# Capital Asset Pricing Model

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**Summary**

The article is about Capital Asset Pricing Model (CAPM) whereby the writer starts by briefly explaining the origin of the model, its formula and finally the importance to an individual investor as well as fund managers. The basic elements of the formula are also discussed such as risk free rate, beta of the security, expected market return and equity market premium as well as the contributors to the model.

**Analysis of the Article**

It is by no doubt that CAPM is one of the fundamental concepts of portfolio theory and asset pricing. It is widely used in applications such as estimating the cost of capital for firms and evaluating the performance of managed portfolios. Investors on one hand would like return on their investment and on the other hand risk is inevitable. This is the reason why the author of the article has indicated the two types of risk in an individual investment; Systematic and Unsystematic risk. Systematic risk cannot be eliminated by diversification while Unsystematic risk which is specific to individual stocks, can be eliminated by diversification.

CAPM is therefore used to measure the systematic risk. This helps the investors to calculate their expected return.

It is important to note that the CAPM builds on the model of portfolio choice developed by Harry Markowitz (1959) which assumes that investors are risk averse and when choosing among portfolios, they care only about the mean and variance of their one period investment return. The only measure of a stock risk as depicted by the article is the beta which is a measure of the stock’s relative volatility.

Earlier empirical tests have confirmed that the relation between expected return and the beta is linear.

On the recent tests, Merton’s (1973) introduced the intertemporal Capital Asset Pricing Model (ICAPM) which is a natural extension of the CAPM. The ICAPM begins with a different assumption about investor objectives. In this, the investors are not only interested with their end of period payoff, but also with the opportunities they will have to consume or invest the payoff.

CAPM as indicated by the author of the article has raised various doubts in recent studies but despite that, it is extensively used for investment decisions.

One of the major problems of CAPM is that portfolios formed by sorting stocks on price ratios produce a wide range of average returns, but the average returns are not positively related to market betas.

**Relevance to financial management**

Financial management, simply explained, refers to that branch of economics which deals with managing financial resources. Time and risk are crucial factors in managing these financial resources. In a real market, institutional complexities, frictions, taxes and certain other complications have a significant effect on the share prices. Investors would like to be compensated for their time and risk and this is the basic purpose of CAPM; to predict the expected return on individual investment or rather to determine the return they deserve for putting their money at risk as indicated by the article.

**Appendix 1: Reference**

Merton Robert C. (1973).”An intertemporal Capital Asset Pricing Model” *Econometrica*.41:5, pp. 867-887

**Appendix 2: Article**** **

**The Capital Asset Pricing Model: An Overview (2006)**** **

**by Ben McClure**

No matter how much we diversify our investments, it’s impossible to get rid of all the risk. As investors, we deserve a rate of return that compensates us for taking on risk. The capital asset pricing model (CAPM) helps us to calculate investment risk and what return on investment we should expect. Here we look at the formula behind the model, the evidence for and against the accuracy of CAPM, and what CAPM means to the average investor.

**Birth of a Model**

The capital asset pricing model was the work of financial economist (and, later, Nobel laureate in economics) William Sharpe, set out in his 1970 book “Portfolio Theory And Capital Markets”. His model starts with the idea that individual investment contains two types of risk:

Systematic Risk – These are market risks that cannot be diversified away. Interest rates, recessions and wars are examples of systematic risks.

Unsystematic Risk – Also known as “specific risk”, this risk is specific to individual stocks and can be diversified away as the investor increases the number of stocks in his or her portfolio. In more technical terms, it represents the component of a stock’s return that is not correlated with general market moves.

Modern portfolio theory shows that specific risk can be removed through diversification. (To learn more, see Modern Portfolio Theory: An Overview.) The trouble is that diversification still doesn’t solve the problem of systematic risk; even a portfolio of all the shares in the stock market can’t eliminate that risk. Therefore, when calculating a deserved return, systematic risk is what plagues investors most. CAPM, therefore, evolved as a way to measure this systematic risk.

The Formula

Sharpe found that the return on an individual stock, or a portfolio of stocks, should equal its cost of capital. The standard formula remains the CAPM, which describes the relationship between risk and expected return.

Here is the formula:

CAPM’s starting point is the risk-free rate – typically a 10-year government bond yield. To this is added a premium that equity investors demand to compensate them for the extra risk they accept. This equity market premium consists of the expected return from the market as a whole less the risk-free rate of return. The equity risk premium is multiplied by a coefficient that Sharpe called “beta”.

**Beta****
**According to CAPM, beta is the only relevant measure of a stock’s risk. It measures a stock’s relative volatility – that is, it shows how much the price of a particular stock jumps up and down compared with how much the stock market as a whole jumps up and down. If a share price moves exactly in line with the market, then the 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%. (For further reading, see Beta: Gauging Price Fluctuations and Beta: Know The Risk.)

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. In their classic 1972 study titled “The Capital Asset Pricing Model”: Some Empirical Tests”, financial economists Fischer Black, Michael C. Jensen and Myron Scholes confirmed a linear relationship between the financial returns of stock portfolios and their betas. They studied the price movements of the stocks on the New York Stock Exchange between 1931 and 1965.

Beta, compared with the equity risk premium, shows the amount of compensation equity investors need for taking on additional risk. If the stock’s beta is 2.0, the risk-free rate is 3% and the market rate of return is 7%, the market’s excess return is 4% (7% – 3%). Accordingly, the stock’s excess return is 8% (2 X 4%, multiplying market return by the beta), and the stock’s total required return is 11% (8% + 3%, the stock’s excess return plus the risk-free rate).

What this shows is 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’s 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 – that is, whether or not the investment is a bargain or too expensive.

**What CAPM Means for You****
**This model presents a very simple theory that delivers a simple result. The theory says that the only reason an investor should earn more, on average, by investing in one stock rather than another is that one stock is riskier. Not surprisingly, the model has come to dominate modern financial theory. But does it really work?

It’s not entirely clear. The big sticking point is beta. When professors Eugene Fama and Kenneth French looked at share returns on the New York Stock Exchange, the American Stock Exchange and Nasdaq between 1963 and 1990, they found that differences in betas over that lengthy period did not explain the performance of different stocks. The linear relationship between beta and individual stock returns also breaks down over shorter periods of time. These findings seem to suggest that CAPM may be wrong.

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.

Not surprisingly, CAPM contributed to the rise in use of indexing – assembling a portfolio of shares to mimic a particular market – by risk averse investors. This is largely due to CAPM’s message that it is only possible to earn higher returns than those of the market as a whole by taking on higher risk (beta). (To learn more, see The Lowdown On Index Funds.)

**Conclusion****
**The capital asset pricing model is by no means a perfect theory. But the spirit of CAPM is correct. It provides a usable measure of risk that helps investors determine what return they deserve for putting their money at risk. To learn more, see Achieving Better Returns In Your Portfolio.

**by Ben McClure**,

Ben is director of McClure & Co., an independent research and consulting firm that specializes in investment analysis and intelligence. Before founding McClure & Co., Ben was a highly-rated European equities analyst at London-based Old Mutual Securities.