# 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?

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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.

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Thank you for you reply, – Pasha Aug 23 '11 at 14:47
@Pasha no problem, and thanks for contributing to the site. If you like an answer, you can mark it as accepted with a check mark. – Tal Fishman Aug 23 '11 at 14:48
Thank you for you reply, i do really appreciate, I agree with you...one more thing arises following the same logic the Russia should have also llittle beta however the betta of Russia 1.35 which is more than USA, Europe and China.. once more thank you for quick reply – Pasha Aug 23 '11 at 14:56
@Pasha I would first try to measure the correlations, variances, and covariances separately, see what is the source of the difference in betas in each case, then investigate further. It may just be the case that China has greater idiosyncratic risk than Russia, so that Russia's greater variance wins out over the lower correlation, while in China the reverse occurs. You should also try running these regressions over different horizons (daily, weekly, monthly returns) and different sub-periods (last 5 years, 10 years, etc.). – Tal Fishman Aug 23 '11 at 14:58
thank you for detailed explanation!! – Pasha Aug 23 '11 at 15:07

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."

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Excellent illustration of some of the practical pitfalls of using beta as a risk measure, particularly with single stocks against non-diversified indices. @Pasha to solve your problem you may want to also dig into the constituents of the MSCI China and Russia indices and see whether they are dominated by just a few companies. – Tal Fishman Aug 23 '11 at 15:21
Quant Guy and @Sheegaon, I do appreciate your explainations, they are really useful.. thank you – Pasha Aug 23 '11 at 15:51