The Portfolio Problem

Portfolio optimization starts before any solver is opened. The first decision is what the portfolio is allowed to be.

A professional allocation problem has five parts:

1. a universe of assets,
2. a forecast or view about return,
3. a risk model,
4. constraints,
5. a rule for trading through time.

The naive version is: choose weights that maximize expected return. The desk version is: choose weights that survive estimation error, turnover, concentration, liquidity, and drawdown review.

Let $w$ be the vector of portfolio weights, $\mu$ expected returns, and $\Sigma$ the covariance matrix. A common objective is: