Beta definition A measure of an asset's risk in relation to the market (for example, the S&P500) or to an alternative benchmark or factors. Roughly speaking, a security with a beta of 1.5, say, will move 50% more than the market. So if the market goes up by 20% the security’s price will go up by 30%. According to asset pricing theory, beta represents that part of the risk of the security called systematic risk that cannot be diversified away. When using beta, there are a number of issues that you need to be aware of: (1) betas may change through time; (2) betas may be different depending on the direction of the market (i.e. betas may be greater for down moves in the market than for up moves); (3) the estimated beta will be biased if the security does not frequently trade; (4) the beta is not necessarily a complete measure of risk (you may need multiple betas).
Regression parameters There are 3 key decisions: • Relative index • Date range • Period or returns interval Raw vs. adjusted beta The beta of a stock can be presented as either an adjusted or raw beta. Raw beta, also known as historical beta, is obtained from linear regression based on the observed relationship between the security’s return (using historical data) and the returns on an index. The adjusted beta is an estimate of a security’s future beta. It is initially derived from historical data, but is modified by the assumption that a security’s true beta will move towards the market average over time. The formula used to adjust beta is: (0.67) x Raw Beta (0.205) + (0.33) x 1 = 0.470
R squared The R squared of 0.029 suggests that 2.9% of the risk in Wal-Mart comes from market sources, and the balance of 97.1% of the risk comes from firm specific components. The latter risk should be diversified away and therefore should not attract a higher expected return.
Standard error of beta At a 67% confidence level (or one standard deviation from the mean): Actual Beta =...