
Explanation:
Option D is false. The low-default, high-correlation scenario actually produces a higher senior bond VaR than the high-default, low-correlation scenario. Because the senior tranche is protected by subordination, it only suffers losses in extreme tail events where many defaults occur simultaneously. Such tail events are much more likely when correlation is high, even if the base default rate is lower. In contrast, when correlation is zero, the law of large numbers prevents a massive number of defaults from occurring simultaneously, keeping the senior tranche safe even at a higher average default rate.
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According to Malz, "For the bonds, we measure the VaR as the difference between the expected loss and the 10th (or 50th) highest loss in the simulations."¹⁴ With respect to the senior bond tranche, each of the following is true EXCEPT which is false?
A
For a given positive default correlation, an increase in the default rate generally implies an increase in (expected) senior bond losses
B
For a given default rate, an increase in the correlation rate implies an increase in (expected) senior bond losses
C
At a very high correlation of 0.90, the senior bond 99% credit VaR is significant (on the order of one-half the par value) but not highly sensitive to the default rate
D
The low-default, high-correlation simulation (default rate=0.0150, rho=0.90) produces a lower senior bond 99% credit VaR than the high-default, low-correlation (default rate=0.0975, rho=0)
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