CHAPTER 6
AN INTRODUCTION TO PORTFOLIO MANAGEMENT
6.1 Some Background Assumptions
▪ Investors want to maximize the returns from the total set of investments for a given level of
6.1.1 Risk Aversion
▪ Portfolio theory assumes that investors are risk averse.
6.1.2 Definition of Risk
6.2 The Markowitz Portfolio Theory
▪ The Markowitz model assumptions:
1. Investors consider each investment alternative as being represented by a probability
distribution of potential returns over some holding period.
3. Investors estimate the risk of the portfolio on the basis of the variability of potential
returns.
5. For a given risk level, investors prefer higher returns to lower returns. Similarly, for a
given level of expected return, investors prefer less risk to more risk.
6.2.1 Alternative Measures of Risk
▪ Variance or standard deviation of expected returns
▪ Range of returns
6.2.2 Expected Rates of Return
▪ Individual investment
6.2.3 Variance (Standard Deviation) of Returns for an Individual Investment
6.2.4 Variance (Standard Deviation) of Returns for a Portfolio
1. Covariance of Returns
▪ Measure of the degree to which two variables move together relative to their
2. Covariance and Correlation
▪ Correlation coefficient is obtained by standardizing (dividing) the covariance by the
6.2.5 Standard Deviation of a Portfolio
1. Portfolio Standard Deviation Formula
▪ Standard deviation for a portfolio of assets is a function of the weighted average of
2. Portfolio Standard Deviation Calculation
▪ Any asset or portfolio of assets can be described by two characteristics: the expected
rate of return and the standard deviation of returns.
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6.2.6 A Three-Asset Portfolio
6.2.7 Estimation Issues
▪ For every asset (or asset class) being considered for inclusion in the portfolio, estimate:
6.3 The Efficient Frontier
▪ Set of risk-minimizing portfolios for each potential expected return goal is called the efficient
6.3.1 The Efficient Frontier: An Example
6.3.2 The Efficient Frontier and Investor Utility
▪ An investor will target a point along the efficient frontier based on utility function, which
reflects attitude toward risk.
6.4 Capital Market Theory: An Overview
6.4.1 Background for Capital Market Theory
▪ Assumptions of Capital Market Theory:
2. Investors can borrow or lend any amount of money at the risk-free rate of return.
4. All investors have the same one-period time horizon.
6. There are no taxes or transactions costs.
8. Capital markets are in equilibrium.
6.4.2 Developing the Capital Market Line
▪ A risky asset is one from which future returns are uncertain.
1. Covariance with a Risk-Free Asset
2. Combining a Risk-Free Asset with a Risky Portfolio
a. Expected Return
▪ Expected rate of return for a portfolio that combines a risk-free asset with a collection
3. The Capital Market Line
▪ There are various possibilities when a risk-free asset is combined with alternative
4. Risk–Return Possibilities with Leverage
6.4.3 Risk, Diversification, and the Market Portfolio
▪ Market portfolio M is a completely diversified portfolio.
▪ Unique or unsystematic risk
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1. Diversification and the Elimination of Unsystematic Risk
▪ A well-diversified portfolio must contain at least 30–40 stocks (Exhibit 6.19)
2. The CML and the Separation Theorem
▪ The decision to invest in the market portfolio is the investment decision.
3. A Risk Measure for the CML
▪ The relevant risk to consider when adding a security to a portfolio is its average
6.4.4 Investing with the CML: An Example