In returns-based style, there is R2 which measures the style fit. and 1 - R2 is Selection. How do we interpret whether the manager is actively managing or replicating the benchmark ?
Does a higher R2 means that the style which was stated is actually the style being followed and the x % returns in portfolio is explained the returns in the style indices and hence the manager is passively managing the porfolio ?
Is my understanding right?
In the example 6 its given R2=91.9% and selection is 8.1%, and it says “The portfolio does indeed appear to be actively managed, because the fraction of return unexplained by style (selection) is 8.1%, the portoflio is not merely replicating the returns on more-passive benchmark”
Here it confuses me, that this 8.1% is consider a high selection % indicating active mgt, or its a low selection % indicating active mgt.
R2 = coefficient of determination, means that xxx % of model is explained by style, and (1-R2) is return described as a selection bias or stock picking skill. In other words, (1-R2) is described by an active management. In more other words, R2 = Return to style, (1-R2) = return to skill.
Style analysis isn’t the same as holdings analysis. There may be a lot of active management, yet still a high R2 with a set of style indices. For example, a portfolio may be 50% small cap stocks and 50% fixed income, yet have an R2 of 0.9 with a large cap index.