Optimal Portfolios: Why and How?
Portfolio optimization is a crucial part of managing risk and maximizing returns from a set of investments. Be it for the fundamental investor, or the quantitative trader, portfolio optimization is imperative for a successful portfolio. This article delves to explain how portfolio optimization works and how to use OptimalPortfolio library to implement it.
Mean-Variance Optimization
The usual framework for optimizing portfolios was developed by Markowitz, and it is also known as the mean-variance optimization. This is due to the fact that the mean and the variance of the portfolios are the ones that are considered in finding the portfolio that maximizes the returns or minimizes risk, both of which will be defined later. The general methodology for the mean-variance optimization, as discussed by Attilio Meucci, is as follows:
- Determine market invariants.
- Estimate distribution of market invariants.
- Estimate the mean and covariance of the portfolio of assets.
- Find optimal weights for given objective function.
Market invariants are quantities that do not evolve over time. For stocks, the market invariants are the log returns. For an exploration of the issue of market invariance, do take a look at the following article…
