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Inverse Relationship between Volatility and Beta
For any isolated equity market, its beta will less resemble the betas of all other interconnected equity markets.  For interconnected markets, beta is not well-dispersed, especially during a world expansion because richer nations have more wealth thus a dominant influence over smaller nations' equity markets causing a convergence.  If the world is in recession, or a country is in recession, all betas or the recessing country's beta will start to diverge, respectively.  If the world's economies diverge, their equity markets' betas will too.  If a country is having financial difficulty, its beta too will diverge. Beta is correlation against a ratio of variance, so variance or "volatiliy" is only half of that equation.  Correlation or "direction" is the other half.  The ratio of variance will give the magnitude of beta, and correlation will give the sign or "direction". Therefore, interconnected emerging equity markets should have higher beta magnitudes because they are more variant but should generally over time have signs that more closely resemble the rest.  A disconnected emerging equity market will improbably have average betas both by magnitude and direction.