**1**Thornhurst Investments Case Scenario

Lisa Jaworski is an equity portfolio manager for Thornhurst Investments, a large investment management company based in Charlotte, North Carolina. Thornhurst currently uses the capital asset pricing model (CAPM) to evaluate securities and mean–variance portfolio optimization to construct equity portfolios. Jaworski is meeting with two assistant portfolio managers, Yaodong Bi and Niyati Ahuja. Bi and Ahuja have been asked to do some research on ways to improve the methods currently being used by Thornhurst to evaluate securities and develop portfolios.

**Jaworski begins the meeting by outlining some issues relating to the CAPM and mean–variance analysis. She makes the following statement:**

Statement 1

One of the reasons I am uncomfortable using the CAPM is that it makes some very restrictive assumptions, such as investors

• pay no taxes on returns and no transaction costs on trades;

• have unique views on expected returns, variances, and correlations of securities; and

• can borrow and lend at the same risk-free rate of interest.

Bi suggests that multifactor models provide a better way to model stock returns. He develops two models on a whiteboard while stating: There are two ways to model stock returns using the following multifactor model:

R_{i }= a_{i} + b_{i1}F_{1} + b_{i2}F_{2} + … + b_{ik}F_{k }+ ε_{i}

Model 1: In this model, stock returns (R_{i}) are determined by surprises in economic factors, such as GDP growth and the level of interest rates.

Model 2: In this model, stock returns (R_{i}) are determined by factors that are company attributes, such as price-to-earnings ratio and market capitalization.

Although the interpretation of the intercept, a_{i}, is similar for both models, the factor sensitivities (b_{i}) are interpreted differently in the two models.

Ahuja notes that a multifactor arbitrage pricing model (APT) provides a much better basis than the CAPM for calculating expected portfolio returns and evaluating portfolio risk exposures. To illustrate the advantages of the multifactor APT model, Ahuja provides information for two portfolios Thornhurst currently manages. The information is provided in Exhibit 1. The current risk-free rate is 2%.

Exhibit 1 Factor Sensitivities and Risk Premia

**Ahuja makes the following statement:**

Statement 3

We can tell from Exhibit 1 that Portfolio A is structured in such a manner that it will benefit from an expanding economy and improving confidence because the factor sensitivities for confidence risk and business cycle risk exceed the factor sensitivities for the benchmark. Portfolio B has very low factor sensitivities for confidence risk and business cycle risk but moderately high exposure to inflation risk, thus Portfolio B can be referred to as a factor portfolio for inflation risk.

Jaworski wants to examine how active management is contributing to portfolio performance.

**Ahuja responds with the following statement:**

Statement 4

Our models show that Portfolio A has an annual tracking error of 1.25% and an information ratio of 1.2, whereas Portfolio B has an annual tracking error of 0.75% and an information ratio of 0.87. The information ratio of 1.2 for Portfolio A and the tracking error of 0.75 for Portfolio B demonstrate that both portfolios have benefited from active management.

1. Which assumption of the CAPM is least likely correct in Jaworski’s Statement 1? The assumption regarding:A. taxes and transaction costs.B. expected returns, variances, and correlations.C. borrowing and lending.2. With regard to Bi’s statement on multifactor models described by Model 2, Bi is least likely correct with respect to the:
A. Description of the factors.

B. Factor sensitivities bi.

C. Intercept value ai.

3. Based on the information in Exhibit 1, the expected return for portfolio A is closest to:

A. 12.2%.

B. 10.2%.

C. 8.4%.

4. Is Ahuja’s Statement 3 most likely correct?

A. No, she is incorrect about Portfolio A.

B. No, she is incorrect about Portfolio B.

C. Yes.

5. In Statement 4, Ahuja is most likely correct about the:

A. tracking error and the information ratio.

B. tracking error.

C. information ratio.

**2**Heddon Investment Advisers case scenario

Vikram Shah works as a portfolio manager for Heddon Investment Advisers. Shah is meeting with the investment committee of a corporate pension fund to discuss portfolio performance as well as strategies and techniques used in the management of the pension fund.

Jerry Cramer, a member of the investment committee, asks Shah, “Can you explain the model that you use to select stocks for inclusion in the equity portion of the pension portfolio?”

Shah responds, “At Heddon, the primary model we use is a multifactor model in which the factors are price-to-earnings ratio (P/E), financial leverage, and market capitalization.”

Shah moves on to a discussion about how Heddon assesses portfolio risk. He states, “We use a risk model to decompose active risk into the following two components:

Component 1

This component is referred to as ‘active factor risk,’ which is systematic risk attributable to differences in factor exposures between the portfolio and the benchmark. Note that the factors in our model are P/E, financial leverage, and market capitalization.

Component 2

The second component is a function of the individual asset’s active weight in the portfolio and the variance of returns unexplained by the three factors. This component is the active specific risk or asset selection risk.”

Shah continues, “We prefer to structure our portfolio so that in addition to being on the efficient frontier, it tilts, relative to the benchmark, toward stocks of large-capitalization companies with lower P/Es and lower levels of leverage. Exhibit 2 shows the factor sensitivities for the recommended portfolio and the benchmark.”

Exhibit 2: Factor Sensitivity

1. Shah’s response to Cramer’s question regarding the model used by Heddon Investment Advisers would imply that the multifactor model is most likely a:
A. statistical factor model.B. macroeconomic factor model.C. fundamental factor model.2. Is Shah correct about the components of active risk?
A. No, he is incorrect about Component 1

B. No, he is incorrect about Component 2

C. Yes

3. With respect to the factor tilts of the portfolio in Exhibit 2, Shah is least likely correct about the:

A. market capitalization.

B. P/E.

C. financial leverage.

### 快速校对：1~3 C C B