Explanation:
The subadditivity risk measure can be thought of as a portfolio broken out into smaller subportfolios with individual risk profiles. Summing the risks of the individual subportfolios will always produce a total that is at least equal to the overall risk of the portfolio, and will likely be greater than overall portfolio risk due to the benefits of diversification. Monotonicity implies less (rather than more) risk is likely for portfolios with greater future returns. Translation invariance implies that adding sure amounts to a portfolio will have a positive impact on reducing overall risk. Positive homogeneity implies that the risk of a position is proportional to its size.
(Book 4, Module 47.2, LO 47.e)
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Question 10
Baker Ltd. offers its new employees a one-day training session that covers all aspects of enterprise risk, including financial risk. For the training, a risk manager has been asked by his supervisor to develop a presentation covering coherent risk measures. The first slide developed lists the four risk measures, along with a brief description for each measure. Which of the following descriptions accurately describes the defined risk measure?
A
Monotonicity implies that more risk is likely for portfolios with greater future returns.
B
Translation invariance states that adding sure amounts to a portfolio has a minimal impact to overall risk.
C
Subadditivity states that overall portfolio risk cannot exceed the sum of the risks of its individual positions (or subportfolios).
D
Positive homogeneity requires that assets contained within a portfolio should have positive correlations to minimize risk.
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