2. Risk & Return
investors demand a premium for bearing risk;
that is, the higher the risk of a security, the
higher its expected return must be to induce
investors to buy (or to hold) it.
if investors are primarily concerned with the
risk of their portfolios rather than the risk of
the individual securities in the portfolio, then
how should the risk of an individual stock be
measured?
3. Risk & Return
One answer is provided by the Capital Asset
Pricing Model (CAPM), an important tool used to
analyze the relationship between risk and rates of
return.
A stock might be quite risky if held by itself, but—
since about half of its risk can be eliminated by
diversification—the stock’s relevant risk is its
contribution to the portfolio’s risk, which is much
smaller than its stand-alone risk.
4. Risk & Return
A simple example will help make this point clear.
Suppose you are offered the chance to flip a coin.
If it comes up heads, you win $20,000, but if it’s
tails, you lose $16,000. This is a good bet—the
expected return is 0.5($20,000) + 0.5(−$16,000) =
$2,000. However, it’s a highly risky proposition
because you have a 50% chance of losing
$16,000. Thus, you might well refuse to make the
bet. Alternatively, suppose that you were to flip
100 coins and that you would win $200 for each
head but lose $160 for each tail.
5. Risk & Return
It is theoretically possible that you would flip
all heads and win $20,000, and it is also
theoretically possible that you would flip all
tails and lose $16,000, but the chances are
very high that you would actually flip about 50
heads and about 50 tails, winning a net of
about $2,000.
6. Risk &Return
Although each individual flip is a risky bet,
collectively you have a low-risk proposition
because most of the risk has been diversified
away. This is the idea behind holding
portfolios of stocks rather than just one stock.
The difference is that, with stocks, not all of
the risk can be eliminated by diversification—
those risks related to broad, systematic
changes in the stock market will remain.
7. The Capital-Asset Pricing Model
(CAPM)
This model was developed in the 1960s, and it
has had important implications for finance ever
since. Though other models also attempt to
capture market behavior, the CAPM is simple in
concept and has real-world applicability.
A model that describes the relationship risk and
expected (required) return; in this model, a
security’s expected(required) return is the risk-
free rate plus a premium based on the systematic
risk of the security.
8. Assumptions of CAPM
First, we assume that capital markets are efficient
in that investors are well informed, transactions
costs are low, there are negligible restrictions on
investment, and no investor is large enough to
affect the market price of a stock.
We also assume that investors are in general
agreement about the likely performance of
individual securities and that their expectations
are based on a common holding period, say
one year.
9. Assumptions of CAPM
There are two types of investment opportunities
with which we will be concerned. The first is a
risk-free security whose return over the holding
period is known with certainty. Frequently, the
rate on short- to intermediate-term Treasury
securities is used as a replacement for the risk-
free rate.
The second is the market portfolio of common
stocks. It is represented by all available common
stocks and weighted according to their total
aggregate market values outstanding
10. What is an “index
An index is a group of stocks, the performance of
which is measured as a whole.
Some are large, containing hundreds or
thousands of companies. These are often used to
gauge the performance of the overall market, as
with an index such as the S&P 500.
Other indexes are smaller, or more focused,
perhaps containing just small companies or
pharmaceutical companies or Latin American
companies.
11. Standard & Poor’s
500 Stock Index
A market-value-weighted index of 500 large
capitalization common stocks selected from a
broad cross-section of industry groups. It is
used as a measure of overall market
performance.
12. The Characteristic Line
A line that describes the relationship between an
individual security’s returns and returns on the
market portfolio. The slope of this line is beta.
We are now in a position to compare the
expected return for an individual stock with the
expected return for the market portfolio.
In our comparison, it is useful to deal with
returns in excess of the risk-free rate, which acts
as a benchmark against which the risky asset
returns are contrasted. The excess return is simply
the expected return less the risk-free return.
13. The Characteristic Line
Figure shows an example of a comparison of
expected excess returns for a specific stock
with those for the market portfolio. The solid
blue line is known as the security’s
characteristic line; it depicts the expected
relationship between excess returns for the
stock and excess returns for the market
portfolio.
14. The Characteristic Line
The expected relationship may be based on past
experience, in which case actual excess returns
for the stock and for the market portfolio would
be plotted on the graph, and a regression line
best characterizing the historical relationship
would be drawn. Such a situation is illustrated by
the scatter diagram shown in the figure. Each
point represents the excess return of the stock
and that of the S&P 500 Index for a given month
in the past (60 months in total)
17. The Characteristic Line
From these returns the monthly risk-free rate
is subtracted to obtain excess returns.
For our example stock, we see that, when
returns on the market portfolio are high,
returns on the stock tend to be high as well.
Instead of using historical return relationships,
one might obtain future return estimates from
security analysts who follow the stock.
18. Beta: An Index of Systematic Risk
An index of systematic risk. It measures the
sensitivity of a stock’s returns to changes in
returns on the market portfolio. The beta of a
portfolio is simply a weighted average of the
individual stock betas in the portfolio.
Beta is simply the slope (i.e., the change in the
excess return on the stock over the change in
excess return on the market portfolio) of the
characteristic line.
19. Beta: An Index of Systematic Risk
If the slope is 1.0, it means that excess returns
for the stock vary proportionally with excess
returns for the market portfolio. In other
words, the stock has the same systematic risk
as the market as a whole.
If the market goes up and provides an excess
return of 5 percent for a month, we would
expect, on average, the stock’s excess return
to be 5 percent as well.
20. Beta: An Index of Systematic Risk
slope steeper(greater) than 1.0 means that the stock’s
excess return varies more than proportionally with the
excess return of the market portfolio. Put another way,
it has more unavoidable risk than the market as a
whole. This type of stock is often called an “aggressive”
investment.
A slope less than 1.0 means that the stock’s excess
return varies less than proportionally with the excess
return of the market portfolio. This type of stock is
often called a “defensive” investment.
21. Beta: An Index of Systematic Risk
The greater the slope of the characteristic line for a
stock, as depicted by its beta, the greater its systematic
risk. This means that, for both upward and downward
movements in market excess returns, movements in
excess returns for the individual stock are greater or
less depending on its beta.
With the beta of the market portfolio equal to 1.0 by
definition, beta is thus an index of a stock’s systematic
or unavoidable risk relative to that of the market
portfolio. This risk cannot be diversified away by
investing in more stocks, because it depends on such
things as changes in the economy and in the political
atmosphere, which affect all stocks.
23. Unsystematic (Diversifiable) Risk
Revisited
Before moving on, we need to mention an
additional feature of Figure. The dispersion of
the data points about the characteristic line is
a measure of the unsystematic risk of the
stock. The wider the relative distance of the
points from the line, the greater the
unsystematic risk of the stocks: this is to say
that the stock’s return has increasingly lower
correlation with the return on the market
portfolio.
24. Unsystematic (Diversifiable) Risk
Revisited
The narrower the dispersion, the higher the
correlation and the lower the unsystematic
risk. From before, we know that unsystematic
risk can be reduced or even eliminated
through efficient diversification. For a
portfolio of 20 carefully selected stocks, the
data points would hover closely around the
characteristic line for the portfolio.
