Interpreting the Relationship Between Stock Returns and Variance

Summary

The document describes an exploratory analysis of whether stocks with greater variance have higher average returns. The author calculates returns over non-overlapping 30-day windows for a historical sample of roughly 2,600 stocks spanning nine years, then compares each stock’s mean return with its variance. The plotted relationship appears negative, which conflicts with the author’s expectation that higher risk should be compensated by higher expected return.

The text raises questions rather than resolving them: whether the apparent pattern could be valid, what might explain it, and why investors would hold stocks that appear to combine high variance with low return. It provides no plot details, statistical tests, controls, or conclusions. The observed association alone therefore does not establish a general risk-return relationship or explain its cause; the result may depend on the return definition, sample, estimation choices, or other factors not discussed.

Key ideas

• The author compares mean returns and variance across individual stocks using non-overlapping 30-day returns.
• The historical sample covers roughly 2,600 stocks over nine years.
• The plotted comparison appears to show a negative association between average return and variance.
• The document asks how this apparent pattern relates to the expectation that investors require compensation for risk.
• No statistical tests or explanation for the observed relationship are provided.

Tags

# Does the expected return increase with variance for stocks?


# Does the expected return increase with variance for stocks?












I took a historical dataset of ~2600 stocks and computed the 30-day returns for non-overlapping windows, for a 9 year period. For the returns, I computed the mean and variance. Then I plotted the mean vs the variance:

I was rather surprised to see that there seems to be a negative correlation between return and variance. I was always in the belief that investments with higher risks should yield a higher expected return, otherwise no rational buyer would go with that option. I was wondering whether this could be correct at all and if so, what would be the explanation and why would anyone consider buying stocks from the lower right side of the plot.

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.