chapter 12 choosing an investment portfolio. objectives to understand the process of personal...
TRANSCRIPT
Chapter 12
Choosing an Investment Portfolio
Objectives
To understand the process of personal portfolio selection in theory and in practice
To build a quantitative model of the trade-off between risk and reward
Contents
1. The Process of Personal Portfolio Selection
2. The Trade-Off between Expected Return and Risk
3. Efficient Diversification with Many Risky Assets
Portfolio Selection
A process of trading off risk and expected return to find the best portfolio of assets and liabilities
Portfolio Selection
The Life Cycle
Time Horizons
Risk Tolerance
The Life Cycle
In portfolio selection the best strategy depends on an individual ‘s personal circumstances:
Family status Occupation Income Wealth
Time Horizons
Planning Horizon: The total length of time for which one plans
Decision Horizon: The length of time between decisions to revise the portfolio
Trading Horizon: The minimum time interval over which investors can revise their portfolios.
Risk Tolerance
The characteristic of a person who is more willing than the average person to take on additional risk to achieve a higher expected return
Correlated Common Stock
The next slide shows statistics of two common stock with these statistics:
mean return 1 = 0.15 mean return 2 = 0.10 standard deviation 1 = 0.20 standard deviation 2 = 0.25 correlation of returns = 0.90 initial price 1 = $57.25 Initial price 2 = $72.625
2-Shares: Is One "Better?"
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 0.05 0.1 0.15 0.2 0.25 0.3
Standard Deviation
Exp
ecte
d R
etu
rn
Share Prices
0
50
100
150
200
250
300
350
0 1 2 3 4 5 6 7 8 9 10
Years
Val
ue
(ad
just
ed f
or
Sp
lits
)
ShareP_1
ShareP_2
Portfolio of Two Securities
0.00
0.05
0.10
0.15
0.20
0.25
0.15 0.17 0.19 0.21 0.23 0.25 0.27 0.29
Standard Deviation
Exp
ecte
d R
etu
rn
Share 1
Share 2
Efficient
Sub-optima
l
MinimumVariance
Formulae for Minimum Variance Portfolio
*1
22212,1
21
212,121*
2
22212,1
21
212,122*
1
1
2
2
w
w
w
Formulae for Tangent Portfolio
32tan
2
32tan
1
22
2tan1
1tan2
221212,121
212
212,12221tan
1
1
2
25.0*10.025.0*20.0*90.0*05.010.020.0*05.0
25.0*20.0*90.0*05.025.0*10.0
1
w
w
w
ww
rrrr
rrw
ffff
ff
Example: What’s the Best Return given a 10% SD?
1261.005.010.02409.0
05.02333.0
2409.0
90.0*25.0*2.0*3
5
3
8225.0
3
520.0
3
8
2
2333.0
10.03
515.0
3
8
tan
tan
tan
22
22
2tan
2,121tan2
tan1
22
2tan2
21
2tan1
2tan
tan
tan
2tan21
tan1tan
ff rr
wwww
ww
Achieving the Target Expected Return (2): Weights
Assume that the investment criterion is to generate a 30% return
This is the weight of the risky portfolio on the CML
3636.105.02333.0
05.030.0
1
1
11
ftangent
fcriterion
ftangentcriterion
r
rw
wrw
Achieving the Target Expected Return (2):Volatility
Now determine the volatility associated with this portfolio
This is the volatility of the portfolio we seek
3285.02409.0*3636.11 tangentw