  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.
