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Financial Risk Manager Part 1

Financial Risk Manager Part 1

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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)]+eiR_i = E(R_i) + \beta_{i1}[I_1 - E(I_1)] + ... + \beta_{ik}[I_k - E(I_k)] + e_iRi​=E(Ri​)+βi1​[I1​−E(I1​)]+...+βik​[Ik​−E(Ik​)]+ei​

In this context:

  • RiR_iRi​ represents the actual return on the security.
  • E(Ri)E(R_i)E(Ri​) is the expected return on the security.
  • βik\beta_{ik}βik​ denotes the sensitivity of the security's return to the k-th factor.
  • IkI_kIk​ is the macroeconomic factor affecting the return.
  • E(Ik)E(I_k)E(Ik​) is the expected value of the k-th macroeconomic factor.
  • eie_iei​ is the idiosyncratic error term, representing the security-specific risk not captured by the factors.

What is the accurate interpretation of the term βik\beta_{ik}βik​?

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