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Explanation:
Option D is false. At low correlations (e.g., rho = 0), the portfolio loss distribution is narrow due to the law of large numbers. As the default rate increases and approaches the attachment point of the mezzanine tranche, the tranche's losses become highly sensitive to further changes in the default rate because the loss distribution quickly sweeps across the narrow mezzanine tranche. Thus, it is highly sensitive to the default rate under low correlation, not "essentially insensitive."
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314.3. In Malz's<sup>15</sup> simulation, the mezzanine tranche has a width of only 10%. It is typical for the mezzanine tranche to be thinner than the senior bond. In regard to the mezzanine tranche, each of the following is true EXCEPT which is false?
A
At low default rates, an increase in correlation increases losses on the mezzanine bond (behaves like a senior bond)
B
At high default rates, an increase in correlation decreases losses on the mezzanine bond (behaves like equity)
C
The mezzanine tranche has negative convexity in default rates for low default rates (behaves like a senior bond) but is positively convex for high default rates (behaves like equity)
D
At low correlations, for example, rho = zero, the mezzanine tranche is essentially insensitive to changes in the default rate (behaves like a senior bond)