Principles of
Corporate Finance
Tenth Edition
Slides by
Matthew Will
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

Topics Covered

Over a Century of Capital Market History

Measuring Portfolio Risk

Calculating Portfolio Risk

How Individual Securities Affect Portfolio
Risk

Diversification & Value Additivity
7-2

7-3
$100,000
$10,000
$1,000
$100
$10
Common Stock
US Govt Bonds
T-Bills
$1
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Start of Year
14,276
241
71

7-4
Real Returns
$1,000
581
Equities
Bonds
Bills
$100
$10
$1
1900 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999
Start of Year
9.85
2.87

Average Market Risk Premia (by country)
Risk premium, %
11
10
9
8
7
6
3
2
1
0
5
4
4.29 4.69
5.05 5.43 5.5
5.61 5.67 6.04
6.29
6.94 7.13
7.94 8.34 8.4
8.74 9.1
9.61
10.21
7-5
Country

Dividend Yield
Dividend yields in the U.S.A. 1900–2008
10,00
9,00
8,00
7,00
6,00
5,00
4,00
3,00
2,00
1,00
0,00
7-6

Rates of Return 1900-2008
Stock Market Index Returns
80,0
60,0
40,0
20,0
0,0
-20,0
-40,0
-60,0
Source: Ibbotson Associates Year
7-7

Measuring Risk
# of Years
24
20
16
12
8
4
0
1
2
Histogram of Annual Stock Market Returns
(1900-2008)
24
21
17
13
11 11
4
3
2
Return %
7-8

Measuring Risk
Variance - Average of squared deviations from mean.
Standard Deviation
– Square root of the variance.
A measure of volatility.
7-9

Measuring Risk
Coin Toss Game-calculating variance and standard deviation
7-10

Measuring Risk
Portfolio rate of return
=
( 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
)
)
7-11

Average Risk (1900-2008)
40
35
30
25
20
15
10
17.02
18.45 19.22 20.16
21.83 22.05 22.99 23.23
23.42 23.51 23.98 24.09
25.28
28.32 29.57
33.93 34.3
5
0
7-12

Annualized Standard Deviation of the DJIA over the preceding 52 weeks
(1900 – 2008)
70
60
50
40
30
20
10
0
7-13
Years

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.”
7-14

Comparing Returns
7-15

Measuring Risk
7-16
0
5 10
Number of Securities
15

Measuring Risk
7-17
0
Unique risk
Market risk
5 10
Number of Securities
15

Portfolio Risk
The variance of a two stock portfolio is the sum of these four boxes
7-18
Stock 1
Stock 2
Stock 1 x 2
1
σ
1
2 x
1 x
2
σ
12
 x
1 x
2
ρ
12
σ
1
σ
2 x
1 x
2
σ
Stock 2

12 x
1 x
2
ρ
12
σ
1
σ
2 x
2
2
σ 2
2

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:
7-19
Expected Return

(.
60

10 )

(.
40

15 )

12 %

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.
Exxon
Coca
-
-
Mobil
Cola
Exxon Mobil x
1
2 σ
1
2 
(.
60 )
2 
( 18 .
2 )
2 x
1 x
2
ρ
12
σ
1
σ
2

1

18 .
2

.
40

27 .
3

.
60 x
1 x
Coca
2
ρ
12
σ
1
σ
2
Cola

.
40

.
60

1

18 .
2

27 .
3 x
2
2
σ 2
2

(.
40 )
2 
( 27 .
3 )
2
7-20

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.
Portfolio Variance

[(.60)
2 x(18.2)
2
]

[(.40)
2 x(27.3)
2
]

2(.40x.60x
18.2x27.3)

477 .
0
Standard Deviation

477 .
0

21.8
%
7-21

Portfolio Risk
Expected Portfolio Return

(x
1 r
1
)

( x
2 r
2
)
Portfolio Variance
 x
1
2 σ
1
2  x
2
2 σ 2
2

2 ( x
1 x
2
ρ
12
σ
1
σ
2
)
7-22

Example
Stocks
ABC Corp
Big Corp
Portfolio Risk s
28
42
Correlation Coefficient = .4
% of Portfolio Avg Return
60%
40%
15%
21%
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Real Standard Deviation:
= (28 2) (.6
2 ) + (42 2 )(.4
2 ) + 2(.4)(.6)(28)(42)(.4)
= 28.1 CORRECT
Return : r = (15%)(.60) + (21%)(.4) = 17.4%
7-23

Example
Stocks
ABC Corp
Big Corp
Portfolio Risk s
28
42
Correlation Coefficient = .4
% of Portfolio Avg Return
60%
40%
15%
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
7-24

Portfolio Risk
Example
Stocks
Portfolio
New Corp s
28.1
30
Correlation Coefficient = .3
% of Portfolio
50%
50%
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
Avg Return
17.4%
19%
7-25

Portfolio Risk
The shaded boxes contain variance terms; the remainder contain covariance terms.
STOCK
3
4
5
6
1
2
To calculate portfolio variance add up the boxes
7-26
N
1 2 3 4 5 6
STOCK
N

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.
7-27

The return on Dell stock changes on average by 1.41% for each additional 1% change in the market return. Beta is therefore 1.41.
Portfolio Risk
7-28

Portfolio Risk
The middle line shows that a well
Diversified portfolio of randomly selected stocks ends up with 1 and a standard deviation equal to the market’s—in this case 20%.
The upper line shows that a well-diversified portfolio with 1.5
has a standard deviation of about
30%—1.5 times that of the market.
The lower line shows that a well-diversified portfolio with .5
has a standard deviation of about
10%—half that of the market.
7-29

Portfolio Risk
B i
 s s im
2 m
7-30

B i
 s s im
2 m
Portfolio Risk
Covariance with the market
7-31
Variance of the market

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 = σ im
/σ m
2
)
(1)
Month
1
4
5
2
3
6
Average
(2)
Market return
-8%
4
12
-6
2
8
2
(3) (7)
Product of
Deviation
Deviation Squared from average deviation deviations from average
Anchovy Q from average Anchovy Q from average returns return
-11%
(4) market return
-10% return
(5)
-13%
(6) market return (cols 4 x 5)
100 130
8
19
-13
3
2
10
-8
0
6
17
-15
1
6 6 4
2 Total
Variance = σ m
2
= 304/6 = 50.67
4
100
64
0
36
304
12
170
120
0
24
456
Covariance = σ im
= 736/6 = 76
Beta (β) = σ im
/σ m
2
= 76/50.67 = 1.5
7-32