Why the Average Beta of Index Constituents Can Fall Below One
Summary
The discussion examines why the mean estimated market-model beta for Australian All Ordinaries constituents can be below one. The researcher estimates separate betas for 300 firms over a one-year window and asks whether the index’s market-cap weighting explains a mean near 0.60, especially given a higher result reported for NASDAQ stocks.
Follow-up experience across several indexes, data sources, frequencies, and estimation windows found average betas generally below one, including after market-cap weighting. The reported results varied over time, and a colleague’s EUROSTOXX 600 work reached one only with a very long estimation window and capitalization weights. The answer suggests that short samples and limited price precision may contribute, particularly for smaller stocks, so a mean below one is not by itself evidence of an error. These are empirical observations rather than a universal rule; the account does not establish a definitive cause or provide a formal test of beta estimation bias.
Key ideas
- A cross-sectional mean of constituent betas need not equal one when estimated over a short window.
- Market-cap weighting alone did not bring the reported average estimates to one.
- Results varied across time periods, indexes, data sources, frequencies, and estimation windows.
- Price rounding and limited precision for smaller firms may affect beta estimates.
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Full text
# Average beta of index consitutents w.r.t. the index is 0.60
# Average beta of index consitutents w.r.t. the index is 0.60
I have 1 year time series data of 300 constituents of the Australian All Ordinaries index (which is composed of 491 firms). The missing firms are mostly smaller firms.
I run the market model $R_{it} = a_i + b_i R_{mt} + e_t$ for $i \in \{1,...,300\}$. Then I take $\textrm{mean}(\hat{b}_i)$ and it's equal to $0.60$.
Is it a problem that it isn't approximately $1.0$? $0.6$ seems a bit low. Is a potential explanation that the AORD is market capitalization weighted, but I'm taking the unweighted mean of $\hat{b}_i$.
Concern is heightened when reading "Stock market crashes, firm characteristics, and stock returns" which took a similar mean over NASDAQ and got 1.20 average market model slope estimate (however they use CRSP).
All data is from Datastream.
## Answer by user2921 (score 1, accepted)
https://quant.stackexchange.com/a/4219
What I did was I got the constituent data for multiple indexes from Datastream. I made 3 constituent datasets for each index, `P`,`PI` and `RI` datatypes in datastream. I also got the index-level price data from multiple sources - Datastream as well as Yahoo Finance. I also got weekly and daily data.
In the end I always arrived at a mean market model beta of 0.6-0.9, even after market capitalization weighted. The mean beta was always around 0.6 before 2004 and generally around 0.7-0.9 around 2008 (all 1 to 8 year estimation windows).
My supervisor says that he had this problem with the EUROSTOXX 600 and the only way that he and his co-author could get the mean beta to 1.0 was using a massive estimation window (30 years) and market capitalization weights.
So I guess it's not that much of an issue when I'm using a shorter window with worse rounding (because All ords has a lot of small stocks which trade to 3 dp that datastream cuts off).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.