Efficient porfolio and well-diversified portfolio.

[joarca1971]

I´m not sure if my idea is correct: I understand that an efficient portfolio always is a well-diversificated portfolio but a well-diversificated portfolio could be an efficient portfolio or not.

I think that because one of the assumptions for the SML it´s that the portfolios are well-diversificated and only have systematic risk ( unsytematic risk is zero because of the diversification).

But one think that I don´t undertand is that the CAMP is for port folios and assets (efficient or not), and then ¿how can a single asset can be well-diversificated?

Can someone explain me the relation this concepts please?

 

[David Harper CFA FRM]

Hi @joarca1971 Interesting! I think you are correct to say that "an efficient portfolio always is a well-diversified portfolio but a well-diversified portfolio could be an efficient portfolio or not;" i.e., efficiency implies diversification, but diversification does not imply efficiency. Below I linked to my favorite distinction between the CML and SML. You reference several ideas, to which Bodie (e.g.) devotes several chapters and over a hundred pages, but I would venture the following summary observations:

• Diversification is the lowest standard here: it is the virtual (i.e., mostly in practice, if not entirely) elimination of idiosyncratic (non systematic) risk. This is what Bodie calls naive diversification, he says a portfolio is well-diversified when it has a "large enough number of securities with each weight, w(i), small enough that for practical purposes the nonsystematic variance, σ^2(e), is negligible." (page 325). In my diagram below, there can exist diversified portfolios that are not on the portfolio possibilities curve (PPC; aka, minimum variance frontier).
• Efficiency is a relative adjective: a portfolio is more efficient than another if it offers lower risk than another with the same return, or higher return than another with the same risk. Graphically, an asset/portfolio (X) is more efficient than Y if it lies anywhere in the upper-left quadrant space. In my diagram below, the YELLOW transparent square identifies the"efficient frontier" segment of the PPC: the lower segment of the PPC is portfolios that are diversified but not efficient. (The market portfolio has the highest Sharpe ratio, is the "best" efficient risky portfolio).
• Per my link below, and the image, the CML is efficient after the risky-free asset is introduced (see how efficiency is relative to the opportunity set?! It changes after we introduce the Rf asset). Hence, the CML is a line of necessarily efficient portfolios. But the SML says the expected return is a function only of the systematic risk: it requires neither a diversified nor efficient portfolio, it says this even about a single asset. I hope that's helpful, your questions is good because it ties together a lot of theoretical material, thanks!

See also https://forum.bionicturtle.com/threads/capm-sml-cml.5347/#post-23187 i.e.,

A portfolio can be on the SML but not on the CML: "the CML is a line of efficient portfolios and only efficient portfolios. The SML/CAPM is a line for ANY portfolio or asset, including inefficient: it will take that asset/portfolio and, because it cares only about the systemic risk, give you back the expected return. But your asset/portfolio is not necessarily on the CML"
see http://forum.bionicturtle.com/threads/capm-sml-cml.5347/#post-14867

 

[joarca1971]

Tank you very much David.

Very usefull as always