A. An analysis of Value-at-Risk (VaR) under three alternatives:

Historical data
Parametric data
Monte Carlo simulated data
B. An analysis Estimated Shortfall.

The paper should be no longer than 6 pages of text (with tables and charts allowed/required on additional pages).

The project can be completed using Excel.

Part A: Value-at-Risk

You manage a \$100 million portfolio comprised of \$10 million invested in each of ten stocks as of December 31, 2019 (Intelâ€”ticker INTC–plus 9 othersâ€”you choose):

1. (~1.5 pages) As of December 31, 2020 (the last day of your sample period), using your Project A return distributions and correlations to calculate the 95%/10-day and 99%/10-day Value-at-Risk (VaR) for each of your 10 stocks, individually by using:

Historical data
Parametric estimates (using the Normal distribution)
Highlight the similarities and differences among the stocks and compare and contrast differences between historical and parametric estimates.

1. (~1.5 pages) Similarly, use your Project A return distributions and correlations to calculate the 95%/10-day and 99%/10-day Value-at-Risk (VaR) for an equal-weighted portfolio of your 10 stocks by using:

Historical data
Parametric estimates (using the Normal distribution)
Monte Carlo simulated data (for 1,000 simulations)
Compare and contrast differences among historical, parametric and Monte Carlo estimates.

1. (~1.5 pages) Calculate the first 10 daily autocorrelations for each of your 10 stocks. Discuss how your VaR estimates in part 1A. and 2A. above would differ if we took into account these autocorrelations.

Part B: Estimated Shortfall (~1 page)

For 2A, 2B and 2C above, calculate the estimated shortfall for your portfolio. Compare and contrast differences among historical, parametric and Monte Carlo estimates

Sample Solution