Absent of Risk Free - Non Standard CAPM

[PL]

Hello David,

according to your notes:

If we assume there is neither riskless lending nor borrowing, CAPM still applies except
borrowing (lending) at the riskfree asset is replaced by shorting (going long) the zerobeta
portfolio. This is the zero-beta CAPM;

The zero beta portfolio is not efficient. Is the market portfolio efficient (as in standard CAPM)?

 

[David Harper CFA FRM]

Hi PL,

Elton (the author of the text) says: yes, the market portfolio remains efficient in the zero-beta CAPM. To be candid, I am not really clear on exactly the location of the efficient frontier in the zero beta CAPM. Selected from among several pages in the text, emphasis mine:

"No Riskless Lending or Borrowing: This model [zero-beta CAPM] is the second most widely used general equilibrium model. The simple capital asset pricing model developed in the last chapter is the most widely used. .... Let us see if we can learn anything about the location of this minimum variance zero-Beta portfolio. First, we know that the expected return on the zero-Beta portfolio must be lower than the expected return on the market portfolio. The market portfolio is on the efficient segment of the minimum variance frontier, and the slope at this point must be positive. Thus, as we move along the line tangent to R–M toward the vertical axis, we lower return. Since R–Z is the intercept of the tangency line and the vertical axis, it has a return less than R–M. Second, as we prove below, the minimum variance zero-Beta portfolio cannot be efficient. the reader of its truth. Those interested in a rigorous proof are referred to Fama (1970).
... With homogeneous expectations, all investors face the same efficient frontier. Recall that with short sales allowed, all combinations of any two minimum variance portfolios are minimum variance. Thus, if we combine any two investors’ portfolios, we have a minimum variance portfolio. The market portfolio is a weighted average or portfolio of each investor’s portfolio where the weights are the proportion each investor owns of the total of all risky assets. Thus, it is minimum variance. Since each investor’s portfolio is efficient and since the return on the market is an average of the return on the portfolios of individual investors, the return on the market portfolio is the return of a portfolio on the efficient segment of the minimum variance frontier. Thus, the market portfolio is not only minimum variance but efficient."

Thanks,

 

[Aleksander Hansen]

My understanding is that the market portfolio is efficient however the opportunity set is no longer unique. That is, one can construct an arbitrary number of portfolios that are efficient, meaning that all investors no longer hold the same mix of risky assets. Although we have an arbitrary number of portfolios giving us the market portfolio (as opposed to the unique mix of risky and risk less in CAPM) the equilibrium return must still be unique.

 

[PL]

dear both thank u for your prompt & detailed replies. from my point of view -now - i understand that
1. market portfolio is still efficient,
2. zero beta is not and
3. investors do not hold the same risky asset portfolio (now its a function of how risk averse or not is the investor).