Suppose that asset returns follow a normal distribution. Consider the case in which you invest 50% and 50% between SPY and XLK. The portfolio return is a linear function of the asset returns and follows a normal distribution as well. Suppose that the true mean vector and the covariance matrix of the asset returns are given by the sample estimates using the period between 2010 and 2020. Given this, address the following:

1. According to the Gaussian assumption, what is the probability that the portfolio's daily return is less than -1%?

2. Rather than computing the probability under the Gaussian assumption, consider the empirical distribution. How does your answer change with respect to the previous one? Elaborate.

3. Consider a more extreme drop of -10%. How do both probabilities compare now? Elaborate.

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