Value at Risk and Stress Testing
Task 1 (16 Points)
As a risk manager, you need to evaluate the downside risk of each portfolio from Question 2 over the next year. In particular, you need to compute the Value at Risk for Portfolio 1, 2, and 3 over a one year period. To do so, you need to do the following steps:
1. Using the back-testing results, you need to calibrate the price path for each portfolio, i.e.
compute ˆμp and ˆp for p = 1, 2, 3 using the daily returns in the OUT period. Report the
results is a 2 × 3 table. (4 Points)
2. Starting with F0,p = 100, the value of Portfolio p for all p = 1, 2, 3 at time t obeys to a
Geometric Brownian Motion (GMB) For each portfolio, you need to simulate N = 1000 paths. Given the simulated paths, provide a distribution plot, e.g. boxplot or histogram, for each portfolio. Provide a couple of insights (4 Points)
3. What’s the expected value of each portfolio one year from now? (4 Points)
4. With 95% level of confidence, what is the Value-at-Risk, i.e. V aR(0.05), for each portfolio? (4 Points)
Note: Ideally, you should report the final numbers in a single table where columns refer to portfolios and rows refer to the computed statistics.
Task 2 (4 Points)
You need to assess the performance of each portfolio under different scenarios. In particular, you need to evaluate the VaR of each portfolio with respect to market risk. To do so, you need to estimate the market p for each portfolio and the market volatility M during the OUT period. Refer to the SPY ETF as the market, as you did in Question 2. After doing so, consider the scenario in which the market volatility increases by a = 10% and generate 1000 paths for each portfolio.
Given these simulations, compute the V aR(0.05) for each portfolio and summarize the results in a single table as you did before.
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