Using the Vasicek single-factor model, the conditional default probability given the market factor $Z$ is: $p(Z) = N\left( \frac{N^{-1}(PD) - \sqrt{\rho} Z}{\sqrt{1 - \rho}} \right)$

Given:

• $PD = 1.0\%$, so $N^{-1}(0.01) \approx -2.3263$ (rounded to $-2.33$ in the question).
• Correlation $\rho = 0.64$, so $\sqrt{\rho} = \beta = 0.80$.
• $\sqrt{1 - \rho} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.60$.

We are asked for the probability that the portfolio loss $p(Z)$ is $0.01$or worse (i.e.,$p(Z) \ge 0.01$): $N\left( \frac{-2.3263 - 0.80 Z}{0.60} \right) \ge 0.01$

Taking the inverse normal cumulative distribution of both sides: $\frac{-2.3263 - 0.80 Z}{0.60} \ge -2.3263$ $-2.3263 - 0.80 Z \ge -1.3958$ $-0.80 Z \ge 0.9305$ $Z \le -1.1631$

The probability that the standard normal market factor $Z$ is less than or equal to $-1.1631$ is $N(-1.1631)$. Using a standard normal table or calculator, $N(-1.1631) \approx 12.24\%$.

Therefore, the nearest probability is 12.24%.