[Solved] MFE409 Homework3-Choosing a VaR technique

Choosing a VaR technique

Download the excel file which contains the time series of gains for a strategy from 1/2/2014 to 12/19/2017.

1. For each day in 2015-2017, compute historical VaR and exponential weighted1-day 99%-VaR (with = 0.995).
2. Backtest the measures for VaR you obtained in Question 1. How manyexceptions did the two measures produce? What do you conclude?
3. For each day in the sample, compute the volatility of the portfolio in theprevious month. Normalize gains with estimated volatility. Compare the distribution of the normalized gain with the original ones.
4. Develop an approach to measure VaR which takes advantage of your response to the previous question. Implement it and compare its exceptions with the previous approaches.
5. Combining your answers to the previous questions, write a proposal to thehead of trading for measuring the risk of this trade in real time, justifying your choices.

2 Short questions

1. Prove that if 8 people are born in a three-year period, at least 3 of themare born within the same one-year period.
2. What is the ten-day 99% VaR of a portfolio with a five-day 98% VaR of$10 million?

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3. What is the probability of having more than one exception in the samemonth? Use the answer this question to come up with a test of a VaR measure based on bunching.

The next regular FOMC meeting is scheduled for end of April. How wouldyou estimate the 2-day 99% VaR of investing $1m in the S&P500 a day before the announcement? Bonus question: Provide a number