https://github.com/eduardgomezescandell/block-bootstrapping

An exploration into asset pricing simulation.
https://github.com/eduardgomezescandell/block-bootstrapping

Last synced: 13 days ago
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An exploration into asset pricing simulation.

• Host: GitHub
• URL: https://github.com/eduardgomezescandell/block-bootstrapping
• Owner: EduardGomezEscandell
• License: mit
• Created: 2023-05-26T18:41:16.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-05-30T16:06:01.000Z (over 1 year ago)
• Last Synced: 2024-11-07T10:53:30.663Z (2 months ago)
• Language: Python
• Size: 27.3 KB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.txt

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README

        
## Asset price simulation

This program is used to simulate future returns of risky assets. The method

used is bootstrapping. The goal is to use historical returns to predict future

ones.

### Standard bootstrapping

Efron (1979) developed a method wherein random samples are taken from the

historical dataset and concatenated to generate a pseudohistory. By generating

a large number of pseudo-histories, we can generate a probability distribution

for the returns of the asset.

However, Efron's method assumes asset prices are independent and identically

distributed (IID) random variables. This is known to be false: asset pricing

is autocorrelated, meaning that an asset's price depends on its history,

particularly in the short term.

### Block bootstrapping

To capture this effect, we concatenate blocks of historical data to create the

pseudo-history. We also generate a large number of pseudohistories and study

their aggregate behavior. The methodology implemented was developed by Politis

and Romano (1994).

The size of each block is chosen randomly from a geometrical distribution, and

the start of the block is chosen from a uniform distribution. If a block were

to stretch beyond the end of history, it is wrapped around to the beginning;

essentially treating the historical dataset like a circular array.

Replacement is allowed, meaning blocks may overlap. The mean length of a block

is a tuned parameter with no consensus on optimality.

### Usage

You need a file containing monthly historical returns from the asset to study.

The file must contain tab-separated values, sorted from old to recent. The

returns must be in a column named "Returns (%)". Then, edit the fields in the

data entry section in `block_bootstrap.py`. Once done, execute the file with

Python.

### Example run

This run samples the history of the S&P 500 index from 1900 to 2023 to simulate

1 million pseudohistories. It shows the distribution of returns year after year

for 30 years, with a piecewise 3rd-order polynomial fitting.

Despite high skewness and kurtosis (fat-tails) in month-to-month stock returns,

we see that after a few years the distribution is highly normal.

![ezgif com-gif-maker](https://github.com/EduardGomezEscandell/block-bootstrapping/assets/47142856/8238be25-105e-4c7f-8808-f114a6478420)

### References

1. Cogneau, P., & Zakamouline, V. (2010). "Bootstrap methods for finance:

   Review and analysis".

2. Efron, B. (1979). "Bootstrap Methods: Another Look at the Jackknife". Annals

   of Statistics, 7 (1), 1-26

3. Politis, D. and Romano, J. (1994). "The Stationary Bootstrap", Journal of

   the American Statistical Association, 89 (428), 1303-1313.