# Models Of Capital Asset Pricing

## The Beta Factor

### Introduction

In an ideal world, the portfolio theory of Markowitz (1952) should provide management with a practical model for measuring the extent to which the pattern of returns from a new project affects the risk of a firm's existing operations. For those playing the stock market, portfolio analysis should also reveal the effects of adding new securities to an existing spread. The objective of efficient portfolio diversification is to achieve an overall standard deviation lower than that of its component parts without compromising overall return.

Unfortunately, as we observed in Part Two, the calculation of the covariance terms in the risk (variance) equation becomes unwieldy as the number of portfolio constituents increase. So much so, that without today's computer technology and software, the operational utility of the basic model is severely limited. Academic contemporaries of Markowitz therefore sought alternative ways to measure investment risk

This began with the realization that the * total risk *of an investment (the standard deviation of its returns) within a diversified portfolio can be divided into

*and*

**systematic***risk. You will recall that the latter can be eliminated entirely by efficient diversification. The other (also termed*

**unsystematic***risk) cannot. It therefore affects the overall risk of the portfolio in which the investment is included.*

**market**Since all rational investors (including management) interested in wealth maximisation should be concerned with individual security (or project) risk relative to the stock market as a whole, portfolio analysts were quick to appreciate the importance of systematic (market) risk. According to Tobin (1958) it represents the only risk that they will pay a premium to avoid.

Using this information and the assumptions of perfect markets with opportunities for risk-free investment, the required return on a risky investment was therefore redefined as the risk-free return, plus a premium for risk. This premium is not determined by the total risk of the investment, but only by its systematic (market) risk.

Of course, the systematic risk of an individual financial security (a company's share, say) might be higher or lower than the overall risk of the market within which it is listed. Likewise, the systematic risk for some projects may differ from others within an individual company. And this is where the theoretical development of the beta factor (b) and the Capital Asset Pricing Model (CAPM) fit into portfolio analysis.

We shall begin Part Three by defining the relationship between an individual investment's systematic risk and market risk measured by (h) its * beta *factor (or coefficient). Using our

*and continuing with the*

**earlier notation***from previous Chapters, which ended with Equation (32):*

**equation numbering**This factor equals the covariance of an investment's return, relative to the market portfolio, divided by the variance of that portfolio.

As we shall discover, beta factors exhibit the following characteristics:

The market as a whole has a b = 1 A risk-free security has a b = 0

A security with systematic risk below the market average has a b < 1 A security with systematic risk above the market average has a b > 1 A security with systematic risk equal to the market average has a b = 1

The significance of a security's b value for the purpose of stock market investment is quite straightforward. If overall returns are expected to fall (a * bear *market) it is worth buying securities with low b values because they are expected to fall less than the market. Conversely, if returns are expected to rise generally (a

*scenario) it is worth buying securities with high b values because they should rise faster than the market.*

**bull**Ideally, beta factors should reflect * expectations *about the

*responsiveness of security (or project) returns to corresponding changes in the market. However, without this information, we shall explain how individual returns can be compared with the market by plotting a*

**future***regression line through*

**linear***data.*

**historical**Armed with an operational measure for the market price of risk (b), in Chapter Six we shall explain the rationale for the Capital Asset Pricing Model (CAPM) as an alternative to Markowitz theory for constructing efficient portfolios.

For any investment with a beta of bj, its expected return is given by the CAPM **equation:**

Similarly, because all the characteristics of systematic betas apply to a * portfolio, *as well as an

*security, any portfolio return (rp) with a portfolio beta (bp) can be defined as:*

**individual**For a given a level of systematic risk, the CAPM determines the expected rate of return for any investment relative to its beta value. This equals the risk-free rate of interest, * plus *the product of a market risk premium and the investment's beta coefficient. For example, the mean return on equity that provides adequate compensation for holding a share is the value obtained by incorporating the appropriate equity beta into the CAPM equation.

The CAPM can be used to estimate the expected return on a security, portfolio, or project, by investors, or management, who desire to eliminate unsystematic risk through efficient diversification and assess the required return for a given level of non-diversifiable, systematic (market) risk. As a consequence, they can tailor their portfolio of investments to suit their individual risk-return (utility) profiles.

Finally, in Chapter Six we shall validate the CAPM by reviewing the balance of empirical evidence for its application within the context of capital markets.

In Chapter Seven we shall then focus on the CAPM's operational relevance for strategic financial management within a corporate capital budgeting framework, characterised by capital gearing. And as we shall explain, the stock market CAPM can be modified to derive a project discount rate based on the systematic risk of an individual investment. Moreover, it can be used to compare different projects across different risk classes.

At the end of Part Three, by cross-referencing this text and its companion Exercises (underpinned by * SFM *and

*material from*

**SFME***you should therefore be able to confirm that:*

**Bookboon)**The CAPM not only represents a viable alternative to managerial investment appraisal techniques using NPV wealth maximisation, mean-variance analysis, expected utility models and the WACC concept. It also establishes a mathematical connection with the seminal leverage theories of Modigliani and Miller (MM 1958 and 1961).