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Transcript of Chapter 7 Principles of Corporate Finance Tenth Edition Introduction to Risk and Return Slides by...
Chapter 7Principles of
Corporate FinanceTenth Edition
Introduction to Risk and Return
Slides by
Matthew Will
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
7-2
Topics Covered
Over a Century of Capital Market HistoryMeasuring Portfolio RiskCalculating Portfolio RiskHow Individual Securities Affect Portfolio
RiskDiversification & Value Additivity
7-3
$1
$10
$100
$1,000
$10,000
$100,000
Start of Year
Dol
lars
(log
sca
le)
Common Stock
US Govt Bonds
T-Bills
14,276
24171
2008
The Value of an Investment of $1 in 1900
7-4
$1
$10
$100
$1,000
Start of Year
Dol
lars
(log
sca
le)
Equities
Bonds
Bills
581
9.85
2.87
2008
Real Returns
The Value of an Investment of $1 in 1900
7-5
Average Market Risk Premia (by country)
4.29 4.69 5.05 5.43 5.5 5.61 5.67 6.04 6.29 6.94 7.137.94 8.34 8.4 8.74 9.1 9.61 10.21
0123456789
1011
Den
mar
k
Bel
giu
m
Sw
itze
rlan
d
Irel
and
Sp
ain
Nor
way
Can
ada
U.K
.
Net
her
lan
ds
Ave
rage
U.S
.
Sw
eden
Au
stra
lia
Sou
th A
fric
a
Ger
man
y
Fra
nce
Jap
an
Ital
y
Risk premium, %
Country
7-6
Dividend Yield
Dividend yields in the U.S.A. 1900–2008
7-7
Rates of Return 1900-2008
Source: Ibbotson Associates Year
Per
cent
age
Ret
urn
Stock Market Index Returns
7-8
Measuring Risk
1 24
11 11
21
17
24
13
32
0
4
8
12
16
20
24
-50
to -
40
-40
to -
30
-30
to -
20
-20
to -
10
-10
to 0
0 to
10
10 t
o 20
20 t
o 30
30 t
o 40
40 t
o 50
50 t
o 60
Return %
# of Years
Histogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns
(1900-2008)(1900-2008)
7-9
Measuring Risk
Variance - Average of squared deviations from mean.
Standard Deviation – Square root of the variance. A measure of volatility.
7-10
Measuring Risk
Coin Toss Game-calculating variance and standard deviation
7-11
Measuring Risk
Portfolio rate
of return=
fraction of portfolio
in first assetx
rate of return
on first asset
+fraction of portfolio
in second assetx
rate of return
on second asset
((
(())
))
7-12
Equity Market Risk (by country)
17.02 18.45 19.22 20.16 21.83 22.05 22.99 23.23 23.42 23.51 23.98 24.09 25.2828.32 29.57
33.93 34.3
0
5
10
15
20
25
30
35
40
Can
ada
Au
stra
lia
Sw
itze
rlan
d
U.S
.
U.K
.
Den
mar
k
Sp
ain
Net
her
lan
ds
Sou
th A
fric
a
Irel
and
Sw
eden
Bel
giu
m
Fra
nce
Nor
way
Jap
an
Ital
y
Ger
man
y
Sta
ndar
d D
evia
tion
of A
nnua
l Ret
urns
, %
Average Risk (1900-2008)
7-13
Dow Jones Risk
Annualized Standard Deviation of the DJIA over the preceding 52 weeks
(1900 – 2008)
Years
Sta
ndar
d D
evia
tion
(%
)
7-14
Measuring 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.”
7-15
Comparing Returns
7-16
Measuring Risk
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
7-17
Measuring Risk
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
7-18
Portfolio Risk
22
22
211221
1221
211221
122121
21
σxσσρxx
σxx2Stock
σσρxx
σxxσx1Stock
2Stock 1Stock
The variance of a two stock portfolio is the sum of these four boxes
7-19
Portfolio Risk
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 expected return on your portfolio is:
%12)1540(.)1060(. ReturnExpected
7-20
Portfolio Risk
2222
22
211221
2112212221
21
)3.27()40(.σx3.272.181
60.40.σσρxxCola-Coca
3.272.181
60.40.σσρxx)2.18()60(.σxMobil-Exxon
Cola-CocaMobil-Exxon
Another 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 1.0 and calculate the portfolio variance.
7-21
Portfolio Risk
Another 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 1.0 and calculate the portfolio variance.
% 21.8 0.477 DeviationStandard
0.47718.2x27.3)2(.40x.60x
]x(27.3)[(.40)
]x(18.2)[(.60) Variance Portfolio22
22
7-22
Portfolio Risk
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
7-23
Portfolio Risk
Example Correlation Coefficient = .4
Stocks % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Real Standard Deviation:
= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= 28.1 CORRECT
Return : r = (15%)(.60) + (21%)(.4) = 17.4%
7-24
Portfolio Risk
Example Correlation Coefficient = .4
Stocks % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
Let’s Add stock New Corp to the portfolio
7-25
Portfolio Risk
Example Correlation Coefficient = .3
Stocks % of Portfolio Avg Return
Portfolio 28.1 50% 17.4%
New Corp 30 50% 19%
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION
7-26
Portfolio Risk
The shaded boxes contain variance terms; the remainder contain covariance terms.
1
2
3
4
5
6
N
1 2 3 4 5 6 N
STOCK
STOCKTo calculate portfolio variance add up the boxes
7-27
Portfolio Risk
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.
Beta - Sensitivity of a stock’s return to the return on the market portfolio.
7-28
Portfolio Risk
The return on Dell stockchanges on averageby 1.41% for eachadditional 1% change inthe market return. Betais therefore 1.41.
7-29
Portfolio Risk
The middle line shows that a wellDiversified portfolio of randomlyselected stocks ends up with 1and a standard deviation equal tothe market’s—in this case 20%.The upper line shows that awell-diversified portfolio with 1.5has a standard deviation of about30%—1.5 times that of the market.The lower line shows that awell-diversified portfolio with .5has a standard deviation of about10%—half that of the market.
7-30
Portfolio Risk
2m
imiB
7-31
Portfolio Risk
2m
imiB
Covariance with the market
Variance of the market
7-32
Beta
(1) (2) (3) (4) (5) (6) (7)Product of
Deviation Squared deviationsDeviation from average deviation from average
Market Anchovy Q from average Anchovy Q from average returnsMonth return return market return return market return (cols 4 x 5)
1 -8% -11% -10% -13% 100 1302 4 8 2 6 4 123 12 19 10 17 100 1704 -6 -13 -8 -15 64 1205 2 3 0 1 0 06 8 6 6 4 36 24
Average 2 2 Total 304 456
Variance = σm2 = 304/6 = 50.67
Covariance = σim = 736/6 = 76
Beta (β) = σim/σm2 = 76/50.67 = 1.5
Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of
the variance to the covariance (i.e., β = σim/σm2)