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LP Money Machine

Stock portfolio optimizer.

This project shows the application of a Nelder-Mead optimization algorithm to the well-known stock portfolio optimization problem. The original Nelder-Mead procedure has been enhanced to cope with the only portfolio constraint: stocks have to sum up to 100%.

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Stock risk and prediction

What we'd like to have is a prediction of what a good investment would be. For an investment to be good, we'd like it to be profitable and safe (kinda), so we'll want to minimize risk, while maximizing profit. A simple objective function would therefore be:

or better, since the created Nelder-Mead optimization is a minimization technique:

Nelder-Mead

Nelder-Mead is an iterative simplex optimization method, which works through for operations: reflection, expansion, contraction, shrinkage. These are usually tried in this order. Basically, what they do is the following:

  • Reflection: tries moving the simplex away from the sub-optimal area, by computing the reflected point through the centroid of the other points, excluding the worst one;
  • Expansion: if reflection generated a point which is better than the current best, the point is moved along the same direction for a bit further;
  • Contraction: if, on the contrary, the reflected point did not improve the result, we'll want to contract the simplex towards the best point;
  • Shrinkage: if none of the previous did work, we'll want to re-calculate all the points except for the best one, computing them through the best one's coordinates.

Simplex initialization

Several solutions have been proposed to create the initial simplex. This implementation uses a popular one (used in the MATLAB implementation too): after selecting the initial point (randomly), the others are created using the i-th dimension unit vector :

where

is a shift coefficient equal to

if the coefficient of

in the definition of

is non-zero,

otherwise.

Constraints

Nelder-Mead is an unconstrained method. To cope with the portfolio constraint, I introduced a fixing function that rescales the results to a percentage.

Termination

The termination is decided basing on the standard deviation of the values of the points, and a maximum number of iterations.

Hyperparameters

Hyperparameter tuning and a little bit of research led to the following parameters:

Stock data retrieval and predictions

Stock data are retrieved from AlphaVantage, a free API that provides real-time stock data.

Timeseries prediction has been added to work on predicted data and not historical data only, using a Temporal Convolutional Network implemented in Darts.

How to use me

First, install the requirements through pip:

$> pip install -r requirements.txt

Then, add your API secret to the code of realtime_stocks.py and run it:

$> python realtime_stocks.py

Different scripts are available:

  • run_me.py is the purest version: it uses the historical data contained in all_stocks_5yr.csv to create a portfolio;
  • realtime_stocks.py is instead able to work on real data: it downloads the history of stocks values from AlphaVantage, then analyzes them through Darts and outputs an optimal portfolio;
  • nelder_mead.py is where the optimization is done: it provides an implementation of the Nelder-Mead iterative optimization technique, using a simplex;
  • tester.py provides a backtesting script that is able to test the techniques found in realtime_stocks.py to actually see if they work.

That's it!

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Stock portfolio optimization using linear programming.

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