Talk:Capital asset pricing model

message: This page is (1) unduly negative toward the capital asset pricing model and (2) unduly technical. (1) Undue negativity: The imperfections that researchers assign to the CAPM tend to be explained by its assumptions or by data mining. For example, tax and lending produce the expectation of a flatter capital market line than the model predicts, as observed. The "error" that the real returns tend to be a tad flatter has been known for decades but people have not been able to profit from it. Other imperfections tend to be a result of data mining and disappear as soon as the research is published and traders act on it. The CAPM is quite accurate. (2) Excess technical nature: One does not need to know higher probability theory to understand the CAPM. The beta is a metric of how much each asset moves given a market move. Instead of being explained as the ratio of the covariance to the variance (which has no intuitive meaning), it should be explained as the beta of the linear regression of the returns of the asset against the returns of the market, approximated in practice by those of the S&P500. Generally, I explain the CAPM without referring to the optimal portfolio frontier, but by showing that if assets are not on the capital market line, then they give rise to an arbitrage opportunity. The trading to implement those arbitrage opportunities pushes the price of assets to the capital market line. For example, if the CML indicates that an asset with beta of .5 should have a return of 4% but we see such assets returning 5% (i.e., they are cheap), traders can buy the assets and synthesize beta half portfolios from the index and the risk-free asset to sell and reap the rewards. Vice verse if such assets returned 3% (being expensive) or beta 1.5 assets that should return 12% are expected to return 13% or 11%. In the real world the error or those expectations precludes traders from making those trades in great quantities but the logic is inescapable. In other words, the page should be rewritten without the focus on imperfections and with an explanation of the CAPM that is more intuitive. I'd be happy to do that or help do it but I do not know how or where to start. Ngeorgak (talk) 21:31, 22 August 2021 (UTC)
thread_title: Page Needs to be Rewriten

message: I am concerned about a recent edit.  There is an article showing that there is a math error in the derivation of the CAPM that was deleted as an irrelevant criticism.  How could a math error in the proof be irrelevant on a model filled with empirical failures?  The error is that the CAPM violates the rules of general summation.  This is not a trivial or irrelevant argument.  Suggestions?  Winning a Nobel prize cannot be a reason to hide its problems.  The possibility that the left hand side does not equal the right hand side is serious.  Wikipedia isn't the place to argue this out, but a lot of people use Wikipedia and the problems are serious.  Laypersons need to be adequately warned.  It doesn't pass muster empirically or mathematically.  It needs to go the way of luminiferous ether.
Response: Dear David, I will refer to you by name because the user "entpdave" who added the (subsequently removed) section here also shows up as a user on the INET website, which David Harris, the author of the criticizing article, is associated withhttp://ineteconomics.org/users/entpdave. Further, the Facebook page of the arguably same David Harris has a URL also featuring "entp.dave"https://www.facebook.com/entp.dave. While somebody could have faked the Wikipedia username to mimic David Harris' credentials, it seems as very unlikely.
Therefore, before I get to the factual criticism of your paper titled "Why heavy tails?", let me suggest that it is rather unethical to promote your own work here while pretending to be a third person, referring to your own article as "There is an article showing ...", rather than "I wrote an article showing...". That's just for starters.
And now to the factual criticism of your own work, which, I believe, can be made using arguments from Section 3.1 of your paperhttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=1678726, section titled "Intuition behind the proof". In this section, you commit a standard logical fallacy. You make a set of assumptions different from those in standard (and numerous) derivations of the CAPM model, then you show that your set of assumptions leads to ill-defined objects of interest, which leads you to conclude that the CAPM model must be wrong.
But of course, there is nothing wrong with the CAPM model. It is your own assumptions that are poorly chosen. What you argue in Section 3.1 is the following. Assume that the value of an investment at time t+1 is w_{t+1} = \mu_R w_t + \epsilon_{t+1}, where \epsilon_{t+1} is normally distributed. Then the gross return R_{t+1} = w_{t+1}/w_t conditional on time t information is normally distributed. You are already running into some troubles here because your normality assumption implies that the value of the investment w_{t+1} is negative with positive probability at time t+1 but that can still be worked around.
The critical problem arises when you try to express the distribution of R_{t+1} conditional on time time t-1 information in your equations (5) and (6). The problem now is that conditional on time t-1 information, not only the numerator of the return R_{t+1} but also its denominator can be negative with a strictly positive probability. Therefore, you have a strictly positive probability of an event that your investment has a negative value at time t, but a positive value at time t+1. This of course violates no-arbitrage and does not make any economic sense.
From this point on, you can still try to express the distribution of such a ratio, but it is economically completely meaningless. The Cauchy distributionhttp://en.wikipedia.org/wiki/Cauchy_distribution that is derived as the distribution of the ratio takes on both positive and negative values, and the negative values are generated by combinations of a negative numerator and a positive denominator, and vice versa (and this vice versa is economic garbage).
It simply does not make sense to even start talking about CAPM in such an environment. And in no way do your assumptions constitute a good model of returns in financial markets.
Your analysis is thus a clear example of "garbage assumptions in, garbage results out". But it simply does not disprove anything about CAPM.
To be constructive, let me suggest to you a modification of your model. A much better assumption (one that is also much closer to the empirical distribution of returns) is that the logarithm of the return is normally distributed. Make this assumption and you will see that your whole analysis goes through without a glitch. Your return R_{t+1} = w_{t+1}/w_t will be lognormally distributed conditional both on information at time t, as well as information at time t-1. Problem solved. CAPM survives.  — Preceding unsigned comment added by 108.6.166.198 (talk) 06:48, 6 August 2014 (UTC)
thread_title: Comments

message: There appears to be a contradiction in the article regarding the risk free rate. At one point it is referred to as "such as interest arising from government bonds", later on as "cash (either borrowed or invested)". There are online references for optimal asset allocation, e.g. http://www.smartmoney.com/invest/stocks/the-perfect-portfolio-1294688341486/, which suggest (subject to an individual's different short-term needs for cash) that the optimal allocation of the non-risky part of an individual's assets should be about three quarters bonds and a quarter cash. What I am hoping is that someone has done some research to reconcile these.Dan88888 (talk) 13:39, 8 May 2012 (UTC)
replies: text: Typically the risk free rate is the interest rate from government bonds (when the government is economically stable, for instance US T-Bills are usually used whereas Greek bonds would not be right now).  I believe this is mentioned in risk-free bond.  As for saying it is "cash", that is because in (simpler) financial math models it is assumed you can always borrow or invest at the risk free rate (with any time maturity).  So from that point of view these are thought of as the same number in theory.  In practice you won't be able to borrow at the risk-free rate because you have a risk of default so a premium is included.  As for how to optimally allocate the riskless assets, I don't think that has a part in this page as that goes much beyond the CAPM model.  I hope this helps. Zfeinst (talk) 14:13, 8 May 2012 (UTC)
replies: text:  OK, I found a piece of original research I could cite (which explains my point better than I could!). So I was bold an edited the article. Do please let me know if you disagree with the edit.  — Preceding unsigned comment added by Dan88888 (talk • contribs) 16:22, 8 May 2012 (UTC)
thread_title:  Risk free rate 

message: The CAPM graph looks wrong for negative betas. You cannot get an expected return less than the risk-free interest rate.
-----> YEs you can -if you buy an asset with a negative beta (i.e. an asset that moves against the market portfolio most of the time). THe benefit is having an asset with a negative beta. but then again you get a lower return than a risk free asset.
_______________________________
I agree with you, the graph isn't really showing the main points of CAPM.  Just for the fun of discussion, though:  You can buy insurance (or an option) that reduces your risk below the risk-free interest rate.  Also, what if you just don't invest at all?  Isn't that a return below the risk-free rate?  
And if you consider the US Treasury bond to be risk free, how much risk does an inflation-protected US Treasury bond have?  Even less?  TIPS have smaller coupons than TSY bonds. Tristanreid 20:08, 20 September 2005 (UTC)
thread_title:  The CAPM graph is wrong for negative betas. 

message: Isn't the expression "for dummies" in this kind of usage copyrighted? And do we really need this section? If its explanations are better than those of the rest of the article, they should be put there, not in an addendum. --Christofurio 15:50, 5 February 2006 (UTC)
thread_title:  For Dummies? 

message: This article was formerly listed as a good article, but was removed from the listing because the intro is just a bit impenetrable.  If you could just explain a few terms a bit more I think it would certainly qualify.  Imagine your reader is intelligent but totally ignorant! Worldtraveller 00:56, 24 February 2006 (UTC)
thread_title: Article removed from [[Wikipedia:Good articles]]

message: The formula is now given for the expected rates, as is done in most introductory texts, but this is not a sufficient assumption for the model. It should be in the form of a linear regression equation Y = a + bX + e, where Y is the excess return of the portfolio and X is the excess return of the benchmark. In the original, strict form of the CAPM the equation is Y = bX + e. The difference with the formula in the article is that the regression equation applies to each individual return, albeit with an error e, not only for the expected returns. The regression equation is necessary to estimate alpha and beta. It is logically impossible to do that from the formula with the expectations alone.
JulesEllis 01:20, 18 January 2007 (UTC)
thread_title:  Formula is insufficient for the model 

message: The most widely used tests such as the Sharpe Ratio, Traynor Ratio and Jensen Alpha should be incorporated within this topic as they ALL measure the efficiency of a portfolio manager using the CAPM as a reference model. The regression equation suggested before is infact the basis for Jensen's Alpha. Abh1984
:I agree with that too. JulesEllis 05:13, 23 January 2007 (UTC)
thread_title: Formula is OK but tests should be mentioned

message: It states that returns are assumed to be normally distributed. However, recent developments have shown that location-scale returns with constant skewness across location-scale choices are sufficient. In fact, this skewness restriction can be removed under some assumptions on the utility function. In fact, location-scale returns are not necessary. This can be generalized to spherical distributions. (see articles by Grootveld/Hallerbach (1999) and Bawa (1975)) Shouldn't there be a note about some of this? --TedPavlic 20:15, 8 May 2007 (UTC)
thread_title: What about location-scale?

message: In the two notes about measuring  the expected market rate of return and the risk-free rate of return arithmetic average is mentioned. Would the geometric average not give a better calculation? -- LJG59 (talk) 13:06, 27 August 2008 (UTC)
thread_title: Formula: Arithmetic vs. Geometric average?

message: Mossin (1966) did not write his article independently of Sharpe (1964), but based on it. Cf. the references of his article.  — Preceding unsigned comment added by NecSpe (talk • contribs) 00:02, 9 February 2012 (UTC)
thread_title:  Link Sharpe/Mossin 

message: Perhaps I'm misunderstanding the model, but I believe "undervalued" and "overvalued" should be reversed in the following sentence from the Asset Pricing section:  "If the observed price is higher than the CAPM valuation, then the asset is undervalued (and overvalued when the estimated price is below the CAPM valuation)."
If observed price is HIGHER than the price the model suggests for the given beta, doesn't that indicate the asset is OVER-valued?  In terms of expected returns, the model associates an expected return with the given beta, which may be used to discount future cash flows to derive an expected price.  An observed price HIGHER than the expected price implies a future return lower than the CAPM-generated expected return, placing the asset below the Security Market Line, which indicates the asset is OVER-valued.  This matches what is written in the Security Market Line section.
If I am wrong, perhaps someone can add language to clarify this matter, because it seems (at least to me) the Security Market Line and Asset Pricing sections contradict each other.
- Mike  — Preceding unsigned comment added by 75.43.223.157 (talk) 16:47, 25 February 2012 (UTC)
thread_title:  Asset pricing correction? 

message: The article currently seems to be discussing Sharpe-Lintner CAPM, but it appears common in the literature to refer to an extention of it by Fischer Black as CAPM (at least from some papers I saw by Fama, et al).  An extension to the article, or at least clarification, seems warranted.  --C S (talk) 03:36, 26 September 2013 (UTC)
thread_title:  Black CAPM 

message: I am willing to add some references to the CAPM variants developed in insurance. For instance, there are demand-supply (econ) approaches described by, e.g., Borch (1986) [Risk theory and serendipity. Insurance: Mathematics and Economics 5, 103 - 112], and also computational ones (math), e.g., Furman and Zitikis (2017). [Beyond the Pearson correlation: Heavy-tailed risks, weighted Gini correlations, and a Gini-type weighted insurance pricing model. ASTIN Bulletin: the Journal of the International Actuarial Association 47(3), 919 - 942.] Would there be any objections to inserting a few references?  — Preceding unsigned comment added by Efurman (talk • contribs) 12:45, 7 October 2017 (UTC)
replies: text: Bear in mind that this is an encyclopedia. So, if you want to add citations, you need to show that the citations are relevant and significant. Significance comes from others, secondary sources, who quote your paper. For example, if there are numerous notable reviews (in peer reviewed journals) of CAPM variants that says that your approach is an important variant, then, perhaps, it can be included. Merely noting the existence of the paper, even if in peer reviewed journals, is not enough. Best. --regentspark (comment) 13:03, 7 October 2017 (UTC)

text: I would say no. The mere fact that a paper has been published is insufficient for inclusion. If that were sufficient, there would likely be many hundreds of candidate peer review papers that could be included here and that's obviously not going to work. It would be preferable to see a survey paper, in a good peer reviewed journal, that states that this paper makes a significant contribution to the field. --regentspark (comment) 14:59, 7 October 2017 (UTC)
thread_title:  Problems 

message: Greetings Wikipedians! I commend all the contributors for their efforts. But sadly, this article lacks inline citations to reliable, verifiable sources. As such, it contains multiple violations of Wikipedia's policy on verifiability, which states: "Even if you are sure something is true, it must be verifiable before you can add it....The burden to demonstrate verifiability lies with the editor who adds or restores material, and it is satisfied by providing an inline citation to a reliable source that directly supports the contribution." The policy is set forth here. 
In my view, this means we'd rather have a sparse article in which every important statement (including all these equations) is supported by an inline citation to a reliable source. There are no citations - none at all - in the following sections: 
* Formula; 
* Modified beta; 
* Security market line; 
* Asset-specific required return; 
* Risk and diversification; and 
* Efficient frontier. 
I hope someone will step forward to remedy this problem, which crops up in a distressing number of articles about financial mathematics. Unsourced material is subject to being removed. My qualifications for this subject are set forth in my user profile. Cordially, BuzzWeiser196 (talk) 14:10, 7 April 2021 (UTC)
thread_title: Well written, but violates Wikipedia's policy on verifiability

message: The Assumptions section does not mention that CAPM math uses variances and covariances. Given that financial instruments generally have statistics governed by stable distributions rather than Gaussian, neither variance nor covariance exist, and the math is thus entirely invalid. Also, see "heavy-tailed" discussion above, which is the same issue.
76.219.79.2 (talk) 17:07, 17 December 2021 (UTC)
thread_title:  Missing significant poor assumption