity of data base that has been used to reach to that conclusion
Abhinav Jog August 1, 2014
Good article, Sir !