Chapter 8
Charles P. Jones, Investments: Analysis and Management,
Twelfth Edition, John Wiley & Sons
81



Diversification is key to optimal risk
management
Asset allocation is most important single
decision
Using Markowitz Principles
◦ Step 1: Identify optimal risk-return combinations
using the Markowitz efficient frontier analysis
 Estimate expected returns, variances and
covariances
◦ Step 2: Choose the final portfolio based on your
preferences for return relative to risk
82


Optimal diversification takes into account all
available information
Assumptions in portfolio theory
◦ A single investment period (one year)
◦ Liquid position (no transaction costs)
◦ Preferences based only on a portfolio’s expected
return and risk
83



Smallest portfolio risk for a given level of
expected return
Or largest expected return for a given level of
portfolio risk
From the set of all possible portfolios
◦ Only locate and analyze the subset known as the
efficient set
84

x
B

E(R) A
y
C
Risk = 

Efficient frontier or
Efficient set
(curved line from A
to B)
Global minimum
variance portfolio
(represented by
point A)
Portfolios on AB
dominate those on
AC
85



Portfolio weights are only variable that can
change in Markowitz analysis
Assume investors are risk averse
Indifference curves help select from efficient
set
◦ Description of preferences for risk and return
◦ Portfolio combinations which are equally desirable
◦ Match investor preferences with portfolio
possibilities
86


International diversification unlikely to offer
as much risk reduction as it has in the past
Markowitz portfolio selection model
◦ Assumes investors use only risk and return to
decide
◦ Generates a set of equally “good” portfolios
◦ Does not address the issues of borrowed money or
risk-free assets
◦ Cumbersome to apply
87

Another way to use Markowitz model is with
asset classes
◦ Allocation of portfolio assets to asset types
 Asset class rather than individual security decisions
likely most important for investors
◦ Can be used when investing internationally
◦ Different asset classes offers various returns and
levels of risk
 Correlation coefficients may be quite low
88

Includes two dimensions
◦ Diversifying between asset classes
◦ Diversifying within asset classes

Asset classes include
◦
◦
◦
◦
◦
◦
International equities
Bonds
Treasury Inflation-Indexed Securities (TIPS)
Real estate
Gold
Commodities
89



Correlation among asset classes must be
considered
Correlations change over time
For individual investors, allocation depends
on
◦ Time horizon
◦ Risk tolerance

Diversified asset allocation doesn’t
necessarily provide benefits or guarantee
against loss
810

Index Mutual Funds and ETFs
◦ Investors can buy funds covering various asset
classes
 Domestic large-cap stocks, domestic small-cap
stocks
 International stocks
 Bond funds

Life Cycle Analysis

No one “correct” approach to allocation
◦ Varies asset allocation based on age of investor
◦ Life-cycle funds (target-date funds) hold various
asset classes and the allocation changes as investor
ages
811
Impact of Diversification on Risk

Total risk = systematic (nondiversifiable) risk
+ nonsystematic (diversifiable) risk
◦ Systematic risk is market risk and common to
virtually all securities
◦ Nonsystematic risk is company-specific risk


Total risk can go no lower than systematic
risk
Both risk components can vary over time
 Affects number of securities needed to diversify
812
p %
35
Total risk
Diversifiable (nonsystematic) risk
20
Nondiversifiable (systematic) risk
0
10
20
30
40
......
Number of securities in portfolio
100+
Copyright 2013 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation of
this work beyond that permitted in section 117 of
the 1976 United States Copyright Act without
express permission of the copyright owner is
unlawful. Request for further information should be
addressed to the Permissions Department, John
Wiley & Sons, Inc. The purchaser may make backup copies for his/her own use only and not for
distribution or resale. The Publisher assumes no
responsibility for errors, omissions, or damages
caused by the use of these programs or from the
use of the information herein.
814