Question

I am asked to calculate a VaR using empirical distirbution ( i have weekly stock price data ), but I don't know how. Also why there is a difference between VaR calculated from individual asset, sum them up and a VaR from a portfolio.

Answer 1

PORTFOLIO VaR:

Step 1 – Calculate the returns (or price changes) of all the assets in the portfolio between each time interval.

Step 2 – Apply the price changes calculated to the current mark-to-market value of the assets and re-value your portfolio.

Step 3 – Sort the series of the portfolio-simulated P&L from the lowest to the highest value.

Step 4 – Read the simulated value that corresponds to the desired confidence level.

For example, if there are 100 days and we want 95%ile VaR take the lowest 5th number (=100*(1-95%))

VaR calculated from a portfolio takes into account correlation between different assets and less than perfect positive correlation would mean VaR from portfolio is lower than summing VaR of individual assets-the property of diversification