Ordinary Least Squares Method

La méthode des moindres carrés ordinaires (MCO) est une technique statistique utilisée pour ajuster une ligne de régression à un ensemble de données en minimisant la somme des carrés des écarts entre les données observées et la ligne de régression.

Le but de cette méthode est de trouver la meilleure ligne de régression pour modéliser la relation entre deux variables en minimisant l'erreur totale entre les valeurs observées et les valeurs prédites par la ligne de régression. Elle est couramment utilisée en économie, finance et en sciences sociales pour établir des relations entre les variables.Elle permet notamment de calculer le beta et l'alpha d'une stratégie d'investissement ou de trading.

Beta is a measure of an asset's sensitivity to market movements. It measures the degree of variation of an asset in response to market fluctuations. Beta is often used to assess the risk of an investment, as it indicates how much the investment is sensitive to market changes. A beta of 1.0 means that the investment has volatility equal to that of the market. A beta greater than 1.0 indicates that the investment is more volatile than the market, while a beta less than 1.0 indicates that the investment is less volatile than the market. It corresponds to the slope of the regression line.

Alpha, on the other hand, is a measure of an investment's performance relative to its beta. It measures the risk-adjusted return of an investment, which is the return that is generated taking into account the investment's sensitivity to market fluctuations. A positive alpha indicates that the investment has outperformed the market, while a negative alpha indicates that the investment has underperformed the market. It corresponds to the y-intercept of the regression line.

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