how is the beta determined for a stock or mutual fund?

Beta is a term that derives from a mathematical model in finance, known as the Capital Asset Pricing Model (or CAPM for short). CAPM is used for pricing an individual security or a portfolio.

In its simplest form (for pricing a single security), the model is represented by the following linear equation:

E = I + B.X

Where:

E is the expected return on the security

I is the interest rate (risk free rate)

B is the Beta of the security

X is the expected excess return of the market (i.e. expected market return - interest rates)

In THEORY, an asset is correctly priced when its estimated price is the same as the required rates of return calculated using the CAPM. The CAPM returns the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness.

A Beta figure greater than one implies more than average "riskiness" for the security being priced. A beta figure of less than one implies lower than average (where averaging is being done in relation to the market the security belongs to).

Calculating the beta of a security (for e.g. a stock or a mutual fund), involves doing two things:

1. Arranging the terms of the equation above, so that B is expressed in terms of the other variables in the equation: (B = (E-I)/X)

2. Determining the expected market rate of return. This is usually estimated by measuring the Geometric Average of the historical returns on a market portfolio (typically, a stock market index).

Note: Remember to extract the interest rate from the calculated expected market return

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