Chapter 13
Return, Risk, and
the Security Market
Line
Copyright © 2012 by McGraw-Hill Education. All rights reserved.
Key Concepts and Skills
•
•
•
•
•
•
Know how to calculate expected returns
Understand the impact of diversification
Understand the systematic risk principle
Understand the security market line
Understand the risk-return trade-off
Be able to use the Capital Asset Pricing
Model
13-2
Chapter Outline
• Expected Returns and Variances
• Portfolios
• Announcements, Surprises, and Expected
Returns
• Risk: Systematic and Unsystematic
• Diversification and Portfolio Risk
• Systematic Risk and Beta
• The Security Market Line
• The SML and the Cost of Capital: A Preview
13-3
Expected Returns
• “ The return on a risky asset expected in
the future.”
• Risk premium is defined as “ the
difference between the return on a risky
investment and that on a risk-free
investment.”
• Risk premium = Expected return – Risk free rate
Expected Returns
• Example: If the risk free investments
are currently offering 8%. Stock Z offers
rate of return 20%. What is stock Z risk
premium?
• Risk premium = 20% - 8% = 12%
Expected Returns
• Expected returns are based on the
probabilities of possible outcomes
• In this context, “expected” means average
if the process is repeated many times
• The “expected” return does not even have
to be a possible return
n
E ( R )   pi Ri
i 1
13-6
Example: Expected Returns
• Suppose you have predicted the following returns
for stocks C and T in three possible states of the
economy. What are the expected returns?
•
State
Boom
Normal
Recession
Probability
0.3
0.5
???
C
15%
10
2
T
25%
20
1
• RC = .3(15) + .5(10) + .2(2) = 9.9%
• RT = .3(25) + .5(20) + .2(1) = 17.7%
13-7
Variance and Standard
Deviation
• Variance and standard deviation measure
the volatility of returns
• Using unequal probabilities for the entire
range of possibilities
• Weighted average of squared deviations
n
σ   pi ( Ri  E ( R ))
2
2
i 1
13-8
Example: Variance and
Standard Deviation
• Consider the previous example. What are the variance
and standard deviation for each stock?
• Stock C
– 2 = .3(15 - 9.9)2 + .5(10 - 9.9)2 + .2(2 - 9.9)2 = 20.29
–  = 4.50%
• Stock T
– 2 = .3(25 - 17.7)2 + .5(20 - 17.7)2 + .2(1 - 17.7)2 = 74.41
–  = 8.63%
13-9
Another Example
• Consider the following information:
State
Boom
Normal
Slowdown
Recession
Probability
.25
.50
.15
.10
ABC, Inc. (%)
15
8
4
-3
• What is the expected return?
• What is the variance?
• What is the standard deviation?
13-10
Solution
1) The expected return = (0.25×15) + (0.5×8) +
(0.15×4) + (0.1×-3) = 8.05
2) The variance = 0.25(15-8.05)2 + 0.5(8-8.05)2
+ 0.15(4-8.05)2 + 0.1(-3-8.05)2 = 26.75
3) The standard deviation = 5.17
Portfolios
• A portfolio is a collection of assets
• An asset’s risk and return are important in
how they affect the risk and return of the
portfolio
• The risk-return trade-off for a portfolio is
measured by the portfolio expected return
and standard deviation, just as with
individual assets
13-12
Portfolio Weights
• Portfolio Weight: “The percentage of a
portfolio’s total value that is in a particular
asset.”
• Notice that: the weights have to add up to
1 because all our money is invested in it.
Example: Portfolio Weights
• Suppose you have $15,000 to invest and
you have purchased securities in the
following amounts. What are your portfolio
weights in each security?
–
–
–
–
$2000 of DCLK
$3000 of KO
$4000 of INTC
$6000 of KEI
•DCLK: 2/15 = .133
•KO: 3/15 = .2
•INTC: 4/15 = .267
•KEI: 6/15 = .4
13-14
Portfolio Expected Returns
• The expected return of a portfolio is the weighted
average of the expected returns of the respective
assets in the portfolio
m
E ( RP )   w j E ( R j )
j 1
• You can also find the expected return by finding the
portfolio return in each possible state and computing
the expected value as we did with individual securities
13-15
Example: Expected Portfolio
Returns
• Consider the portfolio weights computed previously. If
the individual stocks have the following expected
returns, what is the expected return for the portfolio?
–
–
–
–
DCLK: 19.69%
KO: 5.25%
INTC: 16.65%
KEI: 18.24%
• E(RP) = .133(19.69) + .2(5.25) + .267(16.65) +
.4(18.24) = 15.41%
13-16
Portfolio Weights
• N.B.:
This says that the expected return on a
portfolio is a straightforward combination of
the expected returns on the assets in that
portfolio.
Portfolio Variance
• Compute the portfolio return for each
state:
RP = w1R1 + w2R2 + … + wmRm
• Compute the expected portfolio return
using the same formula as for an
individual asset
• Compute the portfolio variance and
standard deviation using the same
formulas as for an individual asset
13-18
Example 13.3 & 13.4
• Suppose we have the following projections
for three stocks:
State of
the
economy
Probability of
the state of
economy
Returns if
state occurs
on stock A
Returns if
state occurs
on stock B
Returns if
state occurs
on stock C
Boom
0.4
10%
15%
20%
Bust
0.6
8
4
0
Example 13.3 & 13.4
• What would be the expected return if half of
the portfolio were in A, with the remainder
equally divided between B and C?
• What are the standard deviation of the
portfolio?
Example 13.3 & 13.4
• First calculate the expected returns on the
individual stocks as follows:
• E(RA) = (0.4×10) + (0.6×8) = 8.8%
• E(RB) = (0.4×15) + (0.6×4) = 8.4%
• E(RC) = (0.4×20) + (0.6×0) = 8.0%
Then,
• E(RP) = (0.5×8.8) + (0.25×8.4) + (0.25×8)
= 8.5%
Example 13.3 & 13.4
• First, calculate the portfolio returns in the
two states.
(1) The portfolio return when the economy
booms is calculated as:
• E(RP) = (0.5×10) + (0.25×15) + (0.25×20)
= 13.75%
Example 13.3 & 13.4
(2) The portfolio return when the economy
busts is calculated as:
• E(RP) = (0.5×8) + (0.25×4) + (0.25×0)
= 5%
• E(RP) = (0.4×13.75) + (0.6×5) = 8.5%
Example 13.3 & 13.4
• The variance is:
σ2P = 0.4 × (0.1375 – 0.085)2 + 0.6 ×
(0.05 – 0.085) 2 = 0.0018375
• The standard deviation is:
σ = 4.3%
End of Chapter
13-25