Figures for Chapter 10
PORTFOLIO THEORY AND
ASSET RETURNS
(Investments : Spot and Derivatives
Markets)
© K. Cuthbertson and D. Nitzsche
Standard deviation
Figure 10.1 : Increasing size of portfolio
Diversifiable /
idiosyncratic risk
C
Market / non-diversifiable risk
0
1
2 ...
20
40
No. of shares in portfolio
© K. Cuthbertson and D. Nitzsche
Figure 10.2 : Individual preferences
ERp
I2 > I1
I2
I1
B
A
Y
s
ERp
Z
sp
© K. Cuthbertson and D. Nitzsche
Figure 10.3 : Efficient frontier
25
0, 1
Expected return (%)
20
0.5, 0.5
15
10
0.75, 0.25
1, 0
5
0
0
5
10
15
Standard deviation
© K. Cuthbertson and D. Nitzsche
20
25
Figure 10.4 : Risk reduction through
diversification
Expected return (%)
25
20
r = -1
15
r = +0.5
r = +1
10
r = -0.5
r=0
5
0
0
10
20
Std. dev.
© K. Cuthbertson and D. Nitzsche
30
Figure 10.5 : Efficient frontier (=AB)
ERp
A
x
B
x
x
P1
x
x
x
x
x
x
x
x
x
P2
x
x
x
x
C
sp
© K. Cuthbertson and D. Nitzsche
Figure 10.6 : Transformation line :
1 riskless + 1 risky asset
35
-0.5 borrowing +
1.5 in 1 risky bundle
Expected Return (%)
30
0.5 lending +
0.5 in 1 risky bundle
25
20
15
No borrowing/
no lending
10
All lending
5
0
0
5
10
15
20
25
Standard deviation
© K. Cuthbertson and D. Nitzsche
30
35
40
Figure 10.7 : Transformation lines :
1 safe + risky ‘bundles’
35
L’
Expected return (%)
30
sk = 25
25
20
L
sk = 30
15
10
5
0
0
10
20
Standard deviation
© K. Cuthbertson and D. Nitzsche
30
40
Figure 10.8 : Efficient frontier and CML
30
CML
Expected return
25
A
20
M
15
10
C
D
5
0
0
5
10
15
Standard deviation
© K. Cuthbertson and D. Nitzsche
20
25
Figure 10.9 : CML and market
portfolio (M)
CML
ER
B
M
ERm
wi - optimal proportions at M
A
r
a
sm
ERm - r
M’s B less risk averse
than M’s A
s
© K. Cuthbertson and D. Nitzsche
Figure 10.10 : Preferences of M’s A
and M’s B
IB
B
ER
IA
ERm
CML
M
wi - optimal proportions at M
A
r
a
sm
ERm - r
M’s B less risk averse
than M’s A
s
© K. Cuthbertson and D. Nitzsche
Figure 10.11 : Security market line
(SML)
Expected return
and
actual return
SML
Q (buy)
M
P
expected
return
T (sell)
r
actual
return
S (sell)
0.5
1
1.2
The larger is bi, the larger is ERi
© K. Cuthbertson and D. Nitzsche
Beta, bi
Incorrect Figure 10.6 as shown
in the textbook to follow
Transformation line :
1 riskless + 1 risky asset
© K. Cuthbertson and D. Nitzsche
Figure 10.6 : Transformation line :
1 riskless + 1 risky asset
20
Expected Return (%)
18
-0.5 borrowing +
1.5 in 1 risky bundle
0.5 lending +
0.5 in 1 risky bundle
16
14
12
No borrowing/
no lending
10
8
All lending
6
0
5
10
15
Standard deviation
© K. Cuthbertson and D. Nitzsche
20
25