Forward

Beta (β) is a measure of a stock's relative volatility.

The 'baseline' beta value is 1.

A stock that has a beta value above 1 is more volatile than the market.

A stock that has a beta value below 1 is less volatile than the market.

For reference, here are the beta values of some well-known companies as of July 2024.

• Amazon.com Inc (AMZN): 1.15

• JPMorgan Chase & Co (JPM): 1.11

• Johnson & Johnson (JNJ): 0.52

Data source: Yahoo Finance 

I had the suspicion that on aggregate, larger companies, as measured by market capitalization (market cap), would tend to have lower beta values than smaller stocks. 

My train of thought is that:

• Larger companies are more consistent in their financial performance (fundamental)

• The stock price of larger companies should be less affected by large buy and sell orders than the stocks of smaller companies, hence lower volatility (technical)

But let's see the findings.

2 separate tests were conducted:

• Median beta by market cap group (large caps vs mid caps vs small caps)

• Regression: Beta vs market cap 

Test 1: Findings

Raw data source: Stockanalysis.com

Calculated & Graphed in Excel

Test 1: Conclusion

As expected, the larger companies as a group do have a lower beta value than the smaller companies as a group.

However, the discrepancy was not as large as I expected. In fact the difference not particulaly significant at all.

Furthermore, based on the standard deviation of each group, I notice that smaller companies tend to have a greater variability in their beta values than larger companies.

Test 2: Findings

R-squared tells us what proportion of the variation in the dependent variable (beta) can be explained by the independent variable (market cap).

An R-squared of 1 means that the 100% of the variation in the dependent variable can be fully explained by the independent variable.

Here, the R-squared is extremely low, implying that there is little relationship between market cap (company size) and beta.

I repeated the test with companies of only positive beta values, which returned similar results (R-squared was 0.000607)

Test 2: Conclusion

Test 2's results are somewhat contradictory to Test 1. 

In Test 1, we concluded that large companies tended to have slightly lower beta values.

In Test 2, we concluded that there is no significant relationship between company size and beta value.

I find Test 2 to be more accurate since it analyzes all the companies in aggregate instead of segmenting them into groups (what qualifies as a a 'large', 'mid', or 'small' cap is rather arbitrary).

Therefore my final conclusion is that there is no significant relationship between company size and beta value.