LOS l, (Part 2): Calculate the expected return on an asset given an asset's factor sensitivities and the factor risk premiums, and determine whether an arbitrage opportunity exists, including how to exploit the opportunity.

Q1. Jose Morales has been investing for years, mostly using index funds. But because he is not satisfied with his returns, he decides to meet with Bill Smale, a financial adviser with Big Gains Asset Management.

Morales lays out his concerns about active management:

• “Mutual funds average returns below their benchmarks.”
• “All the buying and selling makes for less-efficient markets.”
• “Expenses are higher with active management.”
• “Analyst forecasts are often wrong.”

In an effort to win Morales’ business, Smale explains the benefits of active management, starting with the fact that market efficiency is a prime concern of active managers because efficient markets make active management possible. He then explains that active management allows for better protection against systematic risk, and that Big Gains uses multifactor models to adjust investment strategies to account for economic changes. Lastly, Smale tells Morales how Big Gains Asset Management has pledged never to reveal clients’ personal information to third parties.

Morales seems willing to listen, so Smale explains Big Gains’ management strategy, which involves a modified version of the Capital Asset Pricing Model (CAPM) using the Dow Jones Total Market Index. He raves about this valuation model, citing its ability to project future alphas, determine true market betas of individual stocks, create an accurate picture of the market portfolio, and provide an alternative for calculated covariances in the charting of the Markowitz Efficient Frontier.

After an hour of verbal sparring with Smale, Morales is not yet convinced of the wisdom of active management. He turns to Tobin Capital, calling Susan Worthan, a college friend who works as an analyst in the equity department. Tobin Capital uses the arbitrage pricing theory (APT) to value stocks. Worthan explains that APT offers several benefits relative to the CAPM, most notably its dependence on fewer and less restrictive assumptions.

After listening to Worthan’s explanation of the APT, Morales asked her how the theory dealt with mispriced stocks, drawing a table with the following data to illustrate his question:

After seeing Morales’ stock example, Worthan tells him that he still does not understand APT and tries to explain how the theory deals with mispriced stocks. Which of the following statements is most accurate? Under APT:

A)   mispricings cannot occur, and there is no arbitrage opportunity.

B)   the calculation of unsystematic risk is so accurate that mispricings are rare.

C)   any mispricings will be immediately rectified.

Q2. Which of the following is least likely an assumption of the market model?

A)   Unsystematic risk can be diversified away.

B)   The expected value of the error term is zero.

C)   The firm-specific surprises are uncorrelated across assets.

Q3. Smale best makes his point about the superiority of active management with his mention of:

A)   systematic risk.

B)   multifactor models.

C)   market efficiency.

Q4. Which assumption is required by both the CAPM and the APT?

A)   There are no transaction costs.

B)   Asset prices are not discounted for unsystematic risk.

C)   All investors have the same return expectations.

Q5. Which of Morales’ arguments against active management is least accurate?

A)   “Mutual funds average returns below their benchmarks.”

B)   “Expenses are higher with active management.”

C)   “All the buying and selling makes for less-efficient markets.”

Q6. Assuming Morales’ numbers are correct, portfolio allocation of 65% of one stock and 35% of a second would allow arbitrage profits to be closest to:

A)   0.29%.

B)   0%.

C)   0.90%.

Q7. Michael Paul, a portfolio manager, is screening potential investments and suspects that an arbitrage opportunity may be available. The three portfolios that meet his screening criteria are detailed below:

Which of the following portfolio combinations produces the highest return while maintaining a beta of 1.0?

          Portfolio A                               Portfolio B              Portfolio C

A)    25%                                      50%                                            25%

B)    50%                                      18%                                            32%

C)    100%                                   0%                                              0%

Q8. Gold Horizon, an investment firm, utilizes a three-factor APT model for its Unique & Rich (U&R) fund. The risk-free rate equals 4%. Using the table below, determine U&R’s expected return.

A)   7.38%.

B)   4.49%.

C)   11.38%.

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