Portfolio management

tsv · June 1, 2019, 7:49pm

The current macroeconomic factor model has four factors:

R_i = a_i + b_i₁F_GDP + b_i₂F_CAP + b_i₃F_CON + b_i₄F_UNEM + ε__i_,

Where F_GDP, F_CAP, F_CON, and F_UNEM represent unanticipated changes in four factors: gross domestic product, manufacturing capacity utilization, consumer spending, and the rate of unemployment, respectively. Lam assumes the error term is equal to zero when using this model.

Lam estimates the current model using historical monthly returns for three portfolios for the most recent five years. The inputs used in and estimates derived from the macroeconomic factor model are presented in Exhibit 1. The US Treasury bond rate of 2.5% is used as a proxy for the risk-free rate of interest.

Based on the information in Exhibit 1, the expected return for Portfolio 1 is closest to:

Inputs for and Estimates from the Current Macroeconomic Model

Factor Sensitivities and Intercept Coefficients** Factor Portfolio 1 Portfolio 2 Portfolio 3 Benchmark****Factor Surprise (%)** Intercept (%) 2.58 3.20 4.33 F_GDP 0.75 1.00 0.24 0.50 0.8 F_CAP –0.23 0.00 –1.45 –1.00 0.5 F_CON 1.23 0.00 0.50 1.10 2.5 F_UNEM –0.14 0.00 –0.05 –0.10 1.0

And the answer is: When using a macroeconomic factor, the expected return is the intercept (when all model factors take on a value of zero). The intercept coefficient for Portfolio 1 in Exhibit 1 is 2.58.

Do I miss the obvious? Factors in the model are surprises in GDP etc. and they are given in the table! and are not 0? The theory says that the expected surprises in the model are zero and that is why the required return is equal to the expected return on the asset/portfolio, but when we have surprises, the above formula should be used where the intercept is the risk-free.

Any comment on this please?

studyguy18 · June 2, 2019, 7:47am

As you’ve stated, the factors represent sensitivity to economic surprise - i.e. the prints for gross domestic product, manufacturing capacity utilization, consumer spending, and the rate of unemployment are not in line with market expectations. The expected return will be such that there is no economic surprise, meaning that the betas of the surprise factors will be zero as the prints are in line with the expected levels, consequently implying that the intercept is out expected level of return. If we were to integrate different levels of these factors into the base case of the model it would adjust the intercept and (likely) also the size of the respective betas, however the functioning of the model would be the same (i.e. base case all betas are equal to zero unless there is an unanticipated macro print).

Hope that helps.