Investment Volatility: A Critique of Standard Beta Estimation and a   Simple Way Forward
  Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation - least squares regression - is inconsistent with these interpretations. We present the case for an alternative beta estimator which is more appropriate, as well as being easier to understand and to calculate. Unlike regression, the line fit we propose treats both variables in the same way. Remarkably, it provides a slope that is precisely the ratio of the volatility of the investment's rate of return to the volatility of the market index rate of return (or the equivalent excess rates of returns). Hence, this line fitting method gives an alternative beta, which corresponds exactly to the relative volatility of an investment - which is one of the usual interpretations attached to beta. 
Chris Tofallis
q-fin.PM q-fin.RM