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Assume that you are a portfolio manager overseeing $10 million assets, and your broker sets the margin requirement as 30%. In addition, assume the portfolio daily return follows a normal distribution with a mean equal to 10%, and a standard deviation equal to 20%. Consider the following two cases. In the first case, the initial margin of your portfolio is 50% (in other words, you use 50% leverage). In the second case, the initial margin of your portfolio is 70% (in other words, you use 30% leverage). Given the above information, what is the probability that you wil receive a margin call in one trading day? Scenario Initial Margin Leverage Used Requirement Margin One day loss Probability to to receive a receive a margin call margin call >20% 6.68% >40% 0.62% A B 50% 70% 50% 30% 30% 30% Since the portfolio daily return follows a normal distribution, we can calculate the probability that the portfolio will lose more than 20% in one trading day is 6.68%, and the probability that the portfolio will lose more than 40% in one trading day is 0.62%. We can see that the probability of receiving a margin call is 10 times more when using 50% leverage compared to using 30% leverage. Questions: Q1. If your portfolio margin requirement is 40%, and the initial margin is 70%. Assume that the portfolio daily return follows a normal distribution with a mean equal to 12% and a standard deviation equal to 18%, what is the probability that you will receive a margin call in one trading day? Q2. From the reading materials, is leverage trading a main factor of the failure for Archegos Capital Management? Discuss your thoughts

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