Implementation of modern portfolio optimization (mean-variance portfolio optimization) using Monte Carlo simulation and sequential least squares programming (scipy package) in Python
In general, portfolio optimization is the process of creating a portfolio of assets, for which your investment has the maximum return and minimum risk.
Modern Portfolio Theory, or also known as mean-variance analysis is a mathematical process which allows the user to maximize returns for a given risk level. Or in other terms, minmize risk for a given return level.
It was introduced in a 1952 doctoral thesis by Harry Markowitz. It assumes that an investor wants to maximize a portfolio's expected return contingent on any given amount of risk. For portfolios that meet this criterion, known as efficient portfolios, achieving a higher expected return requires taking on more risk, so investors are faced with a trade-off between risk and expected return.
In portfolio theory, the riskiness of an asset is often measured by the variance (or standard deviation) of its returns. Variance is an important indicator of how volatile this investment will be (how returns can fluctuate). Risk-averse investors do not want their wealth to fluctuate wildly.
portfolio return:
portfolio variance:
matrix form:
efficient portfolio for any particular level of return optimzation problem:
