# 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?

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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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