Explanation

In the Arbitrage Pricing Theory (APT) formula: $R_i = E(R_i) + \beta_{i1}[I_1 - E(I_1)] + \cdots + \beta_{iK}[I_K - E(I_K)] + e_i$

• $\beta_{ik}$ represents the sensitivity or factor loading of security i to factor k
• The term $[I_k - E(I_k)]$ represents the surprise or unexpected component of factor k
• Therefore, $\beta_{ik}$ measures how changes in the surprise factor k (the unexpected component) will affect the rate of return of security i

Why other options are incorrect:

• Option A: Incorrect - $\beta_{ik}$ measures the effect of factor k on security i, not the effect of security k on factor l
• Option B: Incorrect - The difference between observed and expected values of factor k is $[I_k - E(I_k)]$, not $\beta_{ik}$
• Option C: Incorrect - The idiosyncratic random shock is represented by $e_i$, not $\beta_{ik}$

Key Concept: In APT, $\beta_{ik}$ is the sensitivity coefficient that quantifies how much security i's return responds to unexpected changes in macroeconomic factor k.