need visual aid to learn about SML and CML, and how they relate to efficient frontier

I understand the efficient frontier (or at least the academic idea of it)

What I don’t understand is how we’re supposed to chart the CML, SML, and the tangent points. If someone has an article with graphs, please link :slight_smile:

Sorry I don’t have what you want but I’ll post what I have in case it helps.

The Efficiency Frontier and CML / CAL can be plotted together because they have the same axes:

x = standard deviation y = returns

The CFA books definitely have graphs of these two plotted together, I’m guessing Schweser will too.

The SML / SCL are not plotted with them because the x axis is beta, not SD. They are measuring different things

On the CML, market portfolio has an x-coordinate of ‘market SD’, but on the SML the market portfolio has an x-coordinate of 1 (market’s beta = 1), but they should be equivalent, you can imagine every point on the CML has it’s x-coordinate divided by the market SD to get the SML. This is because the market portfolio has only systematic.

You can’t do the same for the CAL and SCL because the portfolio may have unsystematic risk, so the CAL and SCL are not necessarily equivalent. (someone correct me if I’m wrong)

Here’s some charts I drew myself for understanding Sharpe Ratio, M- Squares, Treynor Ratio and Jensen’s Alpha. For all of them, it’s the share ratio of portfolio P, treynor ratio of portfolio P etc.:

X-axis is Standard Deviation (total risk):

X-axis is Beta (systematic risk):

and shame on CFAi for not putting something like this in the books, would have saved me a lot of time

Here’s an article I wrote that may be useful: http://financialexamhelp123.com/cal-vs-cml-vs-sml/.