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

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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

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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

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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

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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

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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

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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

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