LOS k: Calculate the expected return on a portfolio of two stocks, given the estimated macroeconomic factor model for each stock.

Q1. Carla Vole has developed the following macroeconomic models:

• Return of Stock A = 6.5% + (9.6 × productivity) + (5.4 × growth in number of businesses)
• Return of Stock B = 18.7% + (2.5 × productivity) + (3.7 × growth in number of businesses)

Assuming a portfolio contains 60% Stock A and 40% Stock B, the portfolio’s sensitivity to productivity is closest to:

A)   4.72.

B)   6.76.

C)   5.34.

Q2. Colonial Capital leans heavily on the capital asset pricing model (CAPM) in its investment-making decisions, but the company’s analysts find it difficult to use. In an effort to make the calculations easier, Colonial has modified the CAPM to use the S& 1500 SuperComposite Index as a benchmark.

Colonial recently hired high-powered money manager Marjorie Kemp away from a rival company in an effort to boost its lagging returns. Kemp understands the appeal of the CAPM but likes to use multiple valuation methods for the purposes of comparison.

In her first act as chief investment officer of Colonial, Kemp sent a memo to all portfolio managers instructing them to start using alternative methods for valuing assets. She opened by touting the benefits of other forms of asset valuation.

• “The CAPM requires a lot of unrealistic assumptions. Arbitrage Pricing Theory’s (APT) assumptions are far less restrictive.”
• “A major benefit of multifactor models relative to the CAPM is their ability to be effectively tested using real-life data.”
• “Under APT, risk is easier to calculate than is the case with the CAPM, for which beta must be estimated based on unobservable returns.”
• “Neither multifactor models nor APT require an estimation of the market risk premium.”

Kemp then called a meeting of Colonial’s analysts to discuss asset-valuation strategies. The debate grew quite spirited.

A longtime Colonial analyst named Smathers said the company had experimented with multifactor models years earlier and could not come up with a model that satisfied everyone. He then proposed creating a number of multifactor models for different sectors. The responses were as follows:

• Florio said he didn’t like APT because it did not indicate what the risk factors were.
• Garcia said he liked APT because it acknowledged that arbitrage opportunities occasionally exist.
• Inge said he disliked APT because it did not allow analysts to consider the market portfolio.

After about 30 minutes, Kemp realized nothing productive would occur, so she set everyone to work analyzing a valuation model. She wrote the following equation on a blackboard:

Expected stock return = expected S& 1500 Index return / 2 + capacity utilization / 15 + 1.5 × GDP growth ? 2 × inflation

Which factors, taken in combination, would create the best multifactor model for utility stocks?

A)   Projected winter low temperature, interest rate term structure, housing starts, price/earnings factor.

B)   Projected change in energy prices, interest rate term structure, estimated GDP growth, projected market return.

C)   Projected winter low temperature, projected change in energy prices, projected change in inflation, projected market return.

Q3. Which statement represents Kemp’s weakest argument?

A)   “Under APT, risk is easier to calculate than is the case with the CAPM, for which beta must be estimated based on unobservable returns.”

B)   “The CAPM requires a lot of unrealistic assumptions. APT’s assumptions are far less restrictive.”

C)   “Neither multifactor models nor APT require an estimation of the market risk premium.”

Q4. Kemp’s equation is closest to:

A)   arbitrage pricing theory.

B)   a macroeconomic multifactor model.

C)   a microeconomic multifactor model.

Q5. Which analyst made the most sense?

A)   Florio.

B)   Garcia.

C)   Inge.

Q6. The Adams portfolio contains 35% Khallin Equipment stock and 65% Giant Semiconductor stock. Analyst Joe Karroll estimates that 40% of Khallin’s return variance is determined by cost trends and 60% is determined by purchasing trends. Karroll also estimates that Giant’s return variance is 75% determined by cost trends and 25 percent determined by purchasing trends. Assuming an estimated return of 7% for Khallin and 16% for Giant and a cost factor of –0.07 and a purchasing factor of 0.0325, the Adams portfolio’s expected return is closest to:

A)   12.9%.

B)   9.7%.

C)   8.0%.

Q7. Mary Carruthers has created the following macroeconomic model for stock in Magma Metro Systems and Clampett Pharmaceuticals:

• R-Magma = 12% + (6.3 × GDP growth) + (0.056 × population growth) + error.
• R-Clampett = 18% + (1.2 × GDP growth) – (0.231 × population growth) + error.

The expected return for a portfolio containing 65% Magma Metro Systems and 35% Clampett Pharmaceuticals is closest to:

A)   14%.

B)   16%.

C)   13%.

LOS k: Calculate the expected return on a portfolio of two stocks, given the estimated macroeconomic factor model for each stock. fficeffice" />

Q1. Carla Vole has developed the following macroeconomic models:

• Return of Stock A = 6.5% + (9.6 × productivity) + (5.4 × growth in number of businesses)
• Return of Stock B = 18.7% + (2.5 × productivity) + (3.7 × growth in number of businesses)

Assuming a portfolio contains 60% Stock A and 40% Stock B, the portfolio’s sensitivity to productivity is closest to:

A)   4.72.

B)   6.76.

C)   5.34.

Correct answer is B)

To calculate the portfolio’s factor sensitivity, we need the weighted average of the factor sensitivity of each stock: (9.6 × 60%) + (2.5 × 40%) = 6.76.

Q2. Colonial Capital leans heavily on the capital asset pricing model (CAPM) in its investment-making decisions, but the company’s analysts find it difficult to use. In an effort to make the calculations easier, Colonial has modified the CAPM to use the S& 1500 SuperComposite Index as a benchmark.

Colonial recently hired high-powered money manager Marjorie Kemp away from a rival company in an effort to boost its lagging returns. Kemp understands the appeal of the CAPM but likes to use multiple valuation methods for the purposes of comparison.

In her first act as chief investment officer of Colonial, Kemp sent a memo to all portfolio managers instructing them to start using alternative methods for valuing assets. She opened by touting the benefits of other forms of asset valuation.

• “The CAPM requires a lot of unrealistic assumptions. Arbitrage Pricing Theory’s (APT) assumptions are far less restrictive.”
• “A major benefit of multifactor models relative to the CAPM is their ability to be effectively tested using real-life data.”
• “Under APT, risk is easier to calculate than is the case with the CAPM, for which beta must be estimated based on unobservable returns.”
• “Neither multifactor models nor APT require an estimation of the market risk premium.”

Kemp then called a meeting of Colonial’s analysts to discuss asset-valuation strategies. The debate grew quite spirited.

A longtime Colonial analyst named Smathers said the company had experimented with multifactor models years earlier and could not come up with a model that satisfied everyone. He then proposed creating a number of multifactor models for different sectors. The responses were as follows:

• Florio said he didn’t like APT because it did not indicate what the risk factors were.
• Garcia said he liked APT because it acknowledged that arbitrage opportunities occasionally exist.
• Inge said he disliked APT because it did not allow analysts to consider the market portfolio.

After about 30 minutes, Kemp realized nothing productive would occur, so she set everyone to work analyzing a valuation model. She wrote the following equation on a blackboard:

Expected stock return = expected S& 1500 Index return / 2 + capacity utilization / 15 + 1.5 × GDP growth ? 2 × inflation

Which factors, taken in combination, would create the best multifactor model for utility stocks?

A)   Projected winter low temperature, interest rate term structure, housing starts, price/earnings factor.

B)   Projected change in energy prices, interest rate term structure, estimated GDP growth, projected market return.

C)   Projected winter low temperature, projected change in energy prices, projected change in inflation, projected market return.

Correct answer is A)

Without knowing the accuracy of the factor sensitivities or actually looking at the numbers generated by the equation, we can only assess the value of a multifactor model by considering whether the individual factors are relevant. Winter low temperatures and energy prices are particularly relevant to utilities, the first on the revenue side, and the second on the cost side. Because utilities tend to be heavily leveraged, interest rates affect them. Inflation rates are relevant for most companies, as are price/earnings ratios. Housing starts are relevant for utilities, as houses are larger than apartments and more expensive to heat and cool. However, utilities are considered diversifiers, and their returns are less correlated to those of the broader market than are the returns of stocks in other sectors. The sector is also less correlated to economic growth than most. As such, models that consider GDP growth or market returns are probably of less value than the one model that considers neither.

Q3. Which statement represents Kemp’s weakest argument?

A)   “Under APT, risk is easier to calculate than is the case with the CAPM, for which beta must be estimated based on unobservable returns.”

B)   “The CAPM requires a lot of unrealistic assumptions. APT’s assumptions are far less restrictive.”

C)   “Neither multifactor models nor APT require an estimation of the market risk premium.”

Correct answer is A)

It is debatable whether risk is easier to calculate under APT. True, the beta of the unobservable market portfolio is not needed, but the risk factors required for the APT equation are not provided. The analyst must select them. As such, the statement about the ease of calculating risk is open for interpretation. Both remaining statements are factually accurate, with no interpretation required.

Q4. Kemp’s equation is closest to:

A)   arbitrage pricing theory.

B)   a macroeconomic multifactor model.

C)   a microeconomic multifactor model.

Correct answer is B)

The arbitrage pricing theory and the capital asset pricing model equations use the risk-free return, so Kemp’s equation is not an APT. That leaves factor models. The market return is technically neither a macroeconomic or microeconomic variable, but it can be used with multifactor models. Since the other three variables represent macro factors, the equation is closest to a macroeconomic multifactor model.

Q5. Which analyst made the most sense?

A)   Florio.

B)   Garcia.

C)   Inge.

Correct answer is A)

Florio’s statement about risk factors is correct, and reflects a weakness in APT. Garcia’s statement is incorrect, because one of the assumptions inherent in the APT is that arbitrage opportunities do not exist. Inge is mistaken because, while APT does not require the use of the market portfolio, an analyst can certainly use the market portfolio as a factor if desired.

Q6. The ffice:smarttags" />Adams portfolio contains 35% Khallin Equipment stock and 65% Giant Semiconductor stock. Analyst Joe Karroll estimates that 40% of Khallin’s return variance is determined by cost trends and 60% is determined by purchasing trends. Karroll also estimates that Giant’s return variance is 75% determined by cost trends and 25 percent determined by purchasing trends. Assuming an estimated return of 7% for Khallin and 16% for Giant and a cost factor of –0.07 and a purchasing factor of 0.0325, the Adams portfolio’s expected return is closest to:

A)   12.9%.

B)   9.7%.

C)   8.0%.

Correct answer is B)

When we have data points for the macroeconomic model, we use the model to calculate expected returns, rather than falling back on the estimated returns of the individual stocks. To calculate portfolio returns using the macroeconomic models, we simply use the weighted average of the models. Here are the models:

Return-Khallin = 0.07 + (0.4 × -0.07) + (0.6 × 0.0325)
Return-Giant = 0.16 + (0.75 × -0.07) + (0.25 × 0.0325)

Assuming a 35% weighting for Khallin stock and a 65% weighting for Giant, the portfolio return = 0.129 + (0.628 × -0.07) + (0.373 × 0.0325) = 12.9% - 4.4% + 1.2% = 9.7%.

Q7. Mary Carruthers has created the following macroeconomic model for stock in Magma Metro Systems and Clampett Pharmaceuticals:

• R-Magma = 12% + (6.3 × GDP growth) + (0.056 × population growth) + error.
• R-Clampett = 18% + (1.2 × GDP growth) – (0.231 × population growth) + error.

The expected return for a portfolio containing 65% Magma Metro Systems and 35% Clampett Pharmaceuticals is closest to:

A)   14%.

B)   16%.

C)   13%.

Correct answer is A)

Given no information about GDP and population growth, we cannot calculate returns using the detailed model. As such, we fall back on the traditional assumption that the factors and random error in a macroeconomic model are expected to equal zero. As such, the expected return for the portfolio is the weighted average of the intercepts: 65% × 12% = 7.8% and 35% × 18% = 6.3% thus 7.8% + 6.3% = 14.1%.

marvelous!

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