Since the default correlation is equal to 1, the portfolio will act as if there is only one credit.

Viewing the portfolio as a variable that takes on the binomial distribution, there are only two possible outcomes for a portfolio acting as one credit - total loss with a probability of 3%, or zero loss with a probability of 97%.

With a recovery rate of zero, the extreme loss given default is the entire portfolio amount, i.e., $1,000,000. The expected loss is equal to the portfolio value times π

Expected loss = 0.03 × $1,000,000 = $30,000.

The credit VaR is defined as the quantile of the credit loss less the expected loss of the portfolio. At the 99% confidence level, the credit VaR is equal to $970,000 ($1,000,000 minus the expected loss of $30,000).

Note that if π was less than (1 - confidence level), the credit VaR would have been calculated as 0 − $30,000 = −$30,000.