Chap 3 From Ruppert, Statistics for Financial Engineering

In this project we attempt to model the volatility of a stock, Berkshire Hathaway and an index, S&P 500. Based on our model, we estimate the long term variance and project the future volatilities, based on the stock returns from 1st January 2019 to 1st January 2022. We then estimate the one day 99%-Value-at-Risk and Expected Shortfall for three hypothetical portfolios based on historical simulations: 1) single stock portfolio consisting of Berkshire Hathaway (BRK-A) 2) single stock portfolio consisting of investment in the index S&P 500 (SPY) 3) equal weighted portfolio consisting of equal weighted investments in BRK-A and SPY For estimating the VaR and ES we use the time period of 1st January 2019 to 1st January 2022. We then Backtest the estimated VaR for the period of 1st March 2021 to 28th February 2022. We then estimate the VaR based on the Normality assumption of results and using the 1% confidence interval. Finally, we determine which portfolio has the best risk adjusted performance based on 99% VaR that is used for economic capital.