Compare and contrast the Value at Risk (VaR) and Expected Shortfall (ES) risk measures, outlining their strengths and weaknesses for different financial instruments.

Value at Risk (VaR) and Expected Shortfall (ES) are two prominent risk measures used to quantify potential losses on financial instruments. While both provide insights into downside risk, they differ in their methodology and the information they convey. VaR measures the maximum potential loss that an investment portfolio is expected to experience over a given time horizon with a certain probability. It essentially provides a single point estimate of the worst-case scenario within a specific confidence interval. For example, a 95% VaR of $1 million implies that there is a 5% chance of losing at least $1 million over the specified period. ES, also known as Conditional Value at Risk (CVaR), goes beyond VaR by considering the average potential loss beyond the VaR threshold. It calculates the expected value of losses that exceed the VaR level. For example, a 95% ES of $1.5 million indicates that the average los....