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

## Explanation In the Arbitrage Pricing Theory (APT) model: - **$\beta_{ik}$** represents the sensitivity or exposure of security $i$ to factor $k$ - It measures how much the security's return ($R_i$) will change in response to a unit change in the surprise component of factor $k$ ($I_k - E(I_k)$) - The surprise component $[I_k - E(I_k)]$ represents the unexpected or unanticipated movement in factor $k$ **Why D is correct:** $\beta_{ik}$ indeed 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:** - **A:** Incorrect - $\beta_{ik}$ measures the effect of factor $k$ on security $i$, not the effect of security $k$ on factor $I$ - **B:** Incorrect - This describes $[I_k - E(I_k)]$, which is the surprise or unexpected component of factor $k$ - **C:** Incorrect - This describes $e_i$, the idiosyncratic error term that represents security-specific risk The APT model decomposes security returns into: 1. Expected return $E(R_i)$ 2. Systematic risk components ($\beta_{ik}[I_k - E(I_k)]$) 3. Idiosyncratic risk ($e_i$)

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