Chapter
7
INTRODUCTION TO RISK
AND RETURN
Brealey, Myers, and Allen
Principles of Corporate Finance
11th Edition
McGraw-Hill/Irwin
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
FIGURE 7.1 THE VALUE OF AN INVESTMENT OF
$1 IN 1900
7-2
FIGURE 7.2 THE VALUE OF AN INVESTMENT OF
$1 IN 1900, REAL RETURNS
7-3
FIGURE 7.3 AVERAGE MARKET RISK PREMIUMS
7-4
FIGURE 7.4 DIVIDEND YIELDS IN THE U.S.
7-5
FIGURE 7.5 STOCK MARKET INDEX RETURNS
7-6
FIGURE 7.6 HISTOGRAM OF ANNUAL STOCK
MARKET RETURNS
7-7
7-2 MEASURING PORTFOLIO RISK
• Variance
• Average value of squared deviations from
mean; measures volatility
• Standard Deviation
• Square root of variance; measures volatility
7-8
TABLE 7.2 COIN-TOSSING GAME
7-9
7-2 MEASURING PORTFOLIO RISK
(
(
)(
Portfolio rate
fraction of portfolio
=
x
of return
in first asset
rate of return
on first asset
)(
)
)
fraction of portfolio
rate of return
+
x
in second asset
on second asset
7-10
FIGURE 7.7 EQUITY MARKET RISK
7-11
FIGURE 7.8 ANNUALIZED STANDARD DEVIATION OF DJIA OVER
PRECEDING 52 WEEKS, 1900-2011
7-12
7-2 MEASURING PORTFOLIO RISK
• Diversification
• Strategy designed to reduce risk by spreading
the 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”
7-13
FIGURE 7.10 COMPARING RETURNS
7-14
FIGURE 7.11 DIVERSIFICATION ELIMINATES
SPECIFIC RISK
7-15
FIGURE 7.12 VARIANCE OF A TWO-STOCK
PORTFOLIO
• Variance of two-stock portfolio is sum of
four boxes
7-16
7-3 CALCULATING PORTFOLIO RISK
• Example
• Invest 60% of portfolio in Heinz and 40% in
ExxonMobil. Expected dollar return on
Campbell Soup stock is 6% and 10% on
Boeing. Expected return on portfolio is:
Expected return  (.60  6)  (.40 10)  7.6%
7-17
7-3 CALCULATING PORTFOLIO RISK
• Example
• Invest 60% of portfolio in Heinz and 40% in ExxonMobil.
Expected dollar return on Heinz stock is 6% and 10%
on ExxonMobil. Standard deviation of annualized daily
returns are 14.6% and 21.9%, respectively. Assume
correlation coefficient of 1.0 and calculate portfolio
variance.
Heinz
ExxonMobil
x1 x2ρ12σ1σ 2  .40  .60
2 2
2
2
Heinz
x1 σ1  (.60)  (14.6)
114.6  21.9
x1 x2ρ12σ1σ 2  .40  .60
ExxonMobil
x22 σ 22  (.40) 2  (21.9) 2
114.6  21.9
7-18
7-3 CALCULATING PORTFOLIO RISK
• Example
• Invest 60% of portfolio in Heinz and 40% in ExxonMobil.
Expected dollar return on Heinz stock is 6% and 10%
on ExxonMobil . Standard deviation of annualized daily
returns are 14.6% and 21.9%, respectively. Assume
correlation coefficient of 1.0 and calculate portfolio
variance.
Portfolio variance  [(.60) 2  (14.6) 2 ]  [(.40) 2  (21.9) 2 ]
 2(.40  .60 14.6  21.9)
 228.7
Standard deviation  228.7  15.1 %
7-19
7-3 CALCULATING PORTFOLIO RISK
Expected portfolio return  ( x1 r1 )  ( x2 r2 )
Portfolio variance  x12σ12  x22σ 22  2( x1 x2ρ12σ1σ 2 )
7-20
7-3 CALCULATING PORTFOLIO RISK
• Example
Correlation Coefficient = .4
Stocks
s
ABC Corp
28
60%
15%
Big Corp
42
40%
21%
% of Portfolio
Average Return
• Standard deviation = weighted average = 33.6
• Standard deviation = portfolio = 28.1
• Real standard deviation:
= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= 28.1
• Return: r = (15%)(.60) + (21%)(.4) = 17.4%
7-21
7-3 CALCULATING PORTFOLIO RISK
• Example, continued
• Adding a third company to the portfolio:
Correlation Coefficient = .3
Stocks
s
Portfolio
28.1
50%
17.4%
New Corp
30
50%
19%
% of Portfolio
Avg Return
• Standard deviation = weighted average = 31.80
• Standard deviation = portfolio = 23.43
• NEW return = weighted average = portfolio = 18.20%
• Higher return, lower risk through diversification
7-22
FIGURE 7.13 PORTFOLIO VARIANCE
• Shaded boxes contain variance terms
• Unshaded boxes contain covariance terms
1
2
To calculate
portfolio
variance, add up
the boxes
3
STOCK 4
5
6
N
1
2
3
4 5 6
STOCK
N
7-23
7-4 HOW INDIVIDUAL SECURITIES AFFECT
PORTFOLIO RISK
• Market Portfolio
• Portfolio of all assets in economy
• Usually uses broad stock market index to
represent market
• Beta
• Sensitivity of stock’s return to return on market
portfolio
7-24
FIGURE 7.14 RETURNS ON FORD
• Return on stock
changes on
average by 1.53%
for each additional
1% change in
market return
• Beta = 1.53
Return on
Ford, %
Return on
market, %
7-25
FIGURE 7.15 BETA
7-26
7-4 HOW INDIVIDUAL SECURITIES AFFECT
PORTFOLIO RISK
• Beta Formula
σ im
βi  2
σm
•
σ im : covariance with market
•
σ
2
m : variance of market
7-27
TABLE 7.7 CALCULATING VARIANCE AND
COVARIANCE
7-28