BUSINESS Financial
Management
RUTGERS SCHOOL
Lecture 17 Return, Risk, and
the Security Market Line
Lecture Sources
Lectures are compiled using the slides provided
by McGraw-Hill for courses based on:
Ross, Westerfield, Jordan. Fundamentals of Corporate Finance
Chapter 13
Brealy, Myers, Allen. Principles of Corporate Finance
Additional material, compilation, and
presentation layout is provided by the lecturer.
Portfolio Risk:
A More Advanced Treatment
w1
w2
Expected Portfolio Return
Portfolio Variance
2
w12 1
1
e
1
(w1 R )
22
w2 2
e
2
(w 2R )
2(w1w 212 1 2 )
Example
Suppose you invest 60% of your portfolio in Exxon Mobil
and 40% in Coca Cola. The expected dollar return on your
Exxon Mobil stock is 10% and on Coca Cola is 15%. The
standard deviation of their annualized daily returns are
18.2% and 27.3%, respectively. Assume a correlation
coefficient of 0.7 and calculate the portfolio variance.
Exxon-Mobil
Exxon-Mobil w
22
11
Coca-Cola
(.60)
2
w1w 212 1 2
0. 7
18.2
Coca-Cola
(18.2)
2
.40
.60
27.3
w1w 212 1 2
0. 7
2
w2 2
2
18.2
(.40)2
.40
.60
27.3
(27.3)2
Realized Return
Realized Return
Total Return = expected return + unexpected return
Unexpected return = systematic portion +
unsystematic portion
Therefore,
total return can be expressed as follows:
Total Return = expected return + systematic portion +
unsystematic portion
Diversification
Portfolio
diversification is the investment in
several different asset classes or sectors
which are as UNRELATED as possible
Diversification is not just holding a lot of
assets. For example, if you own 50 Internet
stocks, you are not diversified. However, if
you own 50 stocks that span 20 different
industries, then you are diversified
The Principle of Diversification
Diversification can substantially reduce the
variability of returns without an equivalent
reduction in expected returns
This reduction in risk arises because worse
than expected returns from one asset are
offset by better than expected returns from
another
There is a minimum level of risk that cannot be
diversified away and that is the systematic
portion
Unsystematic Risk
Risk factors that affect a limited number of
assets
Aka
unique risk, asset-specific risk,
idiosyncratic risk
What
is it? Includes such things as labor
strikes, part shortages, etc.
Diversifiable Risk
The
risk that can be eliminated by
combining assets into a portfolio
Same as unsystematic, unique or asset-specific risk
If we hold only one asset, or assets in the
same industry, then we are exposing
ourselves to risk that we could diversify
away. IS THIS WISE? Under what circumstances?
Systematic Risk
Risk factors that affect a large number of assets
Also known as non-diversifiable risk no matter
how many DIFFERENT risky assets you hold, the
only escape from systematic risk is the risk-free
asset
Another alias market risk
What is systematic risk? Includes such things as
changes in GDP, inflation, interest rates, etc.
Diversification in Action
Diversification in Action
Risk and Diversification
Total risk = systematic risk + unsystematic risk
The
standard deviation of returns is a measure
of total risk
For well-diversified portfolios, unsystematic risk is
very small
Consequently, the total risk for a welldiversified portfolio is essentially equivalent to
the systematic risk
Systematic Risk Principle
There is a reward for bearing calculated
justifiable risk
Qualification: There is no reward for bearing risk
unnecessarily
Diversification is easy and cheap
THUS
The expected return on a risky asset (risk-free
+ risk premia) depends ONLY on that assets
SYSTEMATIC risk
(unsystematic risk can be diversified away)
Max Diversification
Diversification is cheap and beneficial
taking it to the limit seems like a logical
conclusion
Market Portfolio - Portfolio of ALL assets in
the economy
In practice a broad stock market index,
such as the S&P Composite, is used to
represent the market.
Measuring Systematic Risk
Market
portfolio contains ONLY systematic
risk all changes in its value are due to
systematic risk
Measure systematic of risk:
Beta - Sensitivity of a stocks (an assets)
return to the return on the market portfolio.
Linearity Assumption
CAPM Beta
Analytic expression:
im
Bi 2
m
Covariance with the
market
Variance of the market
CAPM Beta: Examples
Understanding Betas
A
beta = 1 implies the asset has the
same systematic risk as the overall
market
A
beta < 1 implies the asset has less
systematic risk than the overall market
A
beta > 1 implies the asset has more
systematic risk than the overall market
Diversification and Compensation
for Systematic Risk
Exercise
Consider the following information:
Std. Dev.
Security C
Security K
Which
Beta
20%
30%
1.25
0.95
security has more total risk?
Which security has more systematic risk?
Which security should have the higher
expected return?
Portfolio Betas
Security
DCLK
KO
INTC
KEI
Weight
0.133
0.2
0.267
0.4
Beta
2.685
0.195
2.161
2.434
What is the portfolio beta?
0.133(2.685) + 0.2(0.195) + 0.267(2.161) +
0.4(2.434) = 1.947
Risk Premium
risk premium = expected return risk-free rate
The higher the beta, the greater the risk premium
should be
No risk premia for idiosyncratic risk. Why?
One can define the relationship between the risk
premium and beta so that we can estimate the
expected return
Risk-Reward Line
30%
Expected Return
25%
20%
15%
10%
5%
???
0%
0
0.5
1
1.5
Beta
2
2.5
3
Reward-to-Risk Ratio
The reward-to-risk ratio is the slope of the
line illustrated in the previous example
Slope = (E(RA) Rf) / (A 0)
Reward-to-risk ratio for previous example =
(20 8) / (1.6 0) = 7.5
What
if an asset has a reward-to-risk ratio
of 8 (implying that the asset plots above
the line)?
What if an asset has a reward-to-risk ratio
of 7 (implying that the asset plots below
the line)?
Market Equilibrium
In
equilibrium, all assets and portfolios
must have the same reward-to-risk ratio,
and they all must equal the reward-to-risk
ratio for the market
Treynor
ratio
E ( RA ) R f
A
E ( RM R f )
M
Security Market Line
The security market line (SML) is the
representation of market equilibrium
The slope of the SML is the reward-to-risk ratio:
(E(RM) Rf) / M
But since the beta for the market is ALWAYS
equal to one, the slope can be rewritten
Slope = E(RM) Rf = market risk premium
The Capital Asset Pricing
Model (CAPM)
The capital asset pricing model defines the
relationship between risk and return
E(RA) = Rf + A(E(RM) Rf)
If we know an assets systematic risk, we can use the
CAPM to determine its expected return
This is true whether we are talking about financial assets
or physical assets
Factors Affecting Expected
Return
Pure
time value of money: measured by
the risk-free rate
Reward
for bearing systematic risk:
measured by the market risk premium
Amount
beta
of systematic risk: measured by
CAPM: Example
Consider the betas for each of the assets given earlier. If
the risk-free rate is 4.15% and the market risk premium is
8.5%, what is the expected return for each?
Security
Beta
Expected Return
DCLK
2.685
4.15 + 2.685(8.5) = 26.97%
KO
0.195
4.15 + 0.195(8.5) = 5.81%
INTC
2.161
4.15 + 2.161(8.5) = 22.52%
KEI
2.434
4.15 + 2.434(8.5) = 24.84%
CAPM Summary
CAPM
Realized
vs. Expected Returns
What does CAPM (SML) focus on?
CAPM (SML): Betas
CAPM (SML): Betas
CAPM (SML): Betas
Quick Quiz
How do you compute the expected return and
standard deviation for an individual asset? For a
portfolio?
What is the difference between systematic and
unsystematic risk?
What type of risk is relevant for determining the
expected return?
Consider an asset with a beta of 1.2, a risk-free rate
of 5%, and a market return of 13%.
What is the reward-to-risk ratio in equilibrium?
What is the expected return on the asset?
Comprehensive Problem
The risk free rate is 4%, and the required return
on the market is 12%. What is the required
return on an asset with a beta of 1.5?
What is the reward/risk ratio?
What is the required return on a portfolio
consisting of 40% of the asset above and the
rest invested in a risk-free asset?