# 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.

• You might try calculating the weighted version as well. Another alternative, if you don't have market caps, is to calculate the return on the equally weighted portfolio of stocks you do have and then calculate the betas with respect to those returns.
– John
Sep 22 '12 at 20:30
• First, I will get the AORD price series from alternative data source and test that. Then I will do what you've suggested. Temporal alignment is NOT a problem. Lagging $R_{mt}$ by 1 day or -1 day makes the mean slope estimate go between -0.05 and 0.05.
– user2921
Sep 23 '12 at 11:29
• Market cap weighted average of the betas improves beta by about $0.05\%$. Still way too low.
– user2921
Sep 25 '12 at 6:47
• How about using the market capitalization weights you have and calculating the returns on this portfolio. Then plot and compare and calculate the beta. My guess is that you have some kind of data problem, like the index being in a different currency or something.
– John
Sep 25 '12 at 15:54
• Ok I'll try this. At least the latest data in the time series is identical to Yahoo AU All Ords adjusted close data. With the older data the levels are a bit different but the % returns are the same up to something like 2 d.p.. I'll report back with (A) what you've suggested, (B) betas on this Yahoo data. FYI The betas on the ASX200 index are like 0.55 average, even worse.
– user2921
Sep 26 '12 at 0:52

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.