CAL VS CML VS SML

Hi everyone,

I am having a really hard time understanding the concepts behind CAL, CML & SML as the schweser notes doesn’t provide a conceptual working of these three, i will really appreciate if anyone can provide me video links regarding the topic or can help me understanding the concept.

CAL :

All the points on the Capital Allocation Line are combinations of

[a] The risk free rate

[b] A portfolio of risky assets

Whether your overall portfolio is 10% invested in rf and 90 % in a risky portfolio or the other way around depends on your preferences and risk tolerance / objectives.

Your CAL will be different from mine (has a different slope) because we have different risk preferences and objectives.

I may be more risk averse than you and invest 20 % in rf and 80 % in a risky portfolio. Hence we will draw different CALs.

Your risky portfolio will be different from mine.

CML :

If you impose a set of conditions on the CAL such as homogeneous expectations with respect to E® and risk of asets across ALL MARKET PARTICIPANTS you will get the CML.

While the CAL is a combination of the rf and a risky portfolio which varies across individuals, the CML is a combination of the rf and the tangency portfolio (market portfolio).

All the points on the CAL are combinations of the rf and a risky portfolio which varies from person to person according to his/her risk preferences.

All the points on the CML are combinations of the rf and market portfolio which is the same for each person.

Whether you invest 10 % in rf and 90 % in market portfolio depends again on indivifual risk preferences BUT the market portfolio is the same for EVERYONE.

There is another way to understand the CML : It is the efficient frontier in a universe where you can invest in risky stocks and the rf asset.

If you can only invest in risky assets : the efficient frontier is the upper portion of the minium variance frontier. All points on the efficinet frontier are combinations of risky assets that generate the highest return for a given level of risk.

if you can invest in risky assets and the rf asset : the efficient frontier is the CML. Remember, the CML connects the rf asset with the risky (market) portfolio…hence all the points on this line segment are combinations of the rf and the market portfolio.

SML :

Graphical representation of the notion embodied in the CAPM, that expected asset returns are linearly related to systematic risk. The greater the systematic risk (Beta) -> the greater the expected return to a risky asset.

This is due to the fact that investors need to be compensated for assuming more systematic risk, the kind of risk that cannot be diversified away by holding a portfolio of diverse assets (i.e.assets that have a less than +1 correlation).

The SML is a simple tool for determining whether an asset offers reasonable expected return for the systematic risk it entails.

A security plotting above the SML is undervalued ( its return is higher than it should be given its systematic risk implying that its price is lower than it should be )

A security plotting below the SML is overvalued (its return is lower than it should be given its systematic risk implying that its price is higher than it should be )

Also remember : the risk measure used by CAL/CML is the standard deviation of asset returns while that used by the SML is the systematic risk.

Hope this is right!

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Here are some videos on this subject which you might find useful.

Portfolio Risk and Return - Part 1B (Efficient Frontier, CAL, Risk Aversion, Optimal Portfolio) Portfolio Risk and Return - Part 2A(CML, Systematic and Unsystematic Risk, Beta, Return Generating Model) Portfolio Risk and Return - Part 2B (CAPM, SML, Sharpe, Treynor, M-Squared, Jensen)

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Thanks Arif, your lectures does provide a complete conceptual clarity…

I thought I had a relatively good understanding of these concepts, but there is one thing I can not grasp.

How can the CAL have a steeper slope, i.e. Portfolios with higher returns and lower total risk than the CML, which is said to hold efficient portfolios only?
Could anyone please explain this Detail to me?

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I have the same doubt, how can a portfolio lies outside efficient frontier, with a more efficient return to risk? Have you found out the answer?

It can’t.