Re: information we can tease from Beta (std. dev & corr)
well, since beta is cov/variance(market), beta * var(m) will give you covariance with the market, not standard deviation.
since beta (or covariance, since they have the same informational content about the security) only gives you one piece of information about the return series of the security, there's no good way to parse out what portion of that is attributable to volatility and what part is attributable to standard deviation.
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