Option C is the correct answer (it is the FALSE statement).

For an equity tranche, the tail worst-case value (e.g., at the 99% confidence level) is typically zero, because the tranche is completely wiped out in high-loss scenarios. Credit Value at Risk (VaR) is defined as the difference between the Expected Value (Mean) and the worst-case quantile value. Thus, for the equity tranche: Credit VaR ≈ Expected Value - 0 = Expected Value.

• Effect of Correlation: As correlation increases, the likelihood of extreme scenarios (either no defaults or all defaults) increases. Since the equity tranche's downside is strictly capped at its par value (it cannot lose more than 100%), it benefits from the increased probability of "zero defaults." This increases its Expected Value. Because the Expected Value increases, the equity Credit VaR actually increases, not decreases.
• Effect of Default Rate: Conversely, an increase in the default rate lowers the Expected Value of the equity tranche. Since Expected Value drops (and the 99% value remains at zero), the Credit VaR decreases, not increases.

Why the other options are true:

• Option A is true: A higher default rate directly increases the expected losses borne by the equity tranche (which takes the first loss), thereby lowering its expected value.
• Option B is true: As explained above, higher correlation concentrates defaults into the tails. The equity tranche benefits from the higher probability of zero/low defaults, meaning its expected value goes up. (The senior tranche takes the hit in the fat tail of high defaults).
• Option D is true: At low correlations, the equity value falls rapidly as the default rate increases from zero, but since the value cannot fall below zero, the curve flattens out. This creates a "smile" or positively convex relationship between the equity value and the default rate.