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November 24 2010| Filed Under Economics, Financial Theory
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. 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. (To learn more, see Modern
Portfolio Theory: An Overview.)
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 McClure is a long-time contributor to Investopedia.com.
Ben is the director of Bay of Thermi Limited, an independent research and
consulting firm that specializes in preparing early stage ventures for new
investment and the marketplace. He works with a wide range of clients in the
North America, Europe and Latin America. Ben was a highly-rated European
equities analyst at London-based Old Mutual Securities, and led new venture
development at a major technology commercialization consulting group in Canada.
He started his career as writer/analyst at the Economist Group. Mr. McClure
graduated from the University of Alberta's School of Business with an MBA.
Ben's hard and fast investing philosophy is that the herd is always wrong, but
heck, if it pays, there's nothing wrong with being a sheep.
He lives in Thessaloniki, Greece. You can learn more about Bay of Thermi
Limited at http://www.bayofthermi.com.