Transcript
Page 1: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

Chapter 12

Choosing an Investment Portfolio

Page 2: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 3: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

Contents

1. The Process of Personal Portfolio Selection

2. The Trade-Off between Expected Return and Risk

3. Efficient Diversification with Many Risky Assets

Page 4: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

Portfolio Selection

A process of trading off risk and expected return to find the best portfolio of assets and liabilities

Page 5: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

Portfolio Selection

The Life Cycle

Time Horizons

Risk Tolerance

Page 6: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

The Life Cycle

In portfolio selection the best strategy depends on an individual ‘s personal circumstances:

Family status Occupation Income Wealth

Page 7: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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.

Page 8: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 9: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 10: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 11: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 12: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 13: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

Formulae for Minimum Variance Portfolio

*1

22212,1

21

212,121*

2

22212,1

21

212,122*

1

1

2

2

w

w

w

Page 14: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 15: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 16: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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

Page 17: Chapter 12 Choosing an Investment Portfolio. Objectives  To understand the process of personal portfolio selection in theory and in practice  To build

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


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