S
sarita
Guest
Dear David. The answer to below is 1. Kindly explain when you have time.
. Kelly Lewis is analyzing daily return data for a stock market index. From the available data, she calculates that the average daily return is 0.0% and the standard deviation is 1.5%. Concerned that a normal distribution likely underestimates tail risk, she recalls from extreme value theory that a generalized Pareto distribution (GPD) can be used to approximate the probability that the daily return is greater than a loss level y, given the daily return is a loss. That is, if X represents the daily return, then:
Using maximum likelihood estimation with the available historical data, she finds that parameter values of ? = 0.005 and ? = 0.015 provide the best fit. Given the daily return is a loss, what is the probability that the daily return exceeds –4.5% using a normal distribution and a generalized Pareto distribution?
1. Using a normal distribution: 99.74%; using a generalized Pareto distribution: 94.91%
2. Using a normal distribution: 99.87%; using a generalized Pareto distribution: 94.91%
3. Using a normal distribution: 99.74%; using a generalized Pareto distribution: 97.45%
4. Using a normal distribution: 99.87%; using a generalized Pareto distribution: 94.45%
. Kelly Lewis is analyzing daily return data for a stock market index. From the available data, she calculates that the average daily return is 0.0% and the standard deviation is 1.5%. Concerned that a normal distribution likely underestimates tail risk, she recalls from extreme value theory that a generalized Pareto distribution (GPD) can be used to approximate the probability that the daily return is greater than a loss level y, given the daily return is a loss. That is, if X represents the daily return, then:
Using maximum likelihood estimation with the available historical data, she finds that parameter values of ? = 0.005 and ? = 0.015 provide the best fit. Given the daily return is a loss, what is the probability that the daily return exceeds –4.5% using a normal distribution and a generalized Pareto distribution?
1. Using a normal distribution: 99.74%; using a generalized Pareto distribution: 94.91%
2. Using a normal distribution: 99.87%; using a generalized Pareto distribution: 94.91%
3. Using a normal distribution: 99.74%; using a generalized Pareto distribution: 97.45%
4. Using a normal distribution: 99.87%; using a generalized Pareto distribution: 94.45%
