Historical Simulation vs. Bootstraping

[Patrick Pan]

Hi David,

Could you please clarify if there is any difference between these two historical-based approaches? I wonder they are actually about the same thing.

Thanks
Patrick

 

[David Harper CFA FRM]

Hi Patrick,

I view bootstrapping as a subclass of historical simulation (a type of, or some would say "an improvement on"). The essential difference is HS is "without replacement" and bootstrap is "with replacement"

Please note: I did construct a simple bootstrap example
here @ http://www.bionicturtle.com/premium/spreadsheet/2.b.3._bootstrap_jorion_12.2.3/

to simplify, a HS runs current portfolio through the historical window; e.g., what distribution would we get if today's portfolio were held over, say, the last 250 trading days (today's weights, historical returns). Sort top to bottom, look near bottom (e.g., 95% %ile) to find the HS VaR.

the bootstrap is similar but instead of running the portfolio through (here a favorite phrase i read somewhere "the one sample that just happened to occur", it selects one of the days (i assume period = daily) in the historical window, uses that random day for a "simulated return" for t+1, then for the next simulated return, it again picks a historical day at random (see how bootstrap is "with replacement? the historical day [a vector of returns] having been randomly selected, it "thrown back into the sample-ocean" and can be randomly selected again).

So, they are similar in that: historical returns constitute the sample. The plain old HS just uses that sample "as is;" but bootstrapping randomizes that sample by selected returns with replacement. Generally, this is statistically an improvement because by re-sampling, the sampling variation, gives us better insight into the accuracy of the estimate.

David