Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk. Factors being considered may range from tangible (such as assets, liabilities, earnings or other fundamentals) to intangible (such as selective divestment).
Modern portfolio theory was introduced in a 1952 doctoral thesis by Harry Markowitz; see Markowitz model.
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. This risk-expected return relationship of efficient portfolios is graphically represented by a curve known as the efficient frontier.
All efficient portfolios, each represented by a point on the efficient frontier, are well-diversified. While ignoring higher moments can lead to significant over-investment in risky securities, especially when volatility is high, the optimization of portfolios when return distributions are non-Gaussian is mathematically challenging.
The portfolio optimization problem is specified as a constrained utility-maximization problem. Common formulations of portfolio utility functions define it as the expected portfolio return (net of transaction and financing costs) minus a cost of risk. The latter component, the cost of risk, is defined as the portfolio risk multiplied by a risk aversion parameter (or unit price of risk). Practitioners often add additional constraints to improve diversification and further limit risk. Examples of such constraints are asset, sector, and region portfolio weight limits.
Portfolio optimization often takes place in two stages: optimizing weights of asset classes to hold, and optimizing weights of assets within the same asset class.
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L'allocation d'actifs est une étape de la gestion d'actifs qui consiste à définir la part à donner à chaque catégorie de valeurs au sein d'un portefeuille d'investissement. L'allocation est généralement faite par secteur (cyclique, défensif, sensible), par profil (croissance, valeur), par géographie et/ou par classe d'actifs (actions, obligations, immobilier, matières premières, etc.) Pour déterminer l'allocation d'actifs optimale, l'investisseur recherche un équilibre entre le rendement attendu des actifs et les risques qu'ils représentent.
Tail risk, sometimes called "fat tail risk," is the financial risk of an asset or portfolio of assets moving more than three standard deviations from its current price, above the risk of a normal distribution. Tail risks include low-probability events arising at both ends of a normal distribution curve, also known as tail events. However, as investors are generally more concerned with unexpected losses rather than gains, a debate about tail risk is focused on the left tail.
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