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Chapter 8
Charles P. Jones, Investments: Analysis and Management,
Twelfth Edition, John Wiley & Sons
8-1
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
8-2
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
8-3
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
8-4
8-5
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
xB
A
Cy
Risk =
E(R)
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
8-6
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
8-7
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
8-8
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
8-9
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
8-10
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◦ 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
No one “correct” approach to allocation
8-11
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
8-12
Impact of Diversification on Risk
p %
35
20
0
Number of securities in portfolio10 20 30 40 ...... 100+
Diversifiable (nonsystematic) risk
Nondiversifiable (systematic) risk
Total risk
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 back-up 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.
8-14