Fundamentals of Investment Management
Hirt • Block
Portfolio Management and Capital
Market Theory- Learning Objectives
1. Understand the basic statistical techniques for
2.
3.
4.
5.
measuring risk and return
Explain how the portfolio effect works to
reduce the risk of an individual security.
Discuss the concept of an efficient portfolio
Explain the importance of the capital asset
pricing model.
Understand the concept of the beta coefficient
1
McGraw-Hill/Irwin
1
Hirt • Block
Fundamentals of Investment Management
Table 21-1 Return and Probabilities for investments I and j
Investment I
Pi
Possible
Return (probability of state of the
economy
Ki
Ki occuring)
5%
0.2
Recession
7
0.3
Slow growth
13
0.3
15
0.2
Ki
5%
7
13
15
Pi
0.2
0.3
0.3
0.2
McGraw-Hill/Irwin
K i Pi
1.0%
2.1%
3.9%
3.0%
10%
Investment j
Pi
(probability of
Return Kj Kj occuring)
20%
0.2
8
0.3
Moderate
growth
Strong
economy
Kj
20%
8
8
6
8
0.3
6
0.2
Pj
0.2
0.3
0.3
0.2
K j Pj
4.0%
2.4%
2.4%
1.2%
10%
2
2
Hirt • Block
Fundamentals of Investment Management
Investment i
ki
5%
7%
13%
15%
ki
10%
10%
10%
10%
(ki - k )
25%
9%
9%
25%
(ki - k )2 Pi
5.0%
2.7%
2.7%
5.0%
(ki - k )2 Pi
15.4%
3.9%
2
Pi (ki - k )
0.2
-5%
0.3
-3%
0.3
3%
0.2
5%
s2=
Deviation= s
Investment Standard
j
ki
20%
8%
8%
6%
ki
10%
10%
10%
10%
Pi
0.2
0.3
0.3
0.2
(ki - k )
100.00%
4.00%
4.00%
16.00%
(ki - k )2 Pi
20.0%
1.2%
1.2%
3.2%
(ki - k )2 Pi
=
25.6%
5.1%
2
(ki - k )
10%
-2%
-2%
-4%
s
2 =
=
Standard Deviation=
s
Note that
the average
is the same
for each
investment
but that the
standard
deviation
is different.
Also note
that
this model
assumes no
correlation
between
i and j.
3
McGraw-Hill/Irwin
3
Hirt • Block
Fundamentals of Investment Management
Portfolio Effect ( 2 stocks, equal weight)
Portfolio Return k
Assume stocks x1 and x2 with parameters:
x1 = .5
K1 = 10%
s1 = 3.9
x2 = .5
K2 = 10%
s2 = 5.1
Definition of portfolio expected return
according to equation 21-3.
Kp = x1 K1 + x2 K2
= .5(10 %) + .5(10 %) = 10%
McGraw-Hill/Irwin
4
4
Hirt • Block
Fundamentals of Investment Management
Standard Deviation of a Two-Stock Portfolio
( 2 stocks, equal weight)
sp =
2
xi
s i  x j s j  2 xi x j rij si s j
2
2
2
= .52(3.9)2+.52(5.1)2+2(.5)(.5) rij (3.9)(5.1)
= 3.85 +6.4 + .5 rij 19.9
rij
sp
-1.0
4.5 p
3.9 Correlation
3.2 Coefficient
2.3
1.8
0.0
Calculated
+1.0
standard deviation + .5
with differing
0.0
- .5
correlation
- .7
coefficients.
McGraw-Hill/Irwin
5
5
Fundamentals of Investment Management
Hirt • Block
Developing and Efficient Portfolio
 Many possible portfolios (i.e., combinations of
investments)
 The investor determines his personal riskreturn criteria
 An investor should select from the most
efficient portfolios (i.e., those with the
maximum return for a given risk).
 Portfolios do not exist above the "efficient
frontier"
6
McGraw-Hill/Irwin
6
Hirt • Block
Fundamentals of Investment Management
Diagram of Risk-Return Trade-Offs
(Figure 21-3)
Expected return Kp
15
14
13
F
G
C
12
11
10
A
9
0
H
B
E
D
Efficient
frontier
1
2
3
4
5
6
7
Portfolio standard deviation (sp) (risk)
McGraw-Hill/Irwin
8
7
7
Hirt • Block
Fundamentals of Investment Management
Diagram of Risk-Return Trade-offs
Expected return Kp
15
14
13
F
G
E
C
12
11
10
A
B
9
0
H
1
2
D
Inefficient
Efficient portfolios
frontier
3
4
5
6
7
Portfolio standard deviation (sp) (risk)
McGraw-Hill/Irwin
8
8
8
Fundamentals of Investment Management
Hirt • Block
Capital Asset Pricing Model
 The CAPM introduces the risk-free
asset where
sRF = 0.
 Under the CAPM, investors combine
the risk-free asset with risky
portfolios on the efficient frontier.
9
McGraw-Hill/Irwin
9
Fundamentals of Investment Management
Hirt • Block
The CAPM and Indifference Curves
(Fig21-8)
Expected return Kp
Initial: risk
free point
Maximum
attainable riskreturn
M
Satisfies
efficient frontier
RF
Z
Risk Return line
Efficient
frontier
Portfolio standard deviation (sp)
McGraw-Hill/Irwin
10
10
Fundamentals of Investment Management
Hirt • Block
Capital Asset Pricing Model
•The RFMZ line represents investment
opportunities that are superior to the
existing efficient frontier.
• RFMZ line is called capital market line.
•How do investors reach points on the
RFMZ line?
11
McGraw-Hill/Irwin
11
Fundamentals of Investment Management
Hirt • Block
Capital Asset Pricing Model
 To attain line RFM

Buy a combination of RFF and M portfolio
 To attain M Z

Buy M portfolio and borrow additional funds
at the risk-free rate.
12
McGraw-Hill/Irwin
12
Fundamentals of Investment Management
Hirt • Block
Capital Asset Pricing Model
Portfolio M is an optimum
“market basket of investments.”
M portfolio can be represented
by NYSE,or S&P 500.
Broadly based index is better
than narrowly based index.
13
McGraw-Hill/Irwin
13
Fundamentals of Investment Management
Hirt • Block
Security Market Line
 Refers to an individual stock


Trade-off between risk & return
Analogous to Capital Market Line for market
portfolios
 Formula is:

Ki = RF + bi (KM - RF)
14
McGraw-Hill/Irwin
14
Fundamentals of Investment Management
Hirt • Block
Illustration
of
the
Capital
Market
Line
(Figure 21-12)
Expected return Kp
return
KM
Security Market
Line (CML)
RF
Market standard deviation
O
McGraw-Hill/Irwin
1.0
2.0
Risk (Beta)
15
15
Hirt • Block
Fundamentals of Investment Management
Sharpe Approach
Sharpe
measure
Total portfolio return - Risk-free rate
= Portfolio standard deviation
Market data: KF = 5%
Portfolio Data: kp = .12
Sharpe
Measure =
bp = 1.2
sp = .14
.12 - .05
= 0.50
.14
Measures excess return per unit of total risk.
Also known as "excess return to variability" ratio.
Higher values indicate superior performance
16
McGraw-Hill/Irwin
16
Hirt • Block
Fundamentals of Investment Management
Treynor Approach
Treynor
measure
=
Total portfolio return - Risk-free rate
Portfolio Beta
Market data: KF = 6%
Portfolio Data: kp = 0.10
Treynor
Measure =
bp = 0.9
.10 - .06
= 0.044
0.9
Measures excess return per unit of systematic risk.
Also known as "excess return to volatility" ratio.
Higher values indicate superior performance
17
McGraw-Hill/Irwin
17
Hirt • Block
Fundamentals of Investment Management
Jensen Approach
 Alpha (average differential) return indicates
the difference between a) the return on the
fund and b) a point on the market line that
corresponds to a beta equal that of the fund.
 Alpha = the actual rate of return minus the rate
of return predicted by the CAPM.
18
McGraw-Hill/Irwin
©The McGraw-Hill Companies,
18 Inc.,1999
Hirt • Block
Fundamentals of Investment Management
Figure 22-2 Risk-Adjusted Portfolio Returns
ML = a  b (EMR)
Excess returns (%) EMR is "excess market return"
6
5
4
3
2
1
O
-1
-2
-3
Market line
Market
M
Z
Y
O
McGraw-Hill/Irwin
.5
1.O
Portfolio Beta
1.5
19
19
Fundamentals of Investment Management
Hirt • Block
Jensen Approach
 Jensen computed the alpha value of 115
mutual funds.
 The average alpha was a negative 1.1%
and only 39 out of 115 funds had a
positive alpha.
20
McGraw-Hill/Irwin
20