CAPM beta = slope

[francisgy]

is beta in the CAMP is the slop of SML, it looks like that the formula are same.
is beta a kinds of correlation?

 

[Northeastern Student]

slope of the SML is the Sharpe Ratio, Beta is the correlation btw a stocks return and the return on the market
B = (Cov, stock, mkt)/var mkt
Sharpe: [E(rm) - rf]/stdev

 

[francisgy]

so beta is not the slope of any line CML, CAL, SML?
by the way, correlation is (COV, stock, MKT)/sigma(stock).Sigma(index), not beta.

 

[rus1bus]

First of all, SML IS presenting CAPM in graphical form. So, SML and CAPM is the same thing.
Second, Beta is not the Slope, ‘Market Risk Premium’ (Rm - Rf) is the slope. SML presents E(R) on Y axis and Beta on X axis. That is, it presents relationship between Expected return from a Security/Asset/Portfolio with its Systematic Risk (Beta).
Third, the easier to understand definition of Beta is: it is Systematic Risk with that Asset/Security/Portfolio. And the technical definition of Beta is: it is correlation between returns of that Asset/Security/Portfolio with the Market Portfolio.

 

[francisgy]

if SML is estabished, you mention beta is correlation, does the market portfolio includes risk free asset like CML and CAL?

 

[rus1bus]

Market Portfolio is of Risky Assets ONLY and does not include Risk Free Asset in it. This is true for all models, CAL, CML or CAPM.
Theoratically, Market Portfolio includes ALL possible Risky Assets available in the market. The weight of each individual asset in such portfolio is determined by a combination that is represented by Tangent Portfolio.
CAL and CML are just trying to mix this Market Portfolio with a Risk Free asset to get to a combination, which gives you maximum Return for your given Risk level.
And CAPM is using returns from this Market Portfolio to establish Market Risk Premium for any security/asset/portfolio whether efficient or not.

 

[francisgy]

I think you have a lot of typo error, but I summarize as follows:
CAPM: efficient and non -efficient, market portfolio whithout risk free assets
CAL: tangent portfolio, no market portfolio, whithout risk free assets, only efficient
CML: market portfolio, with risk free asset,only efficient
TB model: market portfolio with risk free assets
so any difference between TB and CML? I think market portfolio can contain risk free assets

 

[rus1bus]

Not read TB model yet.
But upto CAPM point in the text, Market Portfolio does NOT contain Risk Free Assets.
Anyways, now i have added motivation for my further reading in PM

 

[bpdulog]

francisgy Wrote:
——————————————————-
> I think you have a lot of typo error, but I
> summarize as follows:
>
> CAPM: efficient and non -efficient, market
> portfolio whithout risk free assets
>
> CAL: tangent portfolio, no market portfolio,
> whithout risk free assets, only efficient
>
> CML: market portfolio, with risk free asset,only
> efficient
>
> TB model: market portfolio with risk free assets
>
> so any difference between TB and CML? I think
> market portfolio can contain risk free assets
TB contains risk free assets as well, but since you are actively managing the portfolio, you are able to achieve higher returns per unit of risk than those based on the efficient frontier. Your optimized portfolio is P*, which I believe lies on the point of tangency with the CAL.