# The Capital Asset Pricing Model (Capm)

## Introduction

Basic portfolio theory defines the expected return from a risky investment in general terms as the risk-free return, plus a premium for risk. However, we have observed that this premium is determined not by the overall risk of the investment but only by its systematic (market) risk.

Using the geometry of the Security Market Line (SML) that determines the market risk premium (b), numerous academics, notably Sharpe (1963) followed by Lintner (1965), Treynor (1965) and Mossin (1966) were quick to develop (quite independently) the * Capital Asset Pricing Model *(CAPM) as a logical extension to basic portfolio theory.

Today, the CAPM is regarded by many as a superior model of security price behaviour to others based on wealth maximisation criteria with which you should be familiar. For example, unlike the dividend and earnings share valuation models of Gordon (1962) and Modigliani and Miller (1961) covered in our * SFM *and

*texts, the CAPM explicitly identifies the risk associated with an ordinary share (common stock) as well as the future returns it is expected to generate. Moreover, the CAPM can also express investment returns in two forms*

**SFME**For individual securities:

And because systemic betas apply to a * portfolio, *as well as an

*investment:*

**individual**For a given a level of systematic risk, the CAPM determines the expected rate of return for any investment (security, project, or portfolio) relative to its beta value defined by the SML (a market index). As we shall discover, it also establishes whether individual securities, projects (or their portfolios) are under or over-priced relative to the market, (hence its name).The CAPM can therefore be used 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.

## The CAPM Assumptions

The CAPM is a * single-period *model, which means that all investors make the same decision over the same time horizon. Expected returns arise from expectations over the same period.

The CAPM is a * single-index *model because systemic risk is prescribed entirely by

*factor; the beta factor.*

**one**The CAPM is defined by random variables that are normally distributed, characterised by mean expected returns and covariances, upon which all investors agree.

Markowitz mean-variance efficiency criteria based on perfect markets still determine the optimum portfolio (P).

MAX: R(P), given 8(P) MIN: 8(P), given R(P).

- All investments are infinitely divisible.

- All investors are rational and risk averse.

- All investors are price takers, since no individual, firm or financial institution is large enough to distort prevailing market values.

- All investors can borrow-lend without restriction at the risk-free market rate of interest.

- Transaction costs are zero and the tax system is neutral.

- There is a perfect capital market where all information is available and costless.

The application of the CAPM and beta factors is straight forward as far as stock market tactics are concerned. The model assumes that investors have three options when managing a portfolio:

1) To trade,

2) To hold,

3) To substitute, * (i.e. *securities for property, property for cash, cash for gold

**etc.).**A profitable trade is accomplished by buying (selling), undervalued (overvalued) securities relative to an appropriate measure of systematic risk, a global stock market index such as the FT/ S&P World Index. If the market is "bullish" and prices are expected to rise generally, it is worth buying securities with high b values because they can be expected to rise faster than the market. Conversely, if markets are "bearish" and expected to fall, then securities with low beta factors are more attractive because they can be expected to fall less than prices overall.

To validate the CAPM, however, there are other assumptions (many of which should be familiar) that we will question later. For the moment, they are simply listed in Table 6.1 without comment to develop our analysis.