Chapter 11
Optimal Portfolio Choice and the Capital Asset Pricing Model
I. Chapter Outline
The following chapter outline is correlated to the PowerPoint Lecture Slides. The PowerPoint slides
are referenced in bold. Alternative Examples to selected textbook examples are also available in the
PowerPoint Lecture Slides and are also referenced in bold.
11.1 The Expected Return of a Portfolio (Slides 11-12, 19)
• Example 11.1 Calculating Portfolio Returns (Slides 13–14)
11.2 The Volatility of a Two-Stock Portfolio (Slide 24)
• Combining Risks (Slides 24–27)
• Table 11.1 Returns for Three Stocks, and Portfolios of Pairs of Stocks
• Determining Covariance and Correlation (Slides 28–30)
– Covariance (Slide 29)
– Correlation (Slide 30)
• Figure 11.1 Correlation (Slide 31)
• Example 11.3 The Covariance and Correlation of a Stock with Itself (Slides 32–33)
• Common Mistake: Computing the Variance, Covariance, and Correlation in Excel
• Table 11.2 Computing the Covariance and Correlation between Pairs of Stocks (Slide 34)
11.3 The Volatility of a Large Portfolio (Slide 47)
• Large Portfolio Variance
• Diversification with an Equally Weighted Portfolio (Slide 48)
11.4 Risk Versus Return: Choosing an Efficient Portfolio (Slide 55)
56)
• Figure 11.3 Volatility Versus Expected Return for Portfolios of Intel and Coca-Cola
Stock (Slide 57)
– Identifying Inefficient Portfolios
– Identifying Efficient Portfolios
• Example 11.9 Improving Returns with an Efficient Portfolio (Slides 59–60)
• PowerPoint Alternative Example 11.9 (Slides 61–62)
• The Effect of Correlation (Slide 63)
11.5 Risk-Free Saving and Borrowing (Slide 74)
• Investing in Risk-Free Securities (Slides 75–76)
• Figure 11.9 The Risk-Return Combinations from Combining a Risk-Free Investment and
11.6 The Efficient Portfolio and Required Returns (Slides 88)
• Portfolio Improvement: Beta and the Required Return (Slides 88–92)
11.7 The Capital Asset Pricing Model (Slide 101)
• The CAPM Assumptions (Slides 102–104)
11.8 Determining the Risk Premium (Slide 111)
• Market Risk and Beta (Slide 111)
• Example 11.16 Computing the Expected Return for a Stock (Slides 112–113)
• PowerPoint Alternative Example 11.16 (Slides 114–115)
• Example 11.17 A Negative-Beta Stock (Slides 116–117)
Chapter 11 Appendix: The CAPM with Differing Interest Rates (Slide 134)
• The Efficient Frontier with Differing Saving and Borrowing Rates
II. Learning Objectives
11-1 Given a portfolio of stocks, including the holdings in each stock, and the expected return in
each stock, compute the following:
a. Portfolio weight of each stock (equation 11.1)
b. Expected return on the portfolio (equation 11.3)
f. Standard deviation of the portfolio
11-3 Describe the contribution of each security to the portfolio.
11-5 Explain how an individual investor will choose from the set of efficient portfolios.
11-7 Explain the effect of combining a risk-free asset with a portfolio of risky assets, and compute
the expected return and volatility for that combination.
11-8 Illustrate why the risk-return combinations of the risk-free investment and a risky portfolio lie
11-9 Define the Sharpe ratio, and explain how it helps identify the portfolio with the highest
11-11 Use the beta of a security, expected return on a portfolio, and the risk-free rate to decide
whether buying shares of that security will improve the performance of the portfolio.
11-13 Use the risk-free rate, the expected return on the efficient (tangency) portfolio, and the beta of
a security with the efficient portfolio to calculate the risk premium for an investment.
11-15 Explain why the CAPM implies that the market portfolio of all risky securities is the efficient
portfolio.
11-17 Define beta for an individual stock and for a portfolio.
III. Chapter Overview
11.1 The Expected Return of a Portfolio
The authors begin by showing how to calculate the portfolio weights, then show the calculation of
11.2 The Volatility of a Two-Stock Portfolio
This section describes the statistics that can be used to quantify the diversification benefits described
in Chapter 10. Table 11.1 contains annual returns for three hypothetical stocks—North Air, West Air,
and Tex Oil—along with their average returns and volatilities. The table also includes returns and
11.3 The Volatility of a Large Portfolio
The authors first show the generalized form of the portfolio variance formula in equation 11.11. They
then simplify that formula by assuming that n stocks are equally weighted. Equation 11.12 shows the
11.4 Risk Versus Return: Choosing an Efficient Portfolio
This section begins with a two-stock portfolio of Intel and Coca-Cola. Those two stocks were
uncorrelated during the period examined. Table 11.4 shows the expected returns and volatility for
different portfolio weights of the two stocks. Figure 11.3 is a plot of the expected returns and
volatility, showing the efficient portfolios and the inefficient portfolios. The authors describe how
investors will select among efficient portfolios based on their risk preferences.
Figure 11.4 shows the effect on the risk and return of the portfolio when the correlation
coefficient changes.
11.5 Risk-Free Saving and Borrowing
This section starts by showing the expected return on a portfolio that combines the risk-free asset with
a risky portfolio. Equation 11.5 shows that calculation with a risk premium explicitly included.
11.6 The Efficient Portfolio and Required Returns
This section begins by examining how to determine whether the addition of a particular security, i, to
11.7 The Capital Asset Pricing Model
The CAPM uses actions of investors as input and identifies the efficient portfolio as the market
11.8 Determining the Risk Premium
Equation 11.22 gives the equation of the SML and equation 11.23 shows how beta is calculated:
Chapter 11 Appendix The CAPM with Differing Interest Rates
The appendix examines changes to the CAPM when borrowing and lending rates differ. Figure
11A.1 shows the effect of changing this assumption on the tangent portfolio and the investors’
optimal portfolio choice. The market portfolio must lie between the tangent portfolio implied by the
IV. Spreadsheet Solutions in Excel
The following Problems for Chapter 11 have spreadsheet versions of the problems available: 5, 6, 7,