Corporate finance chapter 012 porfolio selection and diversification

Chapter 12: Portfolio
Selection and Diversification

Objective
To understand the theory of personal
portfolio selection in theory
and in practice
1
Copyright © Prentice Hall Inc. 2000. Author: Nick Bagley, bdellaSoft, Inc.


Chapter 12 Contents
• 12.1 The process of personal portfolio
selection
• 12.2 The trade-off between expected
return and risk
• 12.3 Efficient diversification with many
risky assets
2


Objectives
• To understand the process of personal
portfolio selection in theory and practice

3


Security Prices
100000
Stock

Bond
Stock_Mu
Bond_Mu

Value (Log)

10000

1000

100

10
0

5

10

15

20

25

Years

4

30

35

40


Security Prices
100000
Stock
Bond
Stock_Mu
Bond_Mu

Value (Log)

10000

1000

100

10
0

5

10

15

20

25

Years

5

30

35

40


Security Prices
100000
Stock
Bond
Stock_Mu
Bond_Mu

Value (Log)

10000

1000

100

10
0

5

10

15

20

25

Years

6

30

35

40


…and Lots More!
Security Prices

Security Prices

100000

100000
Stock
Bond
Stock_Mu
Bond_Mu

Stock
Bond
Stock_Mu
Bond_Mu

10000
Value (Log)

Value (Log)

10000

1000

100

1000

100

10
0

5

10

Security
15
20Prices
25

10
30

35

40

0

5

10

Security
15
20Prices
25

Years
100000

100000
Stock
Bond
Stock_Mu
Bond_Mu

1000

100

35

40

30

35

40

Stock
Bond
Stock_Mu
Bond_Mu

10000
Value (Log)

Value (Log)

10000

30

Years

1000

100

10

10
0

5

10

15

20
Years

25

30

35

40

0

7

5

10

15

20
Years

25


Security Prices
100000
Stock
Bond
Stock_Mu
Bond_Mu

Value (Log)

10000

1000

100

10
0

5

10

15

20
Years

25

8

30

35

40


Probability of Future Price
0.035
Prob_Stock_2
Prob_Bond_2

Prob_Stock_5
Prob_Bond_5
Prob_Stock_10
Prob_Bond_10
Prob_Stock_40
Prob_Bond_40

Probability Density

0.030
0.025
0.020
0.015
0.010
0.005
0.000

0

50

100

150

Value

200

9

250

300


Probabilistic Stock Price Changes Over Time
0.020
Stock_Year_1
Stock_Year_2
Stock_Year_3
Stock_Year_4
Stock_Year_5
Stock_Year_6
Stock_Year_7
Stock_Year_8
Stock_Year_9
Stock_Year_10

0.018
Probability Density

0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002

0.000
0

200

400
Price

600

10

800


Probabilistic Bond Price Changes over Time
0.045
Bond_Year_1
Bond_Year_2
Bond_Year_3
Bond_Year_4
Bond_Year_5
Bond_Year_6
Bond_Year_7
Bond_Year_8
Bond_Year_9
Bond_Year_10

0.040
Probability Density

0.035
0.030
0.025
0.020
0.015
0.010
0.005
0.000
0

100

200
Price

300

11

400


Mode =104

Median=104

1-Year Out

Mode =106

Mean =104

0.0450
0.0400

Median=111

Stock_1_Year
Bond_1_Year

0.0350

Mean = 113

Density

0.0300
0.0250
0.0200
0.0150
0.0100
0.0050
0.0000
0

20

40

60

80

100

120

Price

12

140

160

180

200


Two Years Out
0.035
0.030
Stock_2_Year
Bond_2_Year

Density

0.025

0.020
0.015
0.010
0.005
0.000
0

20

40

60

80

100

120

Price

13

140

160

180

200

5-Years Out

Mode = 122

0.020
0.018
Stock_5_Year
Bond_5_Year

0.016

Density

0.014

Median=
126
Mean = 128
Mode = 135

0.012
0.010

Median=
165
Mean = 182

0.008

0.006
0.004
0.002
0.000
0

100

200

300
Price

400

14

500


10-Years Out
0.012
0.010
Stock_10_Year

Density

0.008

Bond_10_Year

0.006
0.004
0.002
0.000
0

200

400

600

800

Value

15

1,000


40 Years Out

Mode =503

0.002

Median=650

0.001

Mean =739

Density

0.001

Stock_40_Year
Bond_40_Year

Mode =1,102

0.001
0.001

Median=5,460

0.001

Mean =12,151

0.000
0.000
0.000
0

5,000

10,000

15,000

20,000

Value

16

25,000

30,000


Value of Central Tendency Statistics for the LogNormal
1_Year

2_Years

5_Years

10_Years 40_Years

Assume: Sig = 0.20, Mu = 0.12
mode
$106.18
$112.75
median
$110.52
$122.14

mean
$112.75
$127.12

$134.99
$164.87
$182.21

$182.21 $1,102.32
$271.83 $5,459.82
$332.01 $12,151.04

Assume: Sig = 0.08, Mu = 0.05
mode
$104.12
$108.42
median
$104.79
$109.81
mean
$105.13
$110.52

$122.38
$126.36
$128.40

$149.78
$159.68
$164.87

mode
median
mean

The most probable price
50% of prices are equal or lower that this
The expected or average price

17

$503.29
$650.13
$738.91


Mortality Table
Male

Female

Age MDePm MExLife FDePm FExLife
60
16.08
17.51
9.47
21.25
61
17.54
16.79

10.13
20.44
65
25.42
14.04
14.59
17.32
70
39.51
10.96
22.11
13.67
75
64.19
8.31
38.24
10.32
80
98.84
6.18
65.99
7.48
85 152.95
4.46
116.1
5.18
90 221.77
3.18 190.75
3.45
95 329.96

1.87 317.32
1.91
18


Deaths Per Thousand M & F
350
300
MDePm

Deaths / 1000

250

FDePm
200
150
100
50
0
60

65

70

75

80

85

Age

19

90

95


Life Expection

Remaining Expected Life

25

20
MExLife
15

FExLife

10

5

0
60

65

70

75

80

85

Age

20

90

95


Combining the Riskless Asset
and a Single Risky Asset
– The expected return of the portfolio is the
weighted average of the component returns

µp = W1*µ1 + W2*µ2
µp = W1*µ1 + (1- W1)*µ2

21

Combining the Riskless Asset
and a Single Risky Asset
– The volatility of the portfolio is not quite as
simple:

σp = ((W1* σ1)2 + 2W1* σ1* W2* σ2
+ (W2* σ2)2)1/2

22


Combining the Riskless Asset
and a Single Risky Asset
– We know something special about the
portfolio, namely that security 2 is riskless, so

σ2 = 0, and σp becomes:

σp = ((W1* σ1)2 + 2W1* σ1* W2* 0 +
(W2* 0)2)1/2
σp = |W1| * σ1
23


Combining the Riskless Asset
and a Single Risky Asset
– In summary

σp = |W1| * σ1, And:
µp = W1*µ1 + (1- W1)*rf , So:

If

W1>0, µp = [(rf -µ1)/ σ1]*σp + rf

Else

µp = [(µ1-rf )/ σ1]*σp + rf
24


A Portfolio of a Risky and a Riskless Security
0.30
0.25
0.20

Return

0.15
0.10
0.05
0.00
0.00
-0.05

0.10

0.20

0.30

-0.10
-0.15
-0.20
Volatility

25

0.40

0.50