A risk analyst at a bank is teaching an intern about the use of the Arbitrage Pricing Theory (APT) to determine the expected return on a security. APT is a multifactor model that explains the returns of a financial asset. The analyst uses the following APT formula during the explanation: [ R_i = E(R_i) + \beta_{i1}[I_1 - E(I_1)] + ... + \beta_{ik}[I_k - E(I_k)] + e_i ]

In this context:

( R_i ) represents the actual return on the security.

( E(R_i) ) is the expected return on the security.

( \beta_{ik} ) denotes the sensitivity of the security's return to the k-th factor.

( I_k ) is the macroeconomic factor affecting the return.

( E(I_k) ) is the expected value of the k-th macroeconomic factor.

( e_i ) is the idiosyncratic error term, representing the security-specific risk not captured by the factors.

What is the accurate interpretation of the term ( \beta_{ik} )?

Exam-Like

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

24.3%

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

10.3%

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

9.6%

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

55.8%

Financial Risk Manager Part 1