# Beta, Systemic Risk and the Characteristic Line

Suppose the price of a share selected for inclusion in a portfolio happens to increase when the equity market rises. Of prime concern to investors is the extent to which the share's total price increased because of unsystematic (specific) risk, which is diversifiable, rather than systematic (market) risk that is not.

A practical solution to the problem is to isolate systemic risk by comparing past trends between individual share price movements with movements in the market as a whole, using an appropriate all-share stock market index.

So, we could plot a "scatter" diagram that correlates percentage movements for:

- The selected share price, on the vertical axis,

- Overall market prices using a relevant index on the horizontal axis.

The "spread" of observations equals unsystematic risk. Our line of "best fit" represents systematic risk determined by regressing historical share prices against the overall market over the time period. Using the statistical method of least squares, this linear regression is termed the share's Characteristic Line.

Figure 5.1: The Relationship between Security Prices and Market Movements The Characteristic Line

As Figure 5.1 reveals, the vertical intercept of the regression line, termed the alpha factor (a) measures the average percentage movement in share price if there is no movement in the market. It represents the amount by which an individual share price is greater or less than the market's systemic risk would lead us to expect. A positive alpha indicates that a share has outperformed the market and vice versa.

The slope of our regression line in relation to the horizontal axis is the beta factor (b) measured by the share's covariance with the market (rather than individual securities) divided by the variance of the market. This calibrates the volatility of an individual share price relative to market movements, (more of which later). For the moment, suffice it to say that the steeper the Characteristic Line the more volatile the share's performance and the higher its systematic risk. Moreover, if the slope of the Characteristic Line is very steep, b will be greater than 1.0. The security's performance is volatile and the systematic risk is high. If we performed a similar analysis for another security, the line might be very shallow. In this case, the security will have a low degree of systematic risk. It is far less volatile than the market portfolio and b will be less than 1.0. Needless to say, when b equals 1.0 then a security's price has "tracked" the market as a whole and exhibits zero volatility.

The beta factor has two further convenient statistical properties applicable to investors generally and management in particular.

First, it is a far simpler, computational proxy for the covariance (relative risk) in our original Markowitz portfolio model. Instead of generating numerous new covariance terms, when portfolio constituents (securities-projects) increase with diversification, all we require is the covariance on the additional investment relative to the efficient market portfolio.

Second, the Characteristic Line applies to investment returns, as well as prices. All risky investments with a market price must have an expected return associated with risk, which justify their inclusion within the market portfolio that all risky investors are willing to hold.

Activity 1

If you read different financial texts, the presentation of the Characteristic Line is a common source of confusion. Authors often define the axes differently, sometimes with prices and sometimes returns.

Consider Figure 5.2, where returns have been substituted for the prices of Figure 5.1. Does this affect our linear interpretation of alpha and beta?

Figure 5.2: The Relationship between Security Returns and Market Returns The Characteristic Line

The substitution of returns for prices in the regression doesn't affect our interpretation of the graph, because returns obviously determine prices.

- The horizontal intercept (a) now measures the extent to which returns on an investment are greater or less than those for the market portfolio.

- The steeper the slope of the Characteristic Line, then the more volatile the return, the higher the systematic risk (b) and vice versa.

We began by graphing the security prices of risky investments and total market capitalization using a stock market index because it serves to remind us that the development of Capital Market Theory initially arose from portfolio theory as a pricing model. However, because theorists discovered that returns (like prices) can also be correlated to the market, with important consequences for internal management decision making, as well as stock market investment, many modern texts focus on returns and skip pricing theory altogether.

Henceforth, we too, shall place increasing emphasis on returns to set the scene for Chapter Seven. There our ultimate concern will relate to strategic financial management and an optimum project selection process derived from models of capital asset pricing using b factors for individual companies that provide the highest expected return in terms of investor attitudes to the risk involved.