Hands-On Machine Learning for Algorithmic Trading

How it works

Diversification works because the variance of portfolio returns depends on the covariance of the assets and can be reduced below the weighted average of the asset variances by including assets with less than perfect correlation. In particular, given a vector, ω, of portfolio weights and the covariance matrix, Σ, the portfolio variance, σ_PF, is defined as:

Markowitz showed that the problem of maximizing the expected portfolio return subject to a target risk has an equivalent dual representation of minimizing portfolio risk subject to a target expected return level, μ_PF. Hence, the optimization problem becomes: