Cross-Sectional Factor Attribution for a Portfolio and Its Benchmark
Summary
The document outlines a way to analyze a portfolio’s style exposures by linking securities’ factor characteristics to subsequent returns. It proposes a cross-sectional regression across the investment universe, with next-period stock returns as the outcome and characteristics such as dividend yield, market capitalization, valuation ratios, and other factors as explanatory variables. The estimated factor premiums then provide a common set of coefficients for analyzing both the fund and its benchmark.
For each portfolio, multiply each security’s weight by its estimated factor contribution and sum across holdings to estimate the return attributed to that factor. The remaining return is assigned to the unexplained component. This approach goes beyond comparing weighted-average characteristics, but requires return observations after the holdings snapshot and relies on a chosen factor model and regression estimates. The response notes that spreadsheet software can perform the analysis, though it may not be the most suitable tool. It gives no empirical results, and its attribution is framed around explaining a subsequent period’s returns rather than only describing static style exposure.
Key ideas
- Estimate factor premiums with a cross-sectional regression of subsequent security returns on factor exposures.
- Apply the same universe-wide factor estimates to the fund and its benchmark for comparable attribution.
- Aggregate weighted security-level factor contributions to estimate each factor’s portfolio return contribution.
- Treat the return not explained by factors as a residual component.
- The method requires subsequent returns and depends on the selected model and regression estimates.
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# Holdings based style analysis
# Holdings based style analysis
This question is not very technical. I have a file with holdings (both for the fund and the benchmark) of a number of securities and need to do a style allocation analysis. For these securities, I have different 'factors' such as dividend yield, market cap, P/E, P/B etc and I have the weights in the fund and in the benchmark. The analysis should be done in excel, but I'm not sure how to do it. I could do a 'weighted average' of each factor and then compare the outcome of portfolio to the outcome of the benchmark. But that seems too straight forward. Do you have any suggestions on how to do such style allocation analysis? Thanks
## Answer by lebelinoz (score 4)
https://quant.stackexchange.com/a/36134
I'm not exactly sure what you're asking, but since you tagged the question as factor-models, I'll assume you are modeling the next month's returns of stocks as a function of the factors:
$$r_i = \alpha_i + \beta_1f_{i1} + \cdots + \beta_Kf_{iK} + \epsilon_i$$ where
- $r_i$ is the next return of stock $i$
- $\alpha_i$ is the part of stock $i$'s return unexplained by factors,
- $f_{i1},..., f_{iK}$ are your current factor exposures (dividend yields, market caps, P/E, P/B),
- $\beta_1,..., \beta_k$ are the factor premiums which we obtain through a multilinear regression analysis, and
- $\epsilon_i$ is an error term.
From your question, it seems like you have a single point-in-time snapshot of all stocks in your universe. Since your question is a couple of months old, I can only assume that you also have the returns $r_i$ from the next month. You can now do a cross-sectional regression, where you model how much of next month's returns can be attributed to your $f_{i1},..., f_{iK}$ factor exposures.
Excel might not be the ideal tool for the job, but it can be done. This isn't the right forum for how to do such things in Excel, but this and this are both links to helpful sites on how to activate and use the Analysis ToolPak add-in for such tasks.
Once you have computed your premiums $\beta_1,..., \beta_k$, you can combine them with the weights of your portfolio. If $w_i$ are the portfolio weights, then $\sum_i w_i r_i$ is the return of your portfolio at the next month, and each $\sum_i w_i \beta_j f_{ji}$ explains how much of the portfolio's return can be attributed to that particular factor. Note that you will most likely have a big chunk leftover $\sum_i w_i \alpha_i$ which can't be explained by factors. Replace the word "portfolio" with "benchmark", and you can repeat the exercise with the whole benchmark using the same $\beta_1,..., \beta_k$ (because you used the whole universe to compute them).
I hope this helps!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.