active risk和active return

问题如下：

Hui Cheung, a portfolio manager, asks her assistant, Ronald Lam, to review the macroeconomic factor model currently in use and to consider a fundamental factor model as an alternative.

The current macroeconomic factor model has four factors:

$R_i=a_i+b_{i1}F_{GDP}+b_{i2}F_{CAP}+b_{i3}F_{CON}+b_{14}F_{UNEM}+\epsilon_i$

Where FGDP, FCAP, FCON, and FUNEM 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 Exhibit 1, the active risk for Portfolio 2 is explained by surprises in:

选项：

A.

GDP.

B.

consumer spending.

C.

all four model factors.

解释：

Active risk, also referred to as tracking risk or tracking error, is the sample standard deviation of the time series of active returns, where the active returns consist of the differences between the portfolio return and the benchmark return. Whereas GDP is the only portfolio non-zero sensitivity for Portfolio 2, the contribution to the portfolio’s active return is the sum of the differences between the portfolio’s and the benchmark’s sensitivities multiplied by the factor return. Because all four of the factor sensitivities of Portfolio 2 are different from the factor sensitivities of the benchmark, all four factors contribute to the portfolio’s active return and, therefore, to its active risk.