Hello - If I remember correctly we are speaking about the 95% VaR .In the case of a bernouilli you 2 outcomes. No default so no loss or default and LGD of $100. The 95% quantile in that case will fall at 0 (no default). So the VaR will be $0
If you combine both portfolios then you are looking at 3 possible outcomes(as explained above) . The 95% VaR will fall at 1 default i.e a loss of 100
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