Relationship between SML & CML and Sharpe & Treynor

[jutda]

I have some trouble understanding the exact relationship between the above mentioned terms.
I understand that on the CML there are efficient portfolios only and it is measured against total risk (sigma) and the SML includes singles assets and is measured against beta (systematic risk).
What I do not understand is why are efficient portfolios (on the CML) measured against total risk (since they are efficient, they dont include any unsystematic risk, right?) so in my opinion they should be measured agains beta.
However, single securities (on the SML) usually include unsystematic risk and are measured in relation to beta (why not total risk?).
When I look at risk-adjusted return analysis (Sharpe and Treynor), here it would make sense to me. Efficient portfolis are ranked with the Treynor ratio (beta / systematic risk) and all other securities with the Sharpe (as they include both unsystematic and systematic risk).
I hope someone can help me understand these relationships (CML, SML, Beta and Treynor, Sharpe). Thanks a lot in advance.

 

[lunacy]

Here is my understanding. Correct me if I am wrong.
First, the SML does not only include individual assets. It can be used to calculate the return of anything that has a beta. The expected return only depends on systematic risk (which is represented by beta), so as long as we have the beta of a security/portfolio, we can calculate its expected return using the SML. The amount of unsystematic risk is irrelevant.
The CML is derived from the calculation of expected return for a portfolio that includes a risky asset and a risk-free asset. Its variables do not include beta, so beta is irrelevant here. The independent variable is total risk, and in order to make the calculation of the dependent variable (expected return) correct, total risk should only include systematic risk. Therefore, the CML is only used for efficient portfolios.

 

[S2000magician]

I wrote an article on CAL, CML, and SML that may be of some help here: http://financialexamhelp123.com/cal-vs-cml-vs-sml/
I haven’t gotten around to writing an article on Sharpe, Treynor, Sortino, and so on, but I will.

 

[IHateMyLIFO]

CML, which has a slope = sharpe ratio , assumes all market participants holds the optimal risk portfolio. Given the assumption that everyone predicts has same expected returns and correlations between assets, the optimal risky portoflio is the market portfolio (which by definition, has a beta of 1). In well diversified portfolios, only systematic risk is relevant because unsystematic (company specific) risk is diversified away. And because diversifcation is assumed to be costless, investors are only compensated for incurring systematic risk ( beta). This is why the SML( graph of CAPM) uses sytematic risk (beta) instead of total risk (beta + unsystematic risk)… to show the compensation one should expect for incurring systematic risk. Since any asset can have a beta, you can derive expected returns for stocks and portfolios alike, just as lunacy said.
An individual asset will plot on the SML, but will plot below the CML if i remember correctly.