This code is a quick and dirty spare time project to evaluate portfolios of ETFs using bootstrapping and optimize asset allocation based on these bootstraps.

Tools

Backtest

Tool for backtesting a portfolio.

Example usage:

./backtest -input=history.csv \
  -pos='WORLD:52200' \
  -pos='USA SMALL CAP VALUE WEIGHTED:16000' \
  -pos='WORLD VALUE:16000' \
  -pos='WORLD QUALITY:8000' \
  -pos='EMERGING MARKETS:7800'
=== Backtest ===
data "Simulated Portfolio" (returns: 7.7%; volatility: 15.7%; sharpe ratio: 0.49)

Forecast

Tool for forecasting a portfolio.

Example usage:

./forecast -input=history.csv \
  -pos='WORLD:52200' \
  -pos='USA SMALL CAP VALUE WEIGHTED:16000' \
  -pos='WORLD VALUE:16000' \
  -pos='WORLD QUALITY:8000' \
  -pos='EMERGING MARKETS:7800'
52% WORLD, 16% USA SMALL CAP VALUE WEIGHTED, 16% WORLD VALUE,  8% WORLD QUALITY,  8% EMERGING MARKETS

=== Monte Carlo ===
[P50] returns: 7.8%; volatility: 15.8%; sharpe ratio: 0.49
[P80] returns: 4.3%; volatility: 14.4%; sharpe ratio: 0.30
[P90] returns: 3.2%; volatility: 15.8%; sharpe ratio: 0.20
[P95] returns: 2.0%; volatility: 15.5%; sharpe ratio: 0.13
[P99] returns: -0.1%; volatility: 19.1%; sharpe ratio: -0.01

=== Markov Chain ===
[P50] returns: 6.4%; volatility: 14.1%; sharpe ratio: 0.46
[P80] returns: 4.1%; volatility: 15.3%; sharpe ratio: 0.27
[P90] returns: 3.0%; volatility: 16.6%; sharpe ratio: 0.18
[P95] returns: 1.9%; volatility: 17.0%; sharpe ratio: 0.11
[P99] returns: -0.4%; volatility: 19.0%; sharpe ratio: -0.02

Optimize allocation

Tool for generating portfolios that perform well with the available data. The generated portfolios are typically overfitted to the available data and tend to have only two positions, as this typically maximizes the sharpe ratio.

Example usage:

./optimize-allocation -input=history.csv -size=100 -iterations=2000

Background

Data

The algorithm uses historic index performance from history.csv. The file is based on data downloaded from the MSCI website. It contains data for the timespan from January 1999 to April 2021.

Bootstrapping

This implementation uses a Monte Carlo Markov Chain (MCMC) method. That is a very fancy way to say that with probability 1/12 a random month in the available data is used, and with probability 11/12 the following month is used. The hope is that this translates some of the inter-month dependence into the generated data set.

Optimizing

To optimize asset allocation, the code implements an evolutionary algorithm. First, 100 completely random portfolios are generated. In each round, a random 30 year sample is generated with the method described above. All portfolios are tested against this sample and sorted by their Sharpe ratio. The worse half of portfolios are then replaced by combining two random portfolios of the better half. Recombination is done by iterating over the positions, randomly picking the weight of one of the parents. Mutation is done by multiplying each position with a random number between 95% and 105%.

Anticipated questions

• How were the indices chosen?

  Indices were chosen based on whether ETFs based on these indices are available in Germany.

• Why use 12 as the expected length of sequential months?

  Many periodic effects happen yearly, so it felt like not the worst choice 🤷.

• You're ignoring the TER, how unrealistic.

  Given the uncertainty of bootstrapping, the difference in TER between fonds is negligible.

Author

Florian Forster (@octo)

License

ISC License