We have a credit card portfolio of 10,000 accounts, each with a 5,000 dollar limit and an average balance of 2,000 dollars today. The model says the probability of default is 3 percent, we recover 20 percent after default, and we assume customers draw down half of their remaining limit before defaulting. What is the expected loss of this portfolio? And what if a downturn doubles the default rate?

我们有一个信用卡组合，1万个账户，每人额度5000美元，目前平均已用2000美元。模型给的违约概率是3%，违约后能收回20%，并假设客户违约前还会再刷掉剩余额度的一半。这个组合的预期损失是多少？如果经济下行、违约率翻倍呢？