Why a Weighted Stock Portfolio Can Have Low Index Regression Fit
Summary
The document asks why a regression of an unequally weighted stock portfolio on a market index produces a lower R-squared and a beta nearer zero than a regression of one constituent stock. The response offers possible explanations rather than a definitive diagnosis: the individual stock may simply track the index more closely, or portfolio constituents may have distinct return behavior that weakens the aggregate relationship.
It recommends examining each holding’s return history for abrupt repricing linked to corporate events, such as takeover activity or downgrades. It also notes that constituent and portfolio volatility can differ from that of the single stock, affecting the regression fit. The answer closes by pointing to standard errors as another diagnostic. The document supplies no data, calculation, or confirmed explanation, so its suggestions are a checklist for investigation rather than evidence about the particular portfolio. It also does not clarify whether the regressions use returns or price levels, an important modeling detail.
Key ideas
- A portfolio’s relationship with an index can differ from that of one constituent stock.
- Corporate actions or other abrupt repricing can reduce the fit of a regression.
- Inspect each holding’s return history to identify unusual moves.
- Differences in return variability may help explain changes in regression fit.
- Standard errors can complement beta and R-squared when assessing a regression.
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Full text
# Regression of Unequally Weighted Portfolio against a Single Index # Regression of Unequally Weighted Portfolio against a Single Index When I regress a single stock against a market index, I get a high value of R2 and beta closer to 1. ``` APPL.fit <- lm(APPL ~ JKSE) ``` When I regress an unequally weighted portfolio against a market index, I get a lower R2 and beta close to 0. ``` portfolio <- APPL*0.3 + WERT*0.1 +QRT*0.2 + POK*0.15 + LOI*0.15 + POI*0.03 +OLI*0.07 Port.fit <- lm(portfolio ~ JKSE) ``` Am I doing it wrong? ## Answer by Matt Wolf (score 2) https://quant.stackexchange.com/a/8415 I find this an applicable question to asked here and there could be several reasons for your stated regression results: - Apple could be simply more highly correlated with the Jakarta stock index than the portfolio you have given with your stated weights. - It could be that one or more of the stocks you specified in your portfolio reflects abnormal returns, such as a takeover bid, merger, analyst downgrade, or any other corporate action which may have caused the stock to be discontinuously repriced 50% higher or lower. That alone could cause a big drop in the R2. I would investigate each individual stock over the observation period and verify that the returns fall into a certain bandwidth around its own long term mean. - Not being familiar with the individual stocks of your given portfolio it could be that despite normal trading conditions that the return variability of some of the stocks and the resulting portfolio variance is way higher than the one of Apple's returns. In summary, you need to understand the individual stock return dynamics in your portfolio if you want to explain the drop in R2. How do your standard errors look like?
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