In the article titled “Portfolio Theory for -Symmetric and Pseudoisotropic Distributions: -Fund Separation and the CAPM,” [1] the rescaling intended to simplify the derivation in the section titled “7. When Do We Have a Capital Asset Pricing Model?” resulted in an elementary error. The error was unnoticed because Proposition and Theorem remained mathematically correct; but, having been scaled by dispersion rather than price, the symbol ended up not being the vector of CAPM betas.
To correct this, the text “” should be deleted from the sentence “Formal differentiation yields ” in section “7. When Do We Have a Capital Asset Pricing Model?”
At the end of Proposition , the excess returns should be written for some .
Assuming the common scaling to unit price , shall read
Also, following [, ] at the end of the section, the wording is imprecise on the scale itself versus its power, the so-called covariation norm. The reader can disregard the sentence starting with “Their approach.” A more thorough treatment on this connection is given in [2].