Explanation:
The correct answer is D.
The given equation represents the decomposition of the total portfolio risk (variance) into two components: the systematic or general market risk, represented by , and the specific or idiosyncratic risk, represented by .
Because the total risk is fixed, the two components have an inverse relationship. If a model incorporates more general market risk factors, it captures a greater portion of the total variance through the systematic component. Consequently, less of the total variance is left unexplained by the systematic part, which means the remaining specific (idiosyncratic) risk component must be smaller. Therefore, with more general market risk factors, there will be less specific risk factors for a fixed amount of total risk.
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Q.1530 In practice, we have to keep the number of risk factors small during mapping. These risk factors include both general market risks and specific market risks for the entire portfolio. Thus the portfolio return is calculated including variance through the following equation on:
This decomposition shows that:
A
with less general market risk factors, there will be less specific risk factors for fixed amount of total risk, .
B
with more general market risk factors, there will be more specific risk factors for fixed amount of total risk, .
C
there will be equal general market and specific risk factors for a fixed amount of total risk, .
D
with more general market risk factors there will be less specific risk factors for fixed amount of total risk, .