Lecture 11
Introduction to Risk, Return, and the
Opportunity Cost of Capital
11-1
Risk and Return
Risk and Return are related.
How?
This chapter will focus on risk and return and their
relationship to the opportunity cost of capital.
11-2
Equity Rates of Return:
A Review
P ercentage R eturn =
D ividend Y ield =
C apital G ain Y ield =
C apital G ain + D ividend
Initial Share Price
D ividend
Initial Share Price
C apital G ain
Initial Share Price
11-3
Rates of Return: Example
Example: You purchase shares of GE stock at $15.13 on December 31, 2009. You
sell them exactly one year later for $18.29. During this time GE paid $.46 in
dividends per share. Ignoring transaction costs, what is your rate of return, dividend
yield and capital gain yield?
P ercentage R eturn 
$18.29  $15.13   $.46
 23.93%
$15.13
$ .4 6
D ivid en d Y ield =
 3 .0 4 %
$ 1 5 .1 3
C apital G ain Y ield 
$18.29  $15.13
$15.13

20.89%
11-4
Real Rates of Return
Recall the relationship between real rates and nominal rates:
1  real rate of return =
1 + nominal rate of return
1 + inflation rate
Example: Suppose inflation from December 2009 to December 2010 was
1.5%. What was GE stock’s real rate of return, if its nominal rate of return
was 23.93%?
11-5
Capital Market History:
Market Indexes
• Market Index - Measure of the investment performance of the
overall market.
• Dow Jones Industrial Average (The Dow)
• Standard & Poor’s Composite Index (S&P 500)
Other Market Indexes?
11-6
Total Returns for Different
Asset Classes
The Value of an Investment of $1 in 1900
11-7
What Drives the Difference in
Total Returns?
Maturity Premium: Extra average return from investing in
long- versus short-term Treasury securities.
Risk Premium: Expected return in excess of risk-free return
as compensation for risk.
11-8
Risk Premium: Example
E xpected M arket R eturn
=
Interest R ate on
+
T reasury B ills
N orm al R isk
P rem ium
1981: 21.6%
=
14%
+
7.6%
2008:
=
2.2%
+
7.6%
9.8%
11-9
Returns and Risk
How are the expected returns and
the risk of a security related?
11-10
Measuring Risk
What is risk?
How can it be measured?
Variance: Average value of squared deviations from
mean. A measure of volatility.
Standard Deviation: Square root of variance.
Also a
measure of volatility.
11-11
Variance and Standard
Deviation: Example
Coin Toss Game: calculating variance and standard deviation
(assume a mean of 10)
(1)
(2)
(3)
P ercent R ate of R etu rn
D eviation from M ean
S quared D eviation
+ 40
+ 30
900
+ 10
0
0
+ 10
0
0
- 20
- 30
900
V ariance = average of squared d eviations = 1 8 0 0 / 4 = 4 5 0
S tandard d eviation = square of root variance =
4 5 0 = 21.2%
11-12
Histogram of Returns
What is the relationship
between the volatility of
these securities and their
expected returns?
11-13
Historical Risk
(1900-2010)
11-14
Risk and Diversification
Diversification
Strategy designed to reduce risk by spreading a portfolio
across many investments.
Unique Risk:
Risk factors affecting only that firm. Also called
“diversifiable risk.”
Market Risk:
Economy-wide sources of risk that affect the overall stock
market. Also called “systematic risk.”
11-15
Diversification:
Building a Portfolio
A portfolio’s rate of return is the weighted sum of each asset’s rate of
return.
Two Asset Case:
P ortfolio R ate of R eturn
=
 fraction of portfolio 


in
first
asset


+
 fraction of portfolio 


in
second
asset


x
 rate of return 


on
first
asset


x
 rate of return 


on
second
asset


11-16
Building a Portfolio: Example
Consider the following portfolio:
Stock
Weight
Rate of Return
IBM
w IBM  50%
rIBM  8.3%
Starbucks
w SBUX  25%
rSBU X  12.5%
Walmart
wW  25%
rW  4.7%
What is the portfolio rate of return?
P ortfolio R ate of R eturn =
 w IB M
 rIB M
   w SB U X
 rSB U X
   wW
 rW

 (50%  8.3% )   25%  12.5%    25%  4.7% 
 8.45%
11-17
Do stock prices move together?
What effect does diversification have on a
portfolio’s total risk, unique risk and market risk?
11-18
Risk and Diversification
11-19
Thinking About Risk
 Message 1
• Some Risks Look Big and Dangerous but Really Are
Diversifiable
 Message 2
• Market Risks Are Macro Risks
 Message 3
• Risk Can Be Measured
11-20