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Chapter

3
Asset Allocation:
The Mean–Variance
Framework
Chapter Outline
3.1

Introduction: Motivation of the Mean–Variance Approach to Asset Allocation

3.2

Theory: Outline of the Mean–Variance Framework

3.3

Practice: Solution of Stylized Problems Using the Mean–Variance Framework

Appendix 1: Returns, Compounding, and Sample Statistics
Appendix 2: Optimization
Appendix 3: Notation

3.1

Introduction: Motivation of the Mean–Variance Approach
to Asset Allocation
Asset allocation is the term used to describe the set of weights of broad classes of
investments within a portfolio. For an individual investor, asset allocation can be represented by the proportional investment in bond mutual funds, stock mutual funds, and
money market investments. For example, if an investor holds $1,500 in bond mutual
funds, $3,000 in stock mutual funds, and $500 in money market funds, this asset allocation can be described as 30 percent bonds, 60 percent stocks, and 10 percent cash.
This set of weights would provide an initial summary of the risk profile of the individual investor’s investments, prior to completing a more detailed description of the
funds owned or an even more detailed description of the individual securities held
in the funds. Why does this allocation represent the risk profile? Certain investments
reflect greater volatility, and investing in multiple asset classes tends to be less risky
than placing 100 percent in any one investment.
Once an investor’s goals and objectives have been defined, setting the asset allocation
target is the first step in developing an investment program. These weights will define
the overall behavior of the portfolio and should be set to match the risk and return targets
for the investor. For example, an investor concerned about total return risk would tend to
have a higher weight in money market funds than would a more risk-tolerant investor.
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