Bootstrapping Value at Risk (VaR)

This is an illustration, using a simple portfolio of four stocks over one week, of the bootstrap method. Like the Monte Carlo, we want to simulate each stock (in the portfolio) forward in time. If today is time t, then we want to simulate the stock on t+1, t+2, t+3, etc. The key difference is: The Monte Carlo uses an algorithm (e.g., geometric Brownian motion) to simulate the stock on t+1. In Monte Carlo Simulation, the randomness is applied in the algorithm; it informs the stochastic process.

But the bootstrap does not have an algorithm. The bootstrap randomizes the selection of a historical period (a day within the historical window). Once that historical day is selected, the cross-section of returns (the vector = the daily return for each stock in the portfolio) is used to simulate the portfolio going forward.