chapter 8 charles p. jones, investments: analysis and management, twelfth edition, john wiley &...
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Chapter 8
Charles P. Jones, Investments: Analysis and Management,
Twelfth Edition, John Wiley & Sons
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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
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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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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)
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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
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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
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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
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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
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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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