CAPM and the Characteristic
Line
The Characteristic Line
 Total risk of any asset can be assessed by
measuring variability of its returns
 Total risk can be divided into two parts—
diversifiable risk (unsystematic risk) and nondiversifiable risk (systematic risk)
 The characteristic line is used to measure
statistically the undiversifiable risk and
diversifiable risk of individual assets and
portfolios
Characteristic line for the ith asset is:
ri,t = ai + birm,t + ei,t OR
ri,t = birm,t + ai + ei,t
Take Variance of both sides of Equation
 VAR (ri,t) = VAR(birm,t ) +VAR(ai) + VAR(ei,t)
 VAR(birm,t ) = VAR (ri,t) - VAR(ei,t) OR
 VAR(ei,t) = VAR(ri,t) - VAR(birm,t )
Beta Coefficients
An index of risk
Measures the volatility of a stock (or
portfolio) relative to the market
Beta Coefficients Combine
The variability of the asset’s return
The variability of the market return
The correlation between
–the stock's return and
–the market return
Beta Coefficients
Beta coefficients are the slope of
the regression line relating
–the return on the market (the
independent variable) to
–the return on the stock (the
dependent variable)
Beta Coefficients
Interpretation of the
Numerical Value of Beta
Beta = 1.0 Stock's return has
same volatility as the market return
Beta > 1.0 Stock's return is more
volatile than the market return
Interpretation of the
Numerical Value of Beta
Interpretation of the Numerical
Value of Beta
Beta < 1.0 Stock's return is less
volatile than the market return
Interpretation of the Numerical
Value of Beta
High Beta Stocks
More systematic market risk
May be appropriate for high-risk
tolerant (aggressive) investors
Low Beta Stocks
Less systematic market risk
May be appropriate for low-risk
tolerant (defensive) investors
Individual Stock Betas
May change over time
Tendency to move toward 1.0, the
market beta
Portfolio Betas
Weighted average of the individual
asset's betas
May be more stable than
individual stock betas
How Characteristic Line leads
to CAPM?
The characteristic regression line of an
asset explains the asset’s systematic
variability of returns in terms of market
forces that affect all assets simultaneously
The portion of total risk not explained by
characteristic line is called unsystematic
risk
Assets with high degrees systematic
risk must be priced to yield high returns
in order to induce investors to accept
high degrees of risk that are
undivesifiable in the market
CAPM illustrates positive relationship
between systematic risk and return on
an asset
Capital Asset Pricing Model
(CAPM)
For a very well-diversified portfolio, beta
is the correct measure of a security’s risk.
All investments and portfolios of
investments must lie along a straight-line
in the return-beta space
Required return on any asset is a linear
function of the systematic risk of that asset
E(ri) = rf + [E(rm) – rf]  i
The Capital Asset Pricing
Model (CAPM)
The CAPM has
–A macro component explains
risk and return in a portfolio
context
–A micro component explains
individual stock returns
–The micro component is also
used to value stocks
Beta Coefficients and
The Security Market Line
The return on a stock depends on
–the risk free rate (rf)
–the return on the market (rm)
–the stock's beta
–the return on a stock:
k= rf + (rm - rf)beta
Beta Coefficients and
The Security Market Line
The figure relating systematic risk
(beta) and the return on a stock
Beta Coefficients and
The Security Market Line
CAPM can be used to price any asset
provided we know the systematic risk of
that asset
In equilibrium, every asset must be priced
so that its risk-adjusted required rate of
return falls exactly on the straight line
If an investment were to lie above or below
that straight line, then an opportunity for
riskless arbitrage would exist.
Examples of CAPM
Stocks
Expected Return
Beta
A
16%
1.2
B
19%
1.3
C
13%
0.75
E(rm) = 18% rf = 14%
Which of these stocks is correctly priced?
Example of CAPM
Given the following security market line
E(ri) = 0.07 + 0.09I
What must be the returns for two stocks
assuming their betas are 1.2 and 0.9?