Returns-based style analysis

Returns-based style analysis is a statistical technique used in finance to deconstruct the returns of investment strategies using a variety of explanatory variables. The model results in a strategy's exposures to asset classes or other factors, interpreted as a measure of a fund or portfolio manager's investment style. While the model is most frequently used to show an equity mutual fund’s style with reference to common style axes (such as large/small and value/growth), recent applications have extended the model’s utility to model more complex strategies, such as those employed by hedge funds. William F. Sharpe first presented the model in his 1988 article "Determining a Fund’s Effective Asset Mix". Under the name RBSA, this model was made available in commercial software soon after and retains a consistent presence in mutual fund analysis reporting. As the investment community has expanded beyond security selection to the embrace of asset allocation as the critical driver of performance, additional papers and studies further supported the concept of using RBSA in conjunction with holdings-based analysis. In 1995, the paper 'Determinants of Portfolio Performance' by Gary Brinson, L. Randolph Hood, and Gilbert L. Beebower, demonstrated that asset allocation decisions accounted for greater than 90% of the variability in a portfolio's performance. RBSA uses the capital asset pricing model as its backbone, of which William Sharpe was also a primary contributor. In CAPM, a single index is often used as a proxy to represent the return of the market. The first step is to extend this to allow for multiple market proxy indices, thus: where: is the time stream of historical manager returns, is a set of time streams of market indices or factors, is the number of indices or factors used in analysis, is the intercept of the regression equation, often interpreted as manager skill, is the error, to be minimized using ordinary least squares regression. The beta coefficients are interpreted as exposures to the types of market returns represented by each chosen index.