Why CAPM Beta Depends on Market Index Composition
Summary
The document explains how a country’s estimated CAPM beta against a world index depends on covariance with that index, not on the country’s standalone volatility alone. A country can have a beta below one even when its market is more volatile than developed markets if its returns have a lower correlation with the chosen benchmark. Conversely, a large index constituent may have a high beta because its returns strongly influence and co-move with the benchmark.
The discussion uses a regression of regional excess returns on a global index and notes that the United States is a large part of the index, which can raise its measured covariance relative to China’s. A second answer warns that concentrated local indices can make betas misleading: estimates may effectively reflect one dominant company, and many smaller stocks can show betas below one even when the weighted average is one. Beta should therefore be interpreted in light of benchmark composition, with other risk measures considered where appropriate.
Key ideas
- CAPM beta equals an asset’s covariance with the benchmark divided by the benchmark’s variance.
- Higher standalone volatility does not guarantee a higher beta when correlation with the benchmark is lower.
- A large benchmark constituent can have high measured covariance with the index that includes it.
- Concentrated market indices can distort beta estimates for smaller constituents.
- Beta is benchmark-dependent and may not fully describe emerging-market risk.
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Full text
# How well does CAPM beta track the risk of a particular market relative to world markets?
# How well does CAPM beta track the risk of a particular market relative to world markets?
Can the CAPM beta of emerging markets be less than the beta of the developed markets?
As part of my research, I run regressions using market indices. I estimate the beta using a regression of MSCI country/region excess returns on the excess returns of the MSCI ACWI. Excess returns are returns minus the risk-free rate (which I take to be the T-bill rate). When running this regression, I found the following strange result. While the beta of China is less than 1, the beta of the USA and of Europe are greater than 1. Can anyone please explain this result?
## Answer by Tal Fishman (score 5, accepted)
https://quant.stackexchange.com/a/1744
What you observe in your regression is not strange at all. The regression beta you estimated is
$\beta_i = \frac {\mathrm{cov}(r_i,r_m)}{\mathrm{var}(r_m)}$
where $i$ represents the country/region (such as the USA or China) and $m$ represents the "market" (which you take to be the ACWI). Since the USA is itself such a large component of the ACWI (about 40%, I believe) it is not surprising to find that its covariance with ACWI is much greater than China's, even though China probably has a much greater variance than the USA. Recall that covariance is
$\mathrm{cov}(r_i,r_m)=\rho_{i,m}\sigma_i\sigma_m$.
Even though $\sigma_i$ is likely higher for China, $\rho$ is much higher for USA.
## Answer by Ram Ahluwalia (score 4)
https://quant.stackexchange.com/a/1745
Beta as a measure of risk has serious drawbacks, particularly in emerging markets. You need to consider alternative risk metrics (cost-of-capital build-up method or volatility, for example), or if you do use beta consider what the market index refers to and the composition of that index.
This paper actually happens to touch on beta estimation and uses Brazil's Bovespa as an illusration.
Here's a choice excerpt:
"The good fit is deceptive, however. Telebras is 40% or more of the Bovespa, and this has some strange consequences. The first is that the beta estimates for all other Brazilian stocks essentially become regressions of those stocks against Telebras, rather than a diversified stock index. The second is that more than 90% of all stocks on the Brazilian index were reporting betas less than one at the time of this regression. Since it is the weighted average beta that is one, and Telebras has a beta greater than one, this asymmetry in beta estimates becomes possible. The third and most troubling consequence is that it is the smallest, riskiest companies in the Brazilian market that have the lowest betas, while the largest and most estabilished firms have the highest betas."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.