Talk:Capital asset pricing model

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[edit] Comments

I think the last point of the shortcomings should be explained better, or be removed:

Because CAPM prices a stock in terms of all stocks and bonds, it is really an arbitrage pricing model which throws no light on how a firm's beta gets determined.

I understand all other points, but do not know what is meant by the last point...128.130.51.88 16:21, 16 March 2007 (UTC)


I think two of the shortcomings are not quite right.

"The model assumes that all investors are risk averse. Some investors (e.g., some day traders), however, can not be considered to be risk averse."

A central idea of the model is that a day trader and a retiree can use the same pricing model, because they can assemble a portfolio that matches their different risk objectives and they can observe the market price for risk.
All the model assumes is that 1) higher returns are preferred to lower returns and 2) lower risk is preferred to higher risk.
In other words, if you offer a day trader two assets -- one highly risky asset and one lower risk asset -- with the same expected return, the day trader will pick the lower risk asset.
One can argue that the model assumes that investor behavior is rational (and that that is a shortcoming).

--->The above is not said clearly. What he/she means to say is that: (i) for a given risk level, an investor will always prefer a higher return, and (ii) for a given expected return level, an investor will always prefer lower risk.

"The model assumes that all investors create mean-variance optimized portfolios. However, there are many investors who don't know what a mean-variance optimized portfolio is."

Again, the only thing the model assumes is that 1) higher returns are preferred to lower returns and 2) lower risk is preferred to higher risk.
Variance is used as a measure of observed risk. There is no assumption that investors are using the model.
Like gravity, you don't need to know :F = G \frac{m_1 m_2}{r^2} for it to work.

If no objections, I will remove these shortcomings. Thoughts? -Chris vLS 20:52, 10 Dec 2004 (UTC)

I agree with you, especially about the day traders. Whoever wrote this sentence confused willingness to accept risk with an actual DESIRE for risk. Evel Knievel was not a day trader. Furthermore, its been 2 weeks since you asked this question and nobody has sought to defend these passages yet, so ... let's roll! --Christofurio 00:43, Dec 22, 2004 (UTC)

Done! Thanks for the encouragement! --Chris vLS 16:01, 22 Dec 2004 (UTC)

Hi there. Although your point is well taken, I'm not sure that you should have removed the part of about investors preference for mean-variance optimized portfolios. That actually IS one of the assumptions of the model. This isn't physics, it's not a model that the market must follow. It's a model that assumes that investors always choose the market portfolio, together with the risk-free asset. This is inherent in the definition of the market portfolio, that it's defined by investor choices, is completely diversified, and has no non-systematic risk. The market portfolio has a beta of exactly 1, and CAPM assumes that investors can choose more or less risk by buying or selling the portfolio and borrowing or lending the risk-free asset. This is known as the separation theorum of capm: that every investor can participate with their own risk preference by buying just a market index fund and the risk free asset.

--Tristan Reid 10 Feb 2005 (UTC)


Actually, let me amend what I said: investors don't prefer mean-variance optimized portfolios, investors choices in aggregate (as contributing parts of the market portfolio) are mean-variance optimized. --Tristan Reid 09:46, Apr 06, 2005 (UTC)

--->Tristan, I'm not sure what you mean when you talk of aggregation. All investors are mean-variance optimisers in that they will prefer, for a given risk level, MAXIMUM returns. that is all. This is THE fundamental assumption of the CAPM.-Ben

Hi Ben. Not all markets are accessible to all people (such as 144a assets, or restrictions on foreign markets). The given risk level is only defined by the covariance of the assets in the portfolio, but some investors are also concerned with other risks, e.g. liquidity. Investors can add these different constraints on the mean-variance objective function without breaking CAPM. That's what I mean by 'in aggregate'. If you model that everyone is chasing the same assets, the liquity constraint will only be satisfied if investors either hold non-zero weighted chunks of the entire market, or that they hold enough of the market to be locally diversified. By considering all investors together, both of these problems are solved and CAPM is satisfied. It's very much like a Nash equilibrium. Tristanreid 21:55, 8 February 2006 (UTC)

[edit] The CAPM graph is wrong for negative betas.

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)

Gold gives you lower than risk free rates of return because it has a negative beta (one of the few real assets that behaves this ways). As mentioned above, insurance gives you a negative return and a negative beta. There's no reason the graph can't extend even farther than shown into negative rates of return. Kjm 20:58, 30 December 2005 (UTC)

The perfect example of a negative beta, less than riskfree rate asset is your homeowner's insurance which is priced to yield negative absolue returns yets freely trades.

[edit] For Dummies?

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)

[edit] Article removed from Wikipedia:Good articles

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)


[edit] Should article include empirical estimation of CAPM?

Hello -- all --- reading this article offers a pretty good intro CAPM. Congrats to all. It explains the structure and assumptions of the model. Some extenstion suggestions to improve this excellent article and make it more comprehensive. Should this article include a brief review of the mail empirical issues in estimating CAPM? Or rather, should a new article, different from this entry, focus on the emprical issues of "correctly" estimating CAPM? Finally, should International CAPM (a la Solnik) be included in this entry or anchor a new one? Psw2xx

[edit] Formula is insufficient for the model

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)

[edit] Formula is OK but tests should be mentioned

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)

[edit] What about location-scale?

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)