The CAPM assumptions is very general and can be generalized to any equilibrium model of optimization . I feels it is week and some of the assumptions are week especially those related to global investment portfolio. actually when Fama got his Nobel prize it was for the number of works that emerged from his work not for genuinely.
The assumptions remain unchanged. No theory is perfect. All subject s to criticism. Most important thing is what we can learn from the theory.
The CAPM assumptions are what we would have in a world that is as sterile and perfect as a chemist's laboratory. Thus we can only start with those assumptions and then add all the imperfections of a realistic economy and make the necessary adjustments. I never thought the CAPM assumptions were intended to be used in a real-world model.
Well I think that the most awkward one is homogeneous expectations. All price movements are assumed to be the result of a change in expectations, yet people often buy and sell shares because they disagree with the price not because they have new information. Financial market prices change far more frequently than the fundamentals which is what one would expect from the process of disagreement. This mixture of information and disagreement unfortunately lies between the traditional CAPM analysis and behavioural approaches, between two opposing camps of academics, so there is little hope of development.
I agree with Roland that most unrelaistic is the homogenous expectations for which we see a lot of anomalies (size, value, momentum etc.) making CAPM alomost redundant empirically. However, in the current research CAPM still has a presence to test against for: how much assets/securities under/overperfrom than the average market expectation!
Well worth reading Frazinni and Pedersen "Betting against beta" paper in Journal of Financial Economics (2013). This suggests beta can form basis of contrarian strategy that yields profits. This is odd as one tends to thing Fama and French (1992) has shown us "beta is dead" and the SML is flat.
1. Capital markets are perfect and efficient where there is free flow of information and no transaction costs.
2. There are no personal and corporate taxes.
3. All investors are single period wealth maximizes.
4. Investors have homogeneous or similar expectations about risks and returns of a security.
5. All investors can borrow and tend at the risk free rate which is assumed to remain constant.
6. There is no inflation in the economy.
7. Investors are risk averse.
8. There is normal distribution of returns of a given security and that there exists a well diversified market portfolio without unsystematic risk.
Most of these assumptions are irrelevant in today's context
today we have transaction costs in almost all business transactions, there are both corporate and individual taxes, there is inflation in the economy
See Jonathan Berk's paper "Necessary Conditions for the CAPM" in the Journal of Economic Theory for an update on what was the classic paper on this question (Cass and Stiglitz, 1970, JET). It's not sufficient to criticize the conditions under which the CAPM arises (which is easy) -- you also have to provide a good alternate asset pricing model (this is the hard part). The APT is always a good alternative, but...do you see it being operationalized...?
Excerpt from http://en.wikipedia.org/wiki/Essays_in_Positive_Economics
In a famous and controversial passage, Friedman writes that:
Truly important and significant hypotheses will be found to have "assumptions" that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions (in this sense) (p. 14).
Why? Because such hypotheses and descriptions extract only those crucial elements sufficient to yield relatively precise, valid predictions, omitting a welter of predictively irrelevant details. Of course descriptive unrealism by itself does not ensure a "significant theory" (pp. 14–15).
From such Friedman rejects testing a theory by the realism of its assumptions. Rather simplicity and fruitfulness incline toward such assumptions and postulates as utility maximization, profit maximization, and ideal types—not merely to describe (which may be beside the point) but to predict economic behavior and to provide an engine of analysis (pp. 30–35). 1).
F=ma is a significant hypothesis, and it doesn't appear to contain any "wildly inaccurate descriptive representations of reality."
The concept of arbitrage pricing theory (APT) is central to theory of capital markets and it stipulates that a relationship between return and risk but it uses different assumptions and techniques.
An arbitrage opportunity arises when an investor can construct a zero investment portfolio what will yield a sure profit. Equilibrium market prices are rational in that they rule out risk-free arbitrage opportunities.
In the CAPM model, if a security is mispriced the ALL INVESTORS will tilt their portfolios toward the underpriced and away from the overpriced securities by a relatively small dollar amount and equilibrium.
In contrast, the implication of no-arbitrage condition is that A FEW INVESTORS who identify an arbitrage opportunity will mobilize large dollar amounts and restore equilibrium.
See my paper on why incomplete markets is the reason why the CAPM naturally becomes the 4 factor Carhart model https://www.researchgate.net/publication/228316204_Growth_Opportunities_Assets_in_Place_Stocks_Migration_and_CAPM_A_Rational_Foundation_for_the_Fama-French_and_Momentum_Factors?ev=prf_pub
Article Growth Opportunities, Assets in Place, Stocks Migration and ...
Christopher, how does your theory explain the low beta anomaly? Low beta stocks earn above market returns, even when controlling for low P/B.
1. Security markets are perfectly competitive.
a) Many small investors
b) Investors are price takers
2. Markets are frictionless
a) There are no taxes or transaction costs.
3. Investors are myopic
a) All investors have only one and the same holding period
4. Investments are limited to publicly traded assets with unlimited borrowing and
lending at the risk-free rate.
a) Assets such as human capital are not part of the investment opportunity set.
5. All investors are rational mean-variance optimizers
a) Everyone uses the Markowitz portfolio selection method.
6. Perfect Information
a) All investors have access to the same information.
b) All investors analyze information in the same manner.
7. Everyone either has quadratic utility or has homogenous beliefs concerning the
distribution of security returns.
a) Everyone uses the same estimates of expected return and the same
variance/covariance matrix.
i think all these assumptions are FAKE
This is true. But I guess the question is (as per Prof. Shanken's contribution) whether this fakery is useful in terms of producing a good predictive model of expected returns.
I think post Fama/French 1992 it is clear they are not useful enough. The alternative offered of size and value seems open to multiple interpretations, as characteristics or just straight mis pricing proxies. In general one feels we "must do better" to produce a sensible asset pricing story. Watching this research agenda unfold will be exciting in the next few years.
you can read this Article : Is Beta Dead?
find it in the link below!!
http://finance.wharton.upenn.edu/~acmack/Chapter_10_app.pdf
Well, If all assumptions are met in the real world then the theory become a fact and all the financial problem of investment decision taking is just resolved.
Therefore, some of the CAPM assumptions became closer to reality given the advanced technology systems such as perfect competition market and that is related to information availability in addition to the rationality assumption. although many of the remaining assumption are not always close to reality.
However, having the muti - factors CAPM models always help to get a better estimations.
Richard ...
"how does your theory explain the low beta anomaly?"
There actually are two anomalies ... the CAPM appears to underestimate required rates of return for low Beta securities and to overestimate them for high Beta ones.
There are two points in the CAPM that are true by definition; at Beta = 0 Ke = Krf and at Beta = 1 Ke = Km. There are an infinite number of lines that could connect those two points. The mathematics that derive the CAPM from prior theory result in an exponent of Beta of 1, hence it is a linear function. But there is no reason empirically that it should be so. Were the exponent >1, it would be an accelerating curve; were it >0
One of the technical problem with CAPM is using beta to measure the risk of return but beta only measures the risk of an investment that cannot be diversified away and does not measure the risk of an investment held on a stand-alone basis.
In the CAPM, beta risk is the only kind of risk for which investors should receive an expected return higher than the risk-free rate of interest. It is an estimate expected return.
In my opinion it never holds, it's a mathematical artifact. The assumptions were taken from those of perfect competition. When it was set in the beginning it was impossible to test given that we don't have the global portfolio and the assumption that they rely upon-on that time-which a sample can do the job. It was a self-fulfilling application.
I do not see that as a "technical problem" as the CAPM is intended to estimate the required rate of return for "well diversified" investors. In the CAPM Beta is intended to measure the risk an investment contributes to the market portfolio. Actual investors range from wholly undiversified (hold one security) to quite diversified (hold the market portfolio proxy). One can calculate stand-alone risk by the standard deviation of a security's returns, and that is one factor one can use to calculate Beta, along with the standard deviation of the market returns and the correlation between security and market returns.
An undiversified investor does face both systematic and unsystematic risk and, therefore, has a greater required rate of return. Market prices assume diversified investors and an undiversified investor cannot be compensated for the additional (unsystematic) risk. Such an investor would need to pay less (to get a higher return) than a diversified investor and there is no reason a willing and uncompelled seller would sell for less than the market price.
I think that terminology over the years has become a bit sloppy. What the CAPM estimates is the rate of return required to justify assuming a level of risk as measured by Beta. It does not predict the return for any specific investment. A well managed company should have a positive EVA ... that is, it should have a return in excess of its cost of capital. There is no economic gain if all it earns is its cost of capital. If all an investor earns is the cost of capital, that is return of investment and not return on investment.
I distinguish to my students three returns: required rate of return being the return needed to justify assuming the risk; expected rate of return being what one expects to happen based on the specifics of the situation; realized rate of return being what actually happened. The first two are ex ante returns and are reflected in the NPV calculation ... a positive NPV means that the expected rate of return exceeds the required rate of return used as the discount rate. Realized rate of return is an ex post return and cannot be known at the time an investment decision must be made.
Capital Asset Pricing Model (CAPM) like any other models is based on assumptions. Most of the CAPM assumptions may be irrelevant in today’s context, but the CAPM theoretical prediction is very strong. Rather than attacks the CAPM assumptions, it is better to look for ways to improve its weaknesses. Over the years, researchers have made significant progress to improve the weaknesses of the basic CAPM and we have more variants of the basic CAPM now.
One set of assumptions is specified on Shapiro's website and another set is specified on the Palmitar website. Part of the confusion results from the fact that Treynor, Sharpe, Lintner, and Mossin all published versions of the CAPM over the period from 1961 to 1966.
http://people.stern.nyu.edu/ashapiro/courses/B01.231103/FFL09.pdf
https://users.wfu.edu/palmitar/Law&Valuation/chapter%202/2-5-3.htm
Roll's critique is probably the best know criticism of the CAPM.
Roll, Richard (March 1977), "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory", Journal of Financial Economics 4 (2): 129–176.
Graham and Harvey survey practitioners to determine which financial models are used and find that about 75% of practitioners use CAPM to determine risk premia. This indicates that practitioners are not bothered by the validity of the assumptions. Given that the CAPM has been around and tested for fifty years, one might assume that the model meets the needs of users regardless of the assumptions.
"The theory and practice of corporate finance: Evidence from the field," with John Graham, Journal of Financial Economics 60, (2001): 187-243.
https://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P67_The_theory_and.pdf
Graham, John R. and Campbell R. Harvey. “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics, 2002, pp. 187-243.
Please see the proof of why the CAPM is just a tautology in the paper of " Yes, the CAPM Is Dead". This paper was presented at the 19th Annual Conference on Pacific Basin Finance, Economics, Accounting, and Management (Taipei, Taiwan, July 9, 2011).
The expected rate of returns (parameters) were assumption be given before the decision variable (optimal portfolio) is derived. Since optimal portfolio is equal to the market portfolio (under the assumption of homogeneous belief), the optimal decision variable (i.e., the optimal portfolio, which is equal to the market portfolio) depends on the parameter (expected rate of return and covariance matrix), not vice versa (which is exactly the CAPM, the parameter of expected rate of return depends on the market portfolio (or the optimal portfolio). In mathematics, parameter is a constant rather than a variable.
In statistics, the expected value (rate of return) must be given before the covariance ( the beta) can be calculated. In other words, we cannot use the covariance (i.e. beta) to explain the expected value (the expected rate of return).
Have a look also here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2505597
Have a look also here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2505597
In Statistics, the expected rate of return (i.e., a population parameter) should only depend on the density function of the random variable and should not depend on the covariance (beta) because covariance is based on the assumption that the expected rate of return is already given. A parameter is a constant, in Mathematics, how can a constant (expected rate of return) depends on other variable(s) (beta, expected market rate of return) ? The true is that the CAPM is Dead and it is useless.
One hidden assumption in the CAPM is that the firm or the asset does not have any default risk. I developed/derived the CAPM with the inclusion of the default risk and tested that with insurance data in my paper, titled as " The Capital Asset Pricing Model with Default Risk-Theory and Application in Insuarnce".
What I personally think as a researcher in Behavioral Finance is that all investors , especially in country like mine (i.e. India) are completely a set of complex & differentiated in nature, having very less financial literacy & full of ethnic bias, as far as investment is concerned. These make them concentrate very heavily on Land and Gold as an traditional ethnic investment vehicle. They are not in a position to maximize economic utilities. May be in a developed economy with less cross sectional ethnicity and higher level of financial literacy it will be in good effect.
- Badges
- Science topic
- Similar topics
- Linguistics
- Composition Studies
- Writing