I added a picture. I have the xfig source, so it is possible to modify it if this is too clunky. CSTAR 04:15, 1 Jul 2004 (UTC)
Oops I noticed in the text that you're plotting risk on the Y-axis, whereas I plotted it on the X-axis. Also I'm callin the measn \mu (which is common ampng probabilists) Well I can fix this, if you think it's worth it. CSTAR 05:07, 1 Jul 2004 (UTC)
I think it would tie in closer with the article if the axes were labelled as per the text -- ie. return and risk -- as well as per the notation as above.
I'll change the graphic, although it seems that yuu changed the text to have risk on X axis.
Is the assumption that between alternatives of equal risk choose one with largest expected return not necessary? (I haven't thought about the minimal number of assumptions so maybe this follows from risk aversion) CSTAR 12:42, 2 Jul 2004 (UTC)
Thanks for the graphic. The arguement is (ultimately) built around standard deviation as opposed to variance, could the graph reflect that?
I think the assumptions are equivalent and are used interchangeably....
- Ooops you're right the CML is linear in the space of standard deviation, risk pairs. Oh well, I'll fix that.CSTAR 15:27, 2 Jul 2004 (UTC)
- I adjusted the graphic; I also take note of the fact that in the article risk is measured by standard deviation, which is necessary in order for the capital market line to be a straight line! CSTAR 16:45, 2 Jul 2004 (UTC)
Shorting
Maybe you should something about shorting? Or at least point to some place in Wikipedia where this is mentioned. CSTAR 18:28, 2 Jul 2004 (UTC)
- Great graphic. Will add discussion on shorting
Risk
In order for the capital market line to be straight, risk should be standard deviation not (variance). I think. CSTAR 22:47, 14 Jul 2004 (UTC)
distribution about the mean
I see no discussion of what happens when there is an asymmetric distribution about the mean, which is always the case in financial models where the asset value is bounded on the low side by ZERO.
- Exactly. This all seems to reply on the Gauss-Markov assumption (returns are normally distributed => wake up, they aren't, just use HRH on Bloomberg for a few indices or stocks). As I understand it, the CAPM can outside of the Gauss Markov assumptions (significantly beyond the scope of the definition given on this page). I do not know of any 'Omega metric' pages on wikipedia (which the derivation comes off), and feel I am probably not the best person to write one, though I would be happy to have a stab and link it in somewhere?
Expected beta
Note that the theory uses an historical parameter, volatility, as a proxy for risk while return is an expectation on the future. Is this an accurate description of the theory or of practice? I would think that the theory says that expected return and expected volatility should be used. I don't the the theory prescribes using historical beta. In practice people use historical return and historical beta, then adjust for their expectations. Since it is very hard to develop numerical estimates of beta, it is usually expected return and historical beta.
If not disagreements in the next few days, I'll make the change. Thanks. Chris vLS 20:44, 19 Nov 2004 (UTC)
OK for the change --Pgreenfinch 22:30, 19 Nov 2004 (UTC)
- Ideally, one should use some kind of time series analysis to estimate these parameters. If one makes an assumption about the nature of the underlying time series process, then there is some rational justification for making estimates of the various parameters characterizing the process. I don't have a clue in fact how the nuts-and-bolts financial analysts actually compute these numbers and whether they would take exception to the characterization given in the article, but I think the person that put that material in (fintor) is knowledgeable about practices in this area. CSTAR 22:40, 19 Nov 2004 (UTC)
- Oh, I'd absolutely agree about it as a statement of practice. I thought that it currently reads like a criticism of the abstract theory itself, claiming the CAPM nonsensically requires you to mix past and future. In practice, there are tons of historical calculations of beta, but only a few proprietary models for predicting beta (see Barra, who sells both [1]]).(Indeed, all theories tell you to focus on good estimates of the future for all modeled parameters, but in practice, detailed analysis of past perfomance gets a lot of weight.) Chris vLS 08:17, 20 Nov 2004 (UTC)
- I totally withdraw my comment. The text is correct. Nearly all forms I can find of the formula use E() to denote what is expected, and do not show E(beta). Hence, the description is correct. Sorry for the trouble. Chris vLS 19:02, 30 Nov 2004 (UTC)
Risk free asset
If you're going to change notation for rf, change it everywhere. CSTAR 18:40, 30 Nov 2004 (UTC)