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CHAPTER 10: Risk and Return,
The Capital Asset Pricing Model



Stand-alone versus Portfolio risk
Firm-specific versus systematic (market
or economic) risk
The Capital Asset Pricing Model (CAPM)
10-1
What drives security or
investment values


The price and/or intrinsic value of any security or
investment should be the Present Value of all future
expected cash flows.
The value of any security, e.g., a common stock, should
change whenever:


The forecast of future cash flows changes.
The perceived risk of the future cash flows changes.
10-2
Introduction to Risk and Return

Every investment has some required rate of return,
based on its level of perceived risk.


Of course, your realized return from an investment may
differ substantially from what you had originally expected or
required – uncertainty concerning the final outcome is
unavoidable.
People tend to be averse to risk, therefore they demand
higher rates of return (additional compensation) for
investments of increasing risk.
10-3
Risk and return of a two stock
portfolio

Stock A’s future return depends on next year’s’
state of the economy.
20%
Good economy,
probability=25%
Average economy,
probability=50%
10%
Bad economy,
probability=25%
0%
10-4
Risk and return of a two stock
portfolio

Stock B’s future return also depends on next year’s
state of the economy.
5%
Good economy,
probability=25%
Average economy,
probability=50%
10%
Bad economy,
probability=25%
15%
10-5
Risk and return of a two stock portfolio (with
two stocks that are perfectly negatively
correlated)


Suppose that we invest $100 in stock A and $200 in stock B.
The performance of investing $300 in this two stock portfolio
is shown below.
We have two risky stocks. Yet, when we combine them here,
we produce a portfolio which is riskless, in that it earns a 10%
return in each future economic state.
Outcomes
Prob. (ps)
CF on
CF on
Total CF
$100 in A $100 in A
% Return on
$300 in A&B
Boom
0.25
$120
$210
$330
10%
Normal
0.50
$110
$220
$330
10%
Bust
0.25
$100
$230
$330
10%
10-6
The two types of investment risk

Stand-alone risk:


The total risk of any single investment, such as Intel Corp.
stock, without regard or reference to any other
investments, usually measured as that security’s standard
deviation of returns.
Portfolio risk:

The total risk of a portfolio of different securities. Often
measured as the standard deviation of an entire portfolio.
How a portfolio’s total risk will change if a particular
security is added or deleted?
10-7
Risk-free rates and risk premiums

The interest rate or yield on a short-term U.S.
government bill or bond, e.g., a Treasury Bill, is
usually considered to be a proxy for the risk-free
rate of return or rRF.


rRF = real interest rate + inflation premium
The required rate of return on any risky investment i
is defined the risk-free rate plus some extra
compensation or premium for the risk:

ri = rRF + Risk Premium
10-8
Average annual returns for selected
investment categories, 1926 – 2002
Small-company stocks
Large-company stocks
L-T corporate bonds
L-T government bonds
U.S. Treasury bills
Inflation
Average
Standard
Return
Deviation
16.9%
33.2%
12.2
20.5
6.2
8.7
5.8
9.4
3.8
3.2
3.1
4.4
Does a risk premium seem to have been realized or earned over the 19262002 period when investment categories of differing perceived levels of
risk are compared?
10-9
Capital Market Equilibrium and
CAPM Model
E(r)
Market portfolio
“M”
Capital Market
Line or CML
Opportunity set of risky
assets, the bullet
E(rM)
individual
securities
rF
M

10-10
Decomposition of the total risk of
a typical common stock

Assume that Boeing common stock is typical. The
total risk of this stock consists of:


Firm specific risk – the risk that is unique to Boeing, e.g.,
competitiveness, managerial effectiveness, lawsuits, labor
disputes, winning or losing a contract, etc. These events
impact Boeing, but do not affect DuPont, IBM, CocaCola, Disney, etc.
Systematic (market or macroeconomic) risk – the risk
that affects all firms to some degree: external events such
as recessions, expansion, interest rates, world events, etc.
10-11
Firm Specific versus Systematic
Risks



Systematic (market or macroeconomic) risk usually
accounts for about 25% of a typical stock’s total
risk.
Firm-specific risk usually accounts for about 75%
of a typical firm’s total risk.
You can eliminate almost all the firm-specific risk
by holding a well-diversified portfolio of stocks.
The random bad and good firm-specific events are
then largely offset within the portfolio.
10-12
Firm Specific versus Systematic
Risk

Most people would never put all of their wealth in one
common stock.


However, many people would put a large amount of
their wealth in a mutual fund that invests in a
diversified portfolio of common stocks.


Too much exposure to firm-specific risk
The relevant risk here is the systematic risk, as the firmspecific risk has been diversified away.
You can never diversify away systematic risk, as all
stocks have exposure to this risk.
10-13
Illustrating diversification effects of a
stock portfolio, standard deviation
versus the number of stocks
p
50%
Diversifiable risk
20%
Market risk
30
No. of
securities
10-14
Which risk should be relevant in the
determination of market prices?



Which investors drive stock prices? Most trading (and
analysis) is conducted by financial institutions: mutual
funds, pension funds, insurance companies, hedge
funds, etc.
We thus must assume that stock prices are mostly
driven by investors that are reasonably or welldiversified. Most investors manage portfolios.
Thus we should only expect a risk premium or extra
compensation for the exposure to systematic (market or
macroeconomic) risk.

No compensation should exist for firm-specific risk.
10-15
Capital Asset Pricing Model or
CAPM

The CAPM (introduced circa 1965) is used to
estimate a stock’s risk premium and required rate
of return. We will use IBM stock as an example.


CAPM→ rIBM = rRF + βIBM[rM - rRF]
rRF is the riskless rate, βIBM is the Beta of IBM,
and rM is the required return on some welldiversified or market portfolio of assets (call it the
market portfolio).


The term [rM - rRF] is the market risk premium
βIBM[rM - rRF] is IBM’s risk premium
10-16
What is the market risk premium,
given as [rM - rRF] in the CAPM?



The additional return over the risk-free rate needed
to compensate investors for assuming an average
amount of risk.
Its size depends on the perceived risk of the overall
stock market and investors’ degree of risk aversion.
Varies across time, but most estimates suggest it
has ranged between 4% and 8% per year; 5 to 6%
seems to be a good current estimate.
10-17
CAPM and required return for
IBM’s common stock


Let rRF=6%, rM=12%, and the Beta of IBM common
stock is βIBM=1.3
rIBM = rRF + βIBM[rM - rRF]
rIBM = 0.06 + 1.3[0.12 – 0.06]
rIBM = 0.06 + 1.3[0.06]
rIBM = 0.06 + 0.078 =0.138 or 13.8%
Note the following items:


The market risk premium is [12% - 6%] = 6%
IBM’s risk premium is 1.3[12% – 6%] = 7.8%.
10-18
How to interpret Betas (β)

Beta measures a stock’s degree of systematic or
market risk. It can also be thought of as the stock’s
contribution to the risk of a well-diversified
portfolio.



β = 1: the stock has average market risk. The stock
generally tends to go up (down) by the same percentage
amount as the market.
β = 1.5: The stock generally tends to go up (down) by
50% (1.5x) more than the market.
β = 0.5: The stock generally tends to go up (down) by half
as much as the market.
10-19
How to interpret Betas (β),
continued




β = 0: the stock has no correlation with movements in the
overall stock market. All of this firm’s risk would actually
be firm-specific risk.
β < 0: The stock generally tends move in a direction
opposite that of the market (very rare).
Firms that supply basic consumer goods (Proctor &
Gamble) and utilities (phone, cable, gas, or electric)
tend to have low Betas (lower than 1.0, often around
0.4 to 0.6).
Firms that are in economically cyclical industries
would have higher Betas (greater then 1.0).
10-20
Expected return and Beta of a
portfolio of stocks


Both portfolio expected returns and portfolio Betas
are always a weighted average of the stocks that
comprise the portfolio.
You invest $10,000: $6000 in Apple Computer and
$4000 in Proctor & Gamble (PG).


Let rRF=5% and rM=10%. Let βAPPLE=1.3 and βPG=0.6
The investment weights are (6000/10000)=0.6 for Apple
and (4000/10000)=0.4 for PG. The weights must always
sum up to 1.
10-21
Expected return and Beta of a
portfolio of stocks, continued


The portfolio Beta is always the weighted
average of each of the stock’s betas.
βP = wappleβapple + wpgβpg
βP = 0.6(1.30) + 0.4(0.6)
βP = 1.02
Now find the portfolio required return.

rP = 0.05 + 1.02[0.10 – 0.05] = 0.101 or 10.1%
10-22
The Security Market Line or
SML

The SML is basically just a graph of the CAPM
equation.


For our example, let rRF=5%, rM=10%, and therefore the
market risk premium is 5%.
In this case the CAPM is represented as:
 ri = rRF + βi[rM - rRF], putting in the numbers we
have:
 ri = 0.05 + 0.05βi
 The required return on any security here is solely
a function of the Beta and SML.
10-23
The Security Market Line or
SML, continued

Below, we plot the SML from the last slide:
ri = 0.05 + 0.05βi
ri (%)
SML
10
Mkt. risk prem. = 5%
5
rRF=5%
0
0.5
1.0
Risk, βi
1.5
10-24
What if the SML changes?

Two possible SML changes can definitely occur.
Each has important effects.


(1) Risk-free rates rRF can change. This can be due to the
Inflation Premium (IP) or the real rate of interest
changing. Note that in this case, the kM must also
increase by the same amount so that the market risk
premium [rM-rRF] is unchanged.
(2) The market risk premium [rM-rRF] can change. This
would typically be due to changing attitudes toward risk
aversion by investors.
10-25
What if the SML changes?

Following slides allow for two separate SML
changes:


In the first case, we let the risk-free rate rRF increase by
2% (from 5% to 7%). The market required return rM
must increase by the same amount (from 10% to 12%),
so that the market risk premium [rM-rRF] remains at 5%.
In the second case, we allow for a 2% increase in the
market risk premium (from 5% to 7%). The risk-free
rate remains the same at 5%, however, rM must increase
by 2% (from 10% to 12%) so that the market risk
premium can now be [rM-rRF] = 7%.
10-26
The Security Market Line or
SML, continued

Risk-free rate increases from 5% to 7%. The
new SML is ri = 0.07 + 0.05βi
ri (%)
SML, new
SML, old
12
10
7
5
Mkt. risk prem. = 5%
rRF=7%
0
0.5
1.0
Risk, βi
1.5
10-27
The Security Market Line or
SML, continued

The market risk premium increases from 5 to
7%. The new SML is ri = 0.05 + 0.07βi
ri (%)
SML, new
SML, old
12
10
Mkt. risk prem. = 7%
5
rRF=5%
0
0.5
1.0
Risk, βi
1.5
10-28
Pros and Cons of the CAPM



The CAPM is relatively simple. Firm specific risk is
diversifiable and irrelevant. Market (macroeconomic)
risk is not diversifiable and is therefore relevant.
Required returns are a function of the risk-free rate,
market risk premium, and the Beta.
The CAPM is very difficult to test empirically. It’s
impossible to measure the true market portfolio. Early
results were in support, in early 1990s there was some
doubt, and more (sophisticated) recent tests are more
in support of the CAPM.
10-29