# 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