StockDiversifier

A portoflio diversification algorithm based on Beta-autoencoders.

You can find our paper here.

Instructions

Note: A fully-working notebook is implemented under tests/jair/test_driver.ipynb; the script below contains bugs for now.

Our project contains a driver that can be called thorugh main.py, with the following help menu:

usage: main.py [-h] [--refetch] [--retrain] [--load_returns] [--verbose VERBOSE] [--recoms_filename RECOMS_FILENAME]
               [--num_portfolios NUM_PORTFOLIOS] [--num_initial_tickers NUM_INITIAL_TICKERS] [--optim_method OPTIM_METHOD]

Modify default configurations

options:
  -h, --help            show this help message and exit
  --refetch             Refetch the loaded sp500 data
  --retrain             Retrain the model
  --load_returns        Refetch returns data for all stocks
  --verbose VERBOSE     Verbosity level
  --recoms_filename RECOMS_FILENAME
                        Custom name for the output recommendation file
  --num_portfolios NUM_PORTFOLIOS
                        Number of portfolios to generate
  --num_initial_tickers NUM_INITIAL_TICKERS
                        Number of initial tickers in the portfolio
  --optim_method OPTIM_METHOD
                        Optimization method for the portfolio 

To run the whole experiment including refetching all data, retraining models, specifying 10 random portfolios with 10 tickers each under the default Max Diversification (max_div) optimization method, you can use:

python main.py --refetch --retrain --num_portfolios 10 --num_initial_tickers 10

The argument optim_method also accepts mean_variance and max_sharpe, to perform portfolio optimization based on these. Experiments were not carried with the latter two methods.

Results

Optimizing an Equally-Weighted Portfolio with MaxDiv

We focus on Max Diversification portfolios, which solve

$$ \boxed{ \begin{matrix} & \max_{\mathbf{w}}DR(\mathbf{w}) = \max_{\mathbf{w}} \dfrac{\mathbf{w}^\top \boldsymbol{\sigma}}{\sqrt{\mathbf{w}^\top \boldsymbol{\Sigma} \mathbf{w}}} \ \\ & \text{subject to} \displaystyle \sum_{j=1}^{p} w_j = 1 ;;\text{ and } ;; \mathbf{w} \geq 0 \\ \end{matrix} } $$

For example, consider the equally-weighted following portfolio:

Max-diversification optimization changes the portfolio distribution increasing the diversification ratio (DR):

Applying the Beta-Encoding-Diversification Algorithm

Given any portfolio, the algorithm swaps stocks based on similarity measure to achieve a better DR with the same number of securities:

After applying the algorithm, we obtain a diversification-optimized portfolio with slightly different securities but higher DR than the original portfolio:

Experiments on Random SP500 Portfolios

We generate N different portfolios drawn from the SP500 tickers, we apply our algorithm and then check the performance in terms of the DR.

Average DR Improvement

We compare the choice of Beta-VAE embeddings to PCA-Embeddings as a baseline:

             Method  Average_Initial_DR  Average_Final_DR  \
0          Beta-VAE            2.335059          3.125257   
2  PCA (Latent Dim)            2.335059          2.726827   
1     PCA (90% Var)            2.335059          2.635625   

   Average_DR_Improvement  
0                34.97845  
2                17.18670  
1                13.37660 

We notice our method with Beta-VAE encodings choice obtains the best average DR across multiple randomly generated portfolios.

Top 3 DR-Improvement Portfolios

We can check the achieved metrics in terms of the top 3 best portfolios in terms of DR improvement. Additioanlly, we also show the Sharpe-Ratio (SR) related metrics:

       Portfolio  Initial_DR  Final_DR  DR_Improvement  Initial_SR  Final_SR  \
48  Portfolio_17    2.008874  3.724985          85.426    0.264460  0.557309   
3    Portfolio_2    2.118884  3.826035          80.568    0.215653  0.517187   
6    Portfolio_3    2.234546  3.663383          63.943    0.378467  0.457902   

    SR_Improvement  
48         110.735  
3          139.824  
6           20.988  

We see that occassionally, our method produces additional significant SR improvements, but we notice this seems to be spurious and unreliable, as in other experiments we also obtain significant decreases in SR.

TODO

• Fix bugs in main.py preventing the script from running smoothly when performing the experiment and portfolio udpates.