Explanation:
In risk mapping, the total portfolio variance is decomposed into systematic (general market) risk and idiosyncratic (specific) risk. The equation illustrates that total risk is the sum of the variance explained by general market risk factors and the specific risk factors.
If the total amount of risk () is fixed, explaining a greater proportion of that risk by introducing more general market risk factors will inherently reduce the residual unexplained variance. Consequently, the portion of risk attributed to specific risk factors will decrease. Therefore, with more general market risk factors, there will be less specific risk factors (or less specific risk variance) for a fixed amount of total risk. This makes option D correct.
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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, .
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