'Capital Asset
Pricing Model - CAPM'
The capital asset pricing model (CAPM) is a model that describes the
relationship between systematic risk and expected return for assets,
particularly stocks. CAPM is widely used throughout finance for the pricing of
risky securities, generating expected returns for assets given the risk of
those assets and calculating costs of capital.
The formula for calculating the expected return of an asset given its
risk is as follows:
The general idea behind CAPM is that investors need to be compensated
in two ways: time value of money and risk. The time value of money is
represented by the risk-free (rf) rate in the formula and compensates the
investors for placing money in any investment over a period of time. The
risk-free rate is customarily the yield on government bonds like U.S.
Treasuries.
The other half of the CAPM formula represents risk and calculates the
amount of compensation the investor needs for taking on additional risk. This
is calculated by taking a risk measure (beta) that compares the returns of the
asset to the market over a period of time and to the market premium (Rm-rf):
the return of the market in excess of the risk-free rate. Beta reflects how risky
an asset is compared to overall market risk and is a function of the volatility
of the asset and the market as well as the correlation between the two. For
stocks, the market is usually represented as the S&P 500 but can be
represented by more robust indexes as well.
The CAPM model says that the expected return of a security or a
portfolio equals the rate on a risk-free security plus a risk premium. If this
expected return does not meet or beat the required return, then the investment
should not be undertaken. The security market line plots the results of the
CAPM for all different risks (betas).
Example of CAPM
Using the CAPM model and the following assumptions, we can compute the
expected return for a stock:
The risk-free rate is 2% and the beta (risk measure) of a stock is 2.
The expected market return over the period is 10%, so that means that the
market risk premium is 8% (10% - 2%) after subtracting the risk-free rate from
the expected market return. Plugging in the preceding values into the CAPM formula
above, we get an expected return of 18% for the stock:
18% = 2% + 2 x (10%-2%)
Like all financial models, the CAPM depends on certain assumptions.
Originally there were nine assumptions, although more recent work in financial
theory has relaxed these rules somewhat. The original assumptions were:
•
Investors are wealth maximizers who select
investments based on expected return and standard deviation.
•
Investors can borrow or lend unlimited
amounts at a risk-free (or zero risk) rate.
•
There are no restrictions on short sales
(selling securities that you don't yet own) of any financial asset.
•
All investors have the same expectations
related to the market.
•
All financial assets are fully divisible (you
can buy and sell as much or as little as you like) and can be sold at any time
at the market price.
•
There are no transaction costs.
•
There are no taxes.
•
No investor's activities can influence
market prices.
•
The quantities of all financial assets are
given and fixed.
Obviously, some of these assumptions are not valid in the real world
(most notably no transaction costs or taxes), but CAPM still works well, and
results can be adjusted to overcome some of these assumptions.
