# The Capital Asset Pricing Model (CAPM). A Detailed Introduction

**Continuing Learning Series**

*This article is a part of ACS Continuing Learning Series, which is a series of short articles, published by ACS Consulting at short regular intervals on a variety of subjects related to strategy, corporate finance, financial planning & analysis, business planning and performance management.*

**Subject: Financial Analysis**

**Relevance:**

Anyone who aspires to pursue a career as an investment analyst.

Anyone who aspires to pursue a career within corporate finance.

Anyone who is generally interested in capital markets and investment appraisals.

Diversification of portfolio is an effective way to manage risk exposure. However, all risk cannot be eliminated and no matter how much one diversifies (investment portfolio) some level of risk will always exist.

All investors seek a rate of return that compensates for the level of risk which they perceive to be taking. The capital asset pricing model (CAPM) helps to calculate investment risk and the return on an investment that investors should/would expect to earn.

**Understanding Systematic Risk and Unsystematic Risk**

The capital asset pricing model was first developed by William Sharpe (a financial economist and also a Nobel laureate in economics) in 1970. In him book ‘Portfolio Theory and Capital Markets’ he argues that any individual investment decision contains two types of risk:

**Systematic Risk.** These are general risks of the market i.e. the risks which are independent of any specific investment decision. Systematic risk cannot be reduced or mitigated by diversification. The examples of systematic risk are interest rates, economic conditions, political uncertainty, high-tax environment etc. Any investor operating in a certain environment/market will be subject to systematic risks.

**Unsystematic Risk**. This represents ‘specific risks’ i.e. the risk that relates to an individual stock. Put in a technical way, unsystematic risk represents the component of an investment’s return that is not correlated with general market conditions. A good example to understand the concept would be of a business with very high financial gearing which is operating in an economic environment where interest rates are expected to rise. Whilst a hike in interest rates gives rise to a general level of risk (systematic risk), a firm with high financial gearing will have more risk compared to a general business with moderate financial gearing levels. This excess risk for an investor, contemplating to invest in that firm is unsystematic risk.

Modern portfolio theory advocates the idea that specific risk (unsystematic risk) can be reduced or mitigated by diversification of a portfolio. However, diversification will not solve the problem of systematic risk i.e. even a portfolio holding all the shares in a stock market cannot fully eliminate that risk. Therefore, when calculating a reasonable rate of return, the assessment and measurement of the systematic risk is extremely important.

**The CAPM Formula**

CAPM provides a way to measure this systematic risk. Sharpe argued that the return on an individual investment/stock, or a portfolio of investments/stocks, should be equal to its cost of capital. The formula remains for CAPM therefore describes the relationship between risk and expected return.

**CAPM formula is given below:**

To utilize the formula, the first thing to establish is the risk-free rate. Usually the yield on long-term treasury bills i.e. the return on long-term (10 years or more) government bonds is taken as a proxy representing the risk-free rate. To the risk-free rate, a premium is added as a compensation for the extra risk the investor is taking by investing in that particular security/stock. This premium in part is represented by the ‘equity market premium’ i.e. the excess of the expected return from the market as a whole less the risk-free rate of return. The other part of that premium i.e. premium needed to compensate for the unsystematic risk of investing in that particular security/stock is derived by multiplying the equity risk premium by a coefficient which Sharpe called ‘beta’

**Understanding ‘beta’**

The CAPM formula relies on ‘beta’ as the sole measure of a particular security/stock’s risk. It measures a stock's relative volatility i.e. it shows how much the price of a particular stock changes (moves up or down) compared with how much the entire stock market changes (moves up or down). If a share’s price has a perfect positive correlation with the market i.e. it moves exactly in line with the market, then that stock's beta is 1. A stock with a beta of 1.5 would rise by 15% if the market rose by 10% and fall by 15% if the market fell by 10%.

Beta is found by statistical analysis of individual, daily share price returns in comparison with the market's daily returns over precisely the same period. Beta, compared with the equity risk premium, shows the amount of compensation equity investors need for taking on additional risk.

To understand that better, let us take an example. Suppose a stock has a beta of 2.5, the risk-free rate is 4% and the overall market rate of return is 8%. Then the equity risk premium (the market’s excess return) is calculated as: 8% - 4% = 4%. In simple terms it means that by investing in the stock market rather than investing in risk free securities (long-term government bonds), an investor wants to earn 4% over and above the risk-free rate of return to compensate for the extra risk.

In the same way, by investing in that particular stock, the investor would want an excess return of 10% (2.5 x 4%, i.e. multiplying the equity risk premium with the beta) over and above the risk-free rate of return to compensate for the extra risk. The stock’s total required rate of return would there be 10% + the risk-free rate of return i.e. 10% + 4% = 14%

The beta calculation shows that a riskier investment should earn a premium over the risk-free rate. The amount over the risk-free rate is calculated by the equity market premium multiplied by its beta. In other words, it is possible, by knowing the individual parts of the CAPM, to gauge whether or not the current price of a stock is consistent with its likely return.

**Interpreting & Evaluating CAPM for Investors**

The CAPM model is based on rather simplistic theory and as result it provides a simple and easy to understand result. The theory assumes that perception/assessment of risk of investing in a particular security/stock is the primary factor which determines the rate of return that an investor should/would expect. The model has without a doubt dominated modern financial theory in past decades. However, it is not without its faults and given below are some of the criticism.

To begin with, it is not clear if the model really work? The main issue is the concept of beta. The original empirical research which gave rise to the development of the concept was done more than 50 years ago. Some relatively recent research has shown that the differences in betas over a lengthy period do not explain the performance of different stocks. The linear relationship between beta and individual stock returns also seem to break-down over shorter periods of time. These findings at its extreme could be used to argue that CAPM is a faulty model.

**While some studies raise doubts about CAPM's validity, the model is still widely used in the investment community. Although it is difficult to predict from beta how individual stocks might react to particular movements, investors can probably safely deduce that a portfolio of high-beta stocks will move more than the market in either direction, and a portfolio of low-beta stocks will move less than the market.**

This is important for investors, especially fund managers, because they may be unwilling to or prevented from holding cash if they feel that the market is likely to fall. If so, they can hold low-beta stocks instead. Investors can tailor a portfolio to their specific risk-return requirements, aiming to hold securities with betas in excess of 1 while the market is rising, and securities with betas of less than 1 when the market is falling.

It is interesting to note that CAPM contributed to the development and use of indexing by risk averse investors i.e. assembling a portfolio of shares to represent a particular market or asset class. The fundamental belief behind this is the message conveyed by CAPM i.e. to earn higher returns than those offered by market as a whole one has to take on higher risk (beta).

**Conclusion**

The Capital Asset Pricing Model (CAPM) as a formula, is for sure, far from being perfect. However, the fundamental thought behind it is correct i.e. the rate of return which an investor should expect to earn from an investment should be linked with the level of risk which that investment carries. It provides a useful and simple to calculate measure which is easy to understand and apply.