I'm reading age 35 of "Advances in Machine Learning" by de Prado.
Consider an IID multivariate Gaussian process characterized by a vector of means μ, of size Nx1, and a covariance matrix V, of size NxN. This stochastic process describes an invariant random variable, like the returns of stocks, the changes in yield of bonds, or changes in options’ volatilities, for a portfolio of N instruments. We would like to compute the vector of allocations ω that conforms to a particular distribution of risks across V’s principal components.
The only way to calculate these means or covariance matrices are from historical data for a particular stock. But this does not seem to be useful at all. The "risk" or variance of a stock will drastically change due to events. Tesla may be a low variance stock from 2008 - 2012, but then balloon like crazy upon news its profit is positive. So how is designing a portfolio using historical statistics of mean or covariance useful at all?