Apr 11

Bootstrapping VaR - 9 minute screencast

by David Harper, CFA, FRM, CIPM

This is an illustration, using a simple portfolio of four stocks over one week, of the bootstrap method (Wilmott, Chapter 22 on VaR). 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 MCS, the randomness is applied in the algorithm; it informs the stochastic process
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.

Question: compared to delta normal VaR, what are two advantages of this approach? Answer below.

Here is the screencast:

Advantages:

No distributional assumption required. We do not assume normality. The historical data reflects its own non-normal, messy shape.
Cross-sectional correlation is preserved as we are the using the cross-sectional vector of returns.

Disadvantages (on the other hand):