Transcript CH10.ppt
Chapter 10
Portfolio Theory
Investments
Figure 3 : Histogram US real return (Feb 1915 – April 2004)
120
100
Frequency
80
60
40
20
0
-0.15
-0.11
-0.07
-0.03
0.01
0.05
0.09
0.13
Correlations and Covariance
3
Correlation is the degree of association between
two variables
Covariance is the product moment of two random
variables about their means
Correlation and covariance are related and generally
measure the same phenomenon
Correlations and Covariance (cont’d)
4
COV ( A, B) AB E ( A A)( B B )
AB
COV ( A, B)
A B
Correlations and Covariance (cont’d)
5
COV ( A, B) AB E ( A A)( B B )
AB
COV ( A, B)
A B
Portfolio Standard deviation
Figure 1 : Random selection of stocks
22%
Specific/Diversifiable /
idiosyncratic risk
10.8%
??%
9.8%
Market / Systematic/
non-diversifiable risk
0
1
2 ... 10
20
35
Number of shares in portfolio
© K. Cuthbertson and D. Nitzsche
Table 2 : Individual stock returns
Returns
State Interest Growth
Prob.
Stock 1
Stock 2
1
High
Low
0.25
-5
45
2
High
High
0.25
5
35
3
Low
Low
0.25
10
10
4
Low
High
0.25
25
-5
© K. Cuthbertson and D. Nitzsche
Table 3 : Summary statistics
Stocks
Stock 1
Stock 2
Mean, ERi
8.75%
21.25%
Std. dev, i
10.83%
19.80%
Correlation
-0.9549
Covariance
-204.688
© K. Cuthbertson and D. Nitzsche
Table 4 : Risky portfolio
Alternativ
e risky
portf.
Share of
Portfolio
Stock 2,
w2
0
ERp
p
A
Stock 1,
w1
1
8.75%
10.83%
G
0.75
0.25
11.88%
3.70%
P
0.5
0.5
15%
5%
Z
0
1
21.25%
19.80%
© K. Cuthbertson and D. Nitzsche
Figure 2 : Efficient frontier
25
(0, 1)
Expected return (%)
20
Z
(0.5, 0.5)
P
G
(0.75, 0.25)
15
10
A
(1, 0 )
5
0
0
5
10
15
Standard deviation
© K. Cuthbertson and D. Nitzsche
20
25
Table 3 : Capital allocation line
50
45
Expected Return (%)
40
L
35
0.25 lending +
0.75 in risky portfolio
30
P
25
-0.5 borrowing
from bank
1.5 in risky portfolio
D
20
No borrowing/
no lending
15
10
5
F
0
0
All lending in bank deposit
At risk-free rate
5
10
15
Standard Deviation
© K. Cuthbertson and D. Nitzsche
20
25
30
Figure 4 : Efficient frontier and CML
45
40
35
Expected Return (%)
Q
30
25
Z
CML
20
CAL
15
X
P
10
5
F
A
G
0
0
5
10
15
Standard Deviation
20
25
Figure 5 : CML and market portfolio
Expected
Return
SRp = (ERp-r)/p
CML
L
ERL
P
ERp
ERD
r
wi - optimal proportions at P
(market portfolio)
ERp - r
D
p
D
© K. Cuthbertson and D. Nitzsche
M’s L less risk averse
than M’s D
p
L
Standard deviation
Figure 6 : Efficient frontier and correlation
Expected return (%)
25
20
= -1
15
= +0.5
= +1
10
= -0.5
=0
5
0
0
10
20
Std. dev.
© K. Cuthbertson and D. Nitzsche
30
Figure 7 : Efficient frontier, many stocks
ERp, % p.m.
=1.1%
=1.0%
x
B
x
x
x
xx x x x x
x x x x
x
x P1
x
xx x
x P2
x
x x
x
x
A
x C
p , % p.m.
© K. Cuthbertson and D. Nitzsche