apt模型

问题如下：

A risk analyst at a bank is explaining to an intern the use of the Arbitrage Pricing Theory (APT) in estimating the expected return of a security. The risk analyst uses the following APT formula in the discussion:

𝑅_𝑖=𝐸(𝑅_𝑖)+ 𝛽_𝑖1[𝐼₁−𝐸(𝐼₁)]+ ⋯ 𝛽_𝑖𝐾[𝐼_𝐾−𝐸(𝐼_𝐾)]+𝑒_𝑖

Which of the following is a correct interpretation of 𝛽_𝑖𝐾?

一家银行的风险分析师正在向一名实习生解释在估计证券预期回报率时套利定价理论（APT）的应用。风险分析师在讨论中使用了以下 APT 公式：Ri​=E(Ri​)+βi1​[I1​−E(I1​)]+⋯+βiK​[IK​−E(IK​)]+ei​ 。以下对βiK​的解释哪一个是正确的？

选项：

A.

It is a coefficient measuring the effect of changes in the rate of return of security k on the expected value of factor I

它是一个系数，衡量证券 k 的回报率变化对因素 I 预期值的影响。

B.

It measures the difference between the observed and expected values of factor k.

它衡量因素 k 的观测值与预期值之间的差异。

C.

It measures the idiosyncratic random shock to the price of security i which has a mean of zero

它衡量对证券 i 价格的特质随机冲击，其均值为零。

D.

It measures how the changes in the surprise factor k will affect the rate of return of security i

它衡量因素 k 的意外变动将如何影响证券 i 的回报率。

解释：

D is correct. βik is a coefficient measuring the effect of changes in Ik (the observed value of factor k) on the rate of return of security i.

A is incorrect. It is a is a coefficient measuring the changes in factor Ik on the rate of return of security i.

B is incorrect. [𝐼_𝐾−(_𝐼𝐾)] is the difference between the observed and expected values in factor k.

C is incorrect. This is the noise factor 𝑒_𝑖.

D选项正确。βik是衡量Ik(因子k的观测值)变化对证券i收益率影响的系数。

A不正确。它是一个系数，衡量因子Ik对证券收益率i的变化。

B不正确。[𝐼𝐾−(𝐼𝐾)]为因子k的实测值与期望值之差。

C选项不正确。这是噪声因子𝑒i。