这个题为什么不能用APT模型求解？

问题如下：

5. Based on the data in Exhibits 2 and 3, the return for Portfolio AC, given the surprises in inflation and GDP growth, is closest to:

选项：

A.

2.02%.

B.

2.40%.

C.

4.98%

解释：

A is correct.

The macroeconomic two-factor model takes the following form: $R_i=a_i+b_{i1}F_{INF}+b_{i2}F_{GDP}+\varepsilon_i,$

where FINF and FGDP represent surprises in inflation and surprises in GDP growth, respectively, and ai represents the expected return to asset i. Using this model and the data in Exhibit 2, the returns for Fund A and Fund C are represented by the following:

R_A = 0.02 + 0.5_FINF + 1.0F_GDP + ε_A R_C = 0.03 + 1.0_FINF + 1.1F_GDP + ε_c

Surprise in a macroeconomic model is defined as actual factor minus predicted factor. The surprise in inflation is 0.2% (= 2.2% – 2.0%). The surprise in GDP growth is –0.5% (= 1.0% – 1.5%). The return for Portfolio AC, composed of a 60% allocation to Fund A and 40% allocation to Fund C, is calculated as the following:

R_AC = (0.6)(0.02) + (0.4)(0.03) + [(0.6)(0.5) + (0.4)(1.0)](0.002)+ [(0.6)(1.0) + (0.4)(1.1)]( –0.005) + 0.6(0) + 0.4(0) = 2.02%

考点：macroeconomic model

解析：

已知Zapata使用的是含有inflation和GDP growth两因子的宏观经济模型，所以写出模型公式：Ri = ai + bi1 F INF + bi2 F GDP + εi,

题干又给出zero value for the error terms的信息，所以ε i=0，因此我们可以将AB基金的数据代入模型：

R_A = 0.02 + 0.5F_INF + 1.0F_GDP

R_C = 0.03 + 1.0F_INF + 1.1F_GDP

根据表3，F_INF = 2.2% – 2.0%=0.2%， F_GDP= 1.0% – 1.5%= –0.5%.

R_A =1.6%

R_C =2.65%

Portfolio AC=60%A+40%C=60%*1.6%+40%*2.65%=2.02%