Reading 68: LOS k ～ Q1- 3

1.Carla Vole has developed the following macroeconomic models:

§ Return of Stock A = 6.5 percent + (9.6 × productivity) + (5.4 × growth in number of businesses)

§ Return of Stock B = 18.7 percent + (2.5 × productivity) + (3.7 × growth in number of businesses)

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

A)   6.76.

B)   4.72.

C)   5.34.

D)   6.05.

The correct answer was A)

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.

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

§ R-Magma = 12 percent + (6.3 × GDP growth) + (0.056 × population growth) + error.

§ R-Clampett = 18 percent + (1.2 × GDP growth) – (0.231 × population growth) + error.

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

A)   13%.

B)   14%.

C)   15%.

D)   16%.

The correct answer was B)

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%.

3.The Adams portfolio contains 35 percent Khallin Equipment stock and 65 percent Giant Semiconductor stock. Analyst Joe Karroll estimates that 40 percent of Khallin’s return variance is determined by cost trends and 60 percent is determined by purchasing trends. Karroll also estimates that Giant’s return variance is 75 percent determined by cost trends and 25 percent determined by purchasing trends. Assuming an estimated return of 7 percent for Khallin and 16 percent 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)   9.7%.

B)   8.0%.

C)   8.9%.

D)   12.9%.

The correct answer was A)

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 = .07 + (0.4 × -0.07) + (0.6 × 0.0325)
Return-Giant = .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 = .129 + (.628 × -0.07) + (.373 × 0.0325) = 12.9% - 4.4% + 1.2% = 9.7%.