chapter 12 choosing an investment portfolio. objectives to understand the process of personal...

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

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rrrr

rrw

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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

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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