Jack L. Treynor
Volume 9, Number 4, Fourth Quarter 2011
Markowitz’ 1959 book introduced a concept of value that could actually be tested. Markowitz’s quite general conditions can lead to the Central Limit Theorem.
Consider weekly returns on Markowitz’s random wheel. Then annual returns on actual prices would have 52 terms reflecting returns on value and 2 for microstructure noise. We can use such annual returns if
1) weeks are short enough that Markowitz’s approximation to the log holds for a reasonable dispersion of weekly returns (on value only, with noise excluded).
2) 52 terms in the sum is enough.
And note: whether Markowitz is a Gaussian depends on the weekly returns – not the annual returns.