Editing Capital asset pricing model (section)

== Problems ==
In their 2004 review, economists [[Eugene Fama]] and [[Kenneth French]] argue that "the failure of the CAPM in empirical tests implies that most applications of the model are invalid".<ref name="FamaFrench2004" />

* The traditional CAPM using historical data as the inputs to solve for a future return of asset i. However, the history may not be sufficient to use for predicting the future and modern CAPM approaches have used betas that rely on future risk estimates.<ref>{{cite journal|last1=French|first1=Jordan|title=Back to the Future Betas: Empirical Asset Pricing of US and Southeast Asian Markets|journal=International Journal of Financial Studies|volume=4|issue=3|page=15|doi=10.3390/ijfs4030015|year=2016|doi-access=free|hdl=10419/167811|hdl-access=free}}</ref>
* Most practitioners and academics agree that risk is of a varying nature (non-constant). A critique of the traditional CAPM is that the risk measure used remains constant (non-varying beta). Recent research has empirically tested time-varying betas to improve the forecast accuracy of the CAPM.<ref>{{cite book|last1=French|first1=Jordan|title=Estimating Time-Varying Beta Coefficients: An Empirical Study of US & ASEAN Portfolios|volume=32|pages=19–34|doi=10.1108/S0196-382120160000032002|series=Research in Finance|year=2016|isbn=978-1-78635-156-2}}</ref>
* The model assumes that the variance of returns is an adequate measurement of risk. This would be implied by the assumption that returns are normally distributed, or indeed are distributed in any two-parameter way, but for general return distributions other risk measures (like [[coherent risk measure]]s) will reflect the active and potential shareholders' preferences more adequately. Indeed, risk in financial investments is not variance in itself, rather it is the probability of losing: it is asymmetric in nature as in the alternative safety-first asset pricing model.<ref>[[A. D. Roy]](1952), "Safety-first and the holding of assets," Econometrica, 20, No. 3, 425-442. [https://www.jstor.org/stable/1907413?Search=yes&resultItemClick=true&searchText=(((Roy%20A.%20D.)%20AND%20(econometrica))%20AND%20(Roy%20A%20D))%20AND%20(Roy%20Safety%20first%20and%20the%20Holding)&searchUri=%2Faction%2FdoBasicSearch%3FQuery%3DRoy%2BSafety%2Bfirst%2Band%2Bthe%2BHolding%26filter%3D%26cty_journal_facet%3Dam91cm5hbA%253D%253D%26prq%3D((Roy%2BA.%2BD.)%2BAND%2B(econometrica))%2BAND%2B(Roy%2BA%2BD)%26swp%3Don&ab_segments=0%2Fbasic_search%2Fcontrol&refreqid=fastly-default%3A5389f8677c56d05f608ced7c284543f6]. Retrieved June 20, 2021.</ref><ref>Jansen, D. W., K.G. Koedijk and C. G. de Vries (2000), "Portfolio selection with limited downside risk," Journal of Empirical Finance, 7, 247-269.[https://ideas.repec.org/a/eee/empfin/v7y2000i3-4p247-269.html]. Retrieved June 20, 2021.</ref> [[Barclays Wealth]] have published some research on asset allocation with non-normal returns which shows that investors with very low risk tolerances should hold more cash than CAPM suggests.<ref>{{Cite web | url=http://www.barclayswealth.com/Images/asset-allocation-february-2013.pdf | title=News and insight &#124; Wealth Management &#124; Barclays}}</ref>
*Some investors prefer positive skewness, all things equal, which means that these investors accept lower returns when returns are positively skewed. For example, [[Problem gambling|Casino gamblers]] pay to take on more risk. The CAPM can be extended to include co-skewness as a priced factor, besides beta.<ref>{{Cite journal|last1=Kraus|first1=Alan|last2=Litzenberger|first2=Robert H.|date=1976|title=Skewness Preference and the Valuation of Risk Assets|url=https://www.jstor.org/stable/2326275|journal=The Journal of Finance|volume=31|issue=4|pages=1085–1100|doi=10.2307/2326275|jstor=2326275|issn=0022-1082|url-access=subscription}}</ref><ref>{{Cite journal|last1=Post|first1=Thierry|last2=van Vliet|first2=Pim|last3=Levy|first3=Haim|date=2008-07-01|title=Risk aversion and skewness preference|url=https://www.sciencedirect.com/science/article/pii/S037842660700297X|journal=Journal of Banking & Finance|language=en|volume=32|issue=7|pages=1178–1187|doi=10.1016/j.jbankfin.2006.02.008|issn=0378-4266|url-access=subscription}}</ref>
* The model assumes that all active and potential shareholders have access to the same information and agree about the risk and expected return of all assets (homogeneous expectations assumption).{{Citation needed|date=August 2009}}
* The model assumes that the probability beliefs of active and potential shareholders match the true distribution of returns. A different possibility is that active and potential shareholders' expectations are biased, causing market prices to be informationally inefficient. This possibility is studied in the field of [[behavioral finance]], which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model of Kent Daniel, [[David Hirshleifer]], and [[Avanidhar Subrahmanyam]] (2001).<ref>{{cite journal |title=Overconfidence, Arbitrage, and Equilibrium Asset Pricing |first1=Kent D. |last1=Daniel |first2=David |last2=Hirshleifer |first3=Avanidhar |last3=Subrahmanyam |journal=Journal of Finance |volume=56 |issue=3 |year=2001 |pages=921–965 |doi=10.1111/0022-1082.00350 }}</ref>
* The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks offer higher returns than the model would predict.<ref>{{Cite journal|last1=Fama|first1=Eugene F.|last2=French|first2=Kenneth R.|date=1992|title=The Cross-Section of Expected Stock Returns|journal=The Journal of Finance|language=en|volume=47|issue=2|pages=427–465|doi=10.1111/j.1540-6261.1992.tb04398.x|issn=1540-6261|doi-access=free}}</ref><ref>{{Cite journal |last1=Baltussen |first1=Guido |last2=van Vliet |first2=Bart |last3=van Vliet |first3=Pim |date=2024-06-11 |title=The Cross-Section of Stock Returns before CRSP |journal=SSRN Working Paper |ssrn=3969743}}</ref>
* Some data to this effect was presented as early as a 1969 conference in [[Buffalo, New York]] in a paper by [[Fischer Black]], [[Michael C. Jensen|Michael Jensen]], and [[Myron Scholes]]. Either that fact is itself rational (which saves the [[efficient-market hypothesis]] but makes CAPM wrong), or it is irrational (which saves CAPM, but makes the EMH wrong – indeed, this possibility makes [[volatility arbitrage]] a strategy for reliably beating the market).<ref>{{Cite journal|last=de Silva|first=Harindra|date=2012-01-20|title=Exploiting the Volatility Anomaly in Financial Markets|journal=CFA Institute Conference Proceedings Quarterly|volume=29|issue=1|pages=47–56|doi=10.2469/cp.v29.n1.2|issn=1930-2703}}</ref><ref>{{Cite journal|last1=Baker|first1=Malcolm|last2=Bradley|first2=Brendan|last3=Wurgler|first3=Jeffrey|date=2010-12-22|title=Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly|journal=Financial Analysts Journal|volume=67|issue=1|pages=40–54|doi=10.2469/faj.v67.n1.4|s2cid=12706642|issn=0015-198X|url=http://archive.nyu.edu/handle/2451/29593 }}</ref><ref>{{Cite journal|last1=Blitz|first1=David|last2=Van Vliet|first2=Pim|last3=Baltussen|first3=Guido|title=The volatility effect revisited|journal=Journal of Portfolio Management|volume=46|issue=1|pages=jpm.2019.1.114|doi=10.3905/jpm.2019.1.114|year=2019|s2cid=212976159}}</ref> The puzzling empirical relationship between risk and return is also referred to as the [[low-volatility anomaly]].
* The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model.<ref>{{Cite book|title=Modern portfolio theory and investment analysis|last1=Elton|first1=E. J.|last2=Gruber|first2=M. J.|last3=Brown|first3=S. J.|last4=Goetzmann|first4=W. N.|publisher=John Wiley & Sons|year=2009|pages=347}}</ref>
* The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. This assumes no preference between markets and assets for individual active and potential shareholders, and that active and potential shareholders choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted.{{Citation needed|date=August 2009}}
* The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, [[human capital]]...) In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that, due to the impossibility of observing the true market portfolio, the CAPM might not be empirically testable. This was presented in greater depth in a paper by [[Richard Roll]] in 1977, and is generally referred to as [[Roll's critique]].<ref>{{cite journal |last=Roll |first=R. |year=1977 |title=A Critique of the Asset Pricing Theory's Tests |journal=Journal of Financial Economics |volume=4 |issue= 2|pages=129–176 |doi=10.1016/0304-405X(77)90009-5 }}</ref> However, others find that the choice of market portfolio may not be that important for empirical tests.<ref>{{cite journal |last=Stambaugh |first=Robert |year=1982 |title=On the exclusion of assets from tests of the two-parameter model: A sensitivity analysis |journal=Journal of Financial Economics |volume=10 |issue= 3|pages=237–268 |doi=10.1016/0304-405X(82)90002-2 }}</ref> Other authors have attempted to document what the world wealth or world market portfolio consists of and what its returns have been.<ref>{{Cite journal|year=1985| last1=Ibbotson|first1=Roger|last2=Siegel|first2=Lawrence|last3=Love|first3=Kathryn|title=World wealth: Market values and returns|journal=Journal of Portfolio Management|volume=12|issue=1|pages=4–23|doi=10.3905/jpm.1985.409036| s2cid=154485834}}</ref><ref>{{Cite journal|year=2014|last1=Doeswijk|first1=Ronald|last2=Lam|first2=Trevin|last3=Swinkels|first3=Laurens|title=The global multi-asset market portfolio, 1960-2012|journal=Financial Analysts Journal|volume=70|issue=2|pages=26–41|doi=10.2469/faj.v70.n2.1|s2cid=704936}}</ref><ref>{{Cite journal|year=2019|last1=Doeswijk|first1=Ronald|last2=Lam|first2=Trevin|last3=Swinkels|first3=Laurens|title=Historical returns of the market portfolio|journal=Review of Asset Pricing Studies|volume=X|issue=X|pages=XX}}</ref>
* The model assumes economic agents optimize over a short-term horizon, and in fact investors with longer-term outlooks would optimally choose long-term inflation-linked bonds instead of short-term rates as this would be a more risk-free asset to such an agent.<ref>{{Cite web |url=http://ciber.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Campbell_Viceira.pdf |title=Archived copy |access-date=2012-05-08 |archive-url=https://web.archive.org/web/20140725120919/https://ciber.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Campbell_Viceira.pdf |archive-date=2014-07-25 |url-status=dead }}</ref><ref>{{cite book|last1=Campbell|first1=John Y. |last2=Viceira|first2=Luis M. |title=Strategic Asset Allocation: Portfolio Choice for Long Term Investors|series=Clarendon Lectures in Economics|year=2002|ISBN=978-0-19-829694-2}}</ref>
* The model assumes just two dates, so that there is no opportunity to consume and rebalance portfolios repeatedly over time. The basic insights of the model are extended and generalized in the [[intertemporal CAPM]] (ICAPM) of Robert Merton,<ref>{{cite journal|last=Merton|first=R.C.|year=1973|title= An Intertemporal Capital Asset Pricing Model|journal= Econometrica |volume= 41|issue= 5|pages=867–887|doi=10.2307/1913811|jstor=1913811}}</ref> and the [[Consumption-based capital asset pricing model|consumption CAPM]] (CCAPM) of Douglas Breeden and Mark Rubinstein.<ref name=Breeden>{{cite journal
| last = Breeden
| first = Douglas
| date = September 1979
| title = An intertemporal asset pricing model with stochastic consumption and investment opportunities
| journal = Journal of Financial Economics
| volume = 7
| issue = 3
| pages = 265–296
| doi = 10.1016/0304-405X(79)90016-3 
| s2cid = 154918812
}}</ref>
* CAPM assumes that all active and potential shareholders will consider all of their assets and optimize one portfolio. This is in sharp contradiction with portfolios that are held by individual shareholders: humans tend to have fragmented portfolios or, rather, multiple portfolios: for each goal one portfolio — see [[behavioral portfolio theory]]<ref>{{cite journal |last1=Shefrin |first1=H. |first2=M. |last2=Statman |year=2000 |title=Behavioral Portfolio Theory |journal=Journal of Financial and Quantitative Analysis |volume=35 |issue=2 |pages=127–151 |doi=10.2307/2676187 |jstor=2676187 |citeseerx=10.1.1.143.8443 |s2cid=51947571 }}</ref> and [[Maslowian portfolio theory]].<ref>{{cite journal |last=De Brouwer |first=Ph. |year=2009 |title=Maslowian Portfolio Theory: An alternative formulation of the Behavioural Portfolio Theory |journal=Journal of Asset Management |volume=9 |issue=6 |pages=359–365 |doi=10.1057/jam.2008.35 |doi-access=free }}</ref>
* Empirical tests show market anomalies like the size and value effect that cannot be explained by the CAPM.<ref name="FamaFrench1993">{{Cite journal |last=Fama |first=Eugene F. |author2=French, Kenneth R. |year=1993 |title=Common Risk Factors in the Returns on Stocks and Bonds |journal=Journal of Financial Economics |volume=33 |issue=1 |pages=3–56 |doi=10.1016/0304-405X(93)90023-5 |citeseerx=10.1.1.139.5892 }}</ref> For details see the [[Fama–French three-factor model]].<ref>{{Cite journal |last=Fama |first=Eugene F. |author2=French, Kenneth R. |year=1992 |title=The Cross-Section of Expected Stock Returns |journal=Journal of Finance |volume=47 |issue=2 |pages=427–465 |doi=10.2307/2329112 |jstor=2329112 |citeseerx=10.1.1.556.954 }}</ref>

Roger Dayala<ref>{{Cite journal |last=Dayala |first=Roger R.S. |year=2012 |title=The Capital Asset Pricing Model: A Fundamental Critique |journal=Business Valuation Review |volume=31 |issue=1 |pages=23–34 |doi=10.5791/BVR-D-12-00001.1 }}</ref> goes a step further and claims the CAPM is fundamentally flawed even within its own narrow assumption set, illustrating the CAPM is either circular or irrational. The circularity refers to the price of total risk being a function of the price of covariance risk only (and vice versa). The irrationality refers to the CAPM proclaimed ‘revision of prices’ resulting in identical discount rates for the (lower) amount of covariance risk only as for the (higher) amount of Total risk (i.e. identical discount rates for different amounts of risk. Roger’s findings have later been supported by Lai & Stohs.<ref>{{Cite journal |last=Lai |first=Tsong-Yue |author2=Stohs, Mark H. |year=2015 |title=Yes, CAPM is dead |journal=International Journal of Business |volume=20 |issue=2 |pages=144–158 |url=https://www.researchgate.net/publication/275893159 }}</ref>