Bootstrapping VaR vs Historical Simulation

[Cipher2014]

Hi David,

I'm looking at page 91 of the Study Note P1.T2 where you compare Monte Carlo with Bootstrapping.

What I'm not clear about is how is Bootstrapping different from Historical Simulation with random sampling? To me, the Bootstrapping method, as discribed in the text, is more in line with Historical Random Samply than to Monte Carlo. Could you kindly elaborate on this?

Thanks,
Ying

 

[Aleksander Hansen]

Historical simulation is just looking at your returns of each asset in your portfolio over the past, say 100 days, and multiplying your current exposure to each asset with that. Then take whatever percentile you want.

Bootstrapping is different in that your are not just running through a series of past returns, but rather, you are creating a sampling distribution by drawing returns (with replacement) from the series randomly. Multiply by current exposure, and take the percentile.

Bootstrapping is analogous to MC in the sense that you are generating random scenarios. MC is similar to Bootstrapping in the sense that you parameterize your simulation based on the moments of a sampling distribution of your data.

Just my take..

 

[Cipher2014]

Hi Aleksander,

Thanks for the detailed explanation! I can see how the randomizing component of bootstrapping is alluding to MC.

My question is then what exactly is "Historical Random Sampling" (I've heard of ppl using this before) Is this the same as Bootstrapping since

Historical = using time series data
Random Sampling (with replacement) = drawing random returns from time series to create a distribution.

Could you kindly clarify?

Thanks in advance!
Ying

 

[Aleksander Hansen]

Hi Aleksander,

Thanks for the detailed explanation! I can see how the randomizing component of bootstrapping is alluding to MC.

My question is then what exactly is "Historical Random Sampling" (I've heard of ppl using this before) Is this the same as Bootstrapping since

Historical = using time series data
Random Sampling (with replacement) = drawing random returns from time series to create a distribution.

Could you kindly clarify?

Thanks in advance!
Ying

Historical random sampling is not a specific method - it can be thought of as a superset of which historical simulation using bootstrapping is a subset.

In particular, historical random sampling encompasses all classes of [historical] random sampling.
That is, you can have a random number generator that draws without replacement.
Another example of random sampling would be a generator which randomly draws a number X1, from the [historical] sample, and then draws another random number X2, but where X2 is less than X1. This would tend to give more weight to lower returns or "stress cases".