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:
Ri​=E(Ri​)+βi1​[I1​−E(I1​)]+...+βik​[Ik​−E(Ik​)]+ei​
In this context:
- Ri​ represents the actual return on the security.
- E(Ri​) is the expected return on the security.
- βik​ denotes the sensitivity of the security's return to the k-th factor.
- Ik​ is the macroeconomic factor affecting the return.
- E(Ik​) is the expected value of the k-th macroeconomic factor.
- ei​ is the idiosyncratic error term, representing the security-specific risk not captured by the factors.
What is the accurate interpretation of the term βik​?