Beta

A widely used statistic which measures the sensitivity of the price of an investment to movements in an underlying market. In other words, beta measures an investment's price volatility, which is a substitute for its risk. The important point is that beta is a relative, not an absolute, measure of risk. In stock market terms, it defines the relationship between the returns on a share relative to the market's returns (the most commonly used absolute measure of risk is standard deviation). But in so far as much of portfolio theory says that a share's returns will be driven by its sensitivity to market returns, then beta is a key determinant of value in price models for share or portfolio returns.

An investment's beta is expressed as a ratio of the market's beta, which is always 1.0. Therefore a share with a beta of 1.5 would be expected to rise 15% when the market goes up 10% and fall 15% when the market drops 10%. In technical terms, beta is calculated using a least-squared regression equation and it is the coefficient that defines the slope of the regression line on a chart measuring, say, the relative returns of a share and its underlying market. However, the beta values derived from the regression calculation can vary tremendously depending on the data used. A share's beta generated from weekly returns over, say, one year might be very different from the beta produced from monthly returns over five years.

This highlights a major weakness of beta: that it is not good at predicting future price volatility based on past performance. This is certainly true of individual shares. For portfolios of shares beta works far better, basically because the effects of erratically changing betas on individual shares generally cancel each other out in a portfolio. Also, to the extent that portfolio theory is all about reducing risk through aggregating investments, beta remains a useful tool in price modeling.

Alpha

A term borrowed from statistics which is used to show how much of the investment performance of a stock or portfolio of stocks is independent of the stock market in which they trade.

• Within a simplified pricing model used to identify those portfolios of investments that deliver the best combination of risk and return, alpha is used to describe the expected return from a security or a portfolio assuming that the return from the market is zero. Thus in this model the expected return for, say, an ordinary share would be its alpha plus the market return leveraged by the share's sensitivity to market returns (its beta). Here both alpha and beta are estimated based on comparison of the historical returns of the share and the market (see also single index model).

• In measuring portfolio performance, alpha is used to define to what extent a portfolio has done better or worse than it should have done, given the amount of risk it held. If it is accepted that a portfolio's performance will (simply speaking) depend on market returns times the portfolio's sensitivity to the market, then alpha quantifies the extent to which the portfolio's return varies from its expected return. Thus it measures the extent to which the manager adds or erodes value.