
Explanation:
The correct answer is D.
Statement D is false. The senior tranche of a structured product (like a CDO) is heavily protected by the subordination of equity and mezzanine tranches. It is only exposed to extreme tail risk, which requires a large number of simultaneous defaults.
When the default correlation () is 0, defaults are independent. According to the Law of Large Numbers, the actual number of portfolio defaults will cluster tightly around the expected default rate, with a very thin tail. Even with a high default rate (), the probability of defaults breaching the high attachment point of the senior tranche is extremely low. Thus, the 99% credit VaR for the senior bond under zero correlation is typically near zero.
Conversely, when the default correlation is high (), defaults are highly interdependent. The portfolio behaves almost systemically—either very few defaults occur, or many occur simultaneously. This creates a "fat tail" in the loss distribution. Consequently, even with a low expected default rate (), the 99% worst-case scenario entails a massive wave of clustered defaults that effortlessly burns through the equity/mezzanine protections and severely impacts the senior tranche.
Therefore, the low-default, high-correlation scenario actually produces a higher senior bond 99% credit VaR than the high-default, zero-correlation scenario.
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314.2. Senior Bond Tranche: The following is the graphical summary of the distribution of simulated senior bond tranche losses (Malz Figure 9.4 below⁴). Please notice, in contrast to the equity tranche (above), which displays VALUES, the bond tranches are graphed according to their LOSSES:
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)