Say I have a time series of portfolio returns (mutual fund xyz), time series for the benchmark, and time series for MSCI style indices (value, momentum, quality, low vol). Note: style indices are long only portfolios and not long short (therefore they are somewhat correlated)

Problem

US equity Mutual fund (xyz) with a growth tilt that is benchmarked relative to the S&P 500 have generated in 2020 absolute returns of 40% and have outperformed the benchmark by 15% in 2020. (as such benchmark absolute returns is 25%)

Objective

Is to attribute the return of the portfolio to the market and specific styles. The ultimate goal is to make a decision whether to maintain exposure to the active mutual fund or I am better off by investing in smart beta funds with lower management fees.

Desired outcome

Is to explain the outperformance of 15% by saying:

1. Portfolio exposure to the market contributed 27%
2. Portfolio underweight exposure to value contributed 16%

Therefore total return of the portfolio is:

$$R_p$$ = stock selection + factor contribution

Or: 40% = stock selection + 27% + 16%

Therefore: Stock selection = -3%\$

Additional information I have explored the topic and it seems that a popular approach is to use OLS regression beta’s however, given that style indices are highly correlated, OLS assumptions tend to be unstable. Further, some funds may have a short track record hence OLS betas may not be accurate.

The goal from posting this is to obtain your feedback and knowledge on ways to approach this problem.

Thank you and your help and input is highly appreciated.