Portfolio optimization is one of the most important topics in quantitative finance. This is one of the first areas in quant finance to receive the attention of serious academic work; in fact, the case could easily be made that the father of quantitative analysis is Harry Markowitz, who published a landmark paper entitled "Portfolio Selection."[] He invented a technique known as mean variance optimization, which is still ubiquitous today, though much sophistication has been built around its core. In 1990, he shared a Nobel Prize with William Sharpe for both their contributions to the understanding of the quantitative analysis of portfolio construction.

Portfolio optimizers are based on the principles of modern portfolio theory (MPT), which are canonical in the asset management industry. The core tenet of MPT is that investors are inherently risk averse, meaning that if two assets offer the same return but different levels of risk, investors will prefer the less risky asset. A corollary is that investors will take on extra risk only if they expect to receive extra return as compensation. This introduced the concept of risk-adjusted return. Mean variance optimization is a formal way of building portfolios based on MPT. Mean and variance are two of the inputs to the optimizer, and the output is a set of portfolios that have the highest return at each level of risk. The mean in question is the average expected return of each asset being evaluated. Variance ...

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