Mean Variance Optimization by Gradient Descent (PyTorch)
- Mean-Variance Optimization to maximize Sharpe ratio using Deep Learning (PyTorch)
- 1 layer GRU / Transformer / TCN
- 1 FC layer
- loss_fn : minimize negative sharpe (or Risk Parity)
- optimizer : SAM (base SGD)
- Mean-Variance Optimization
- Maximize Annualized Sharpe Ratio
- SAM optimizer (base optimizer : SGD with momentum 0.9) was used
- the original source is here
- Of course, you can use Adam as base optimizer of SAM, or just Adam not SAM
- but SAM optim (SGD) shows better performance than other options, empirically
- Learning Rate : 5e-3 (No Scheduler)
def max_sharpe(y_return, weights):
weights = torch.unsqueeze(weights, 1)
meanReturn = torch.unsqueeze(torch.mean(y_return, axis=1), 2)
covmat = torch.Tensor([np.cov(batch.cpu().T, ddof=0) for batch in y_return]).to('cuda')
portReturn = torch.matmul(weights, meanReturn)
portVol = torch.matmul(weights, torch.matmul(covmat, torch.transpose(weights, 2, 1)))
objective = ((portReturn * 12 - 0.02) / (torch.sqrt(portVol * 12)))
return -objective.mean()
- You can configure upper/lower bound for portfolio weights
- this bounds are handled in UB and LB key in train_config.json
- if you don't need any bounds, just set LB=0 and UB=1
- portfolio weights are adjusted by the function below, before backpropagation
def rebalance(self, weight, lb, ub):
old = weight
weight_clamped = torch.clamp(old, lb, ub)
while True:
leftover = (old - weight_clamped).sum().item()
nominees = weight_clamped[torch.where(weight_clamped != ub)[0]]
gift = leftover * (nominees / nominees.sum())
weight_clamped[torch.where(weight_clamped != ub)[0]] += gift
old = weight_clamped
if len(torch.where(weight_clamped > ub)[0]) == 0:
break
else:
weight_clamped = torch.clamp(old, lb, ub)
return weight_clamped
- As of December 27, 2021, stocks with more than 5,000 daily price data were selected.
- AAPL, ABT, AMZN, CSCO, JPM, etc.
- Survivorship Bias (Look-ahead Bias)
- We didn't know in the past that these selected stocks would be in S&P500 until November 2021.
- So, the performance might (must) be different in real stock market
- Make Dataset for Training model
python dataload/data_download.py
python dataload/make_dataset.py
{
"MODEL" : "GRU",
"BATCH": 32,
"SEED": 42,
"EPOCHS" : 500,
"EARLY_STOP" : 50,
"LR" : 0.005,
"MOMENTUM": 0.9,
"USE_CUDA" : true,
"N_LAYER": 1,
"HIDDEN_DIM": 128,
"N_HEAD" : 10,
"N_FEAT": 50,
"DROPOUT": 0.3,
"BIDIRECTIONAL": false,
"LB": 0,
"UB": 0.2
}{
"START" : "2001-01-01",
"END" : "2021-12-27",
"N_STOCK" : 50,
"LEN_DATA" : 5000,
"TRAIN_LEN" : 63,
"PRED_LEN" : 21,
"TRAIN_RATIO": 0.75
}
- Test Date
- From 2017-04-11 To 2021-11-11
- Model
- GRU (hidden_dim = 128), Dropout (0.3), Lower/Upper Bounds (0, 0.2)
- Performance (Transaction costs are NOT considered)
- Expected Return : 0.310951 (snp500 : 0.134716)
- Volatility : 0.180532 (snp500 : 0.166945)
- Sharpe Ratio : 1.722411 (snp500 : 0.806953)
- MDD : -0.179543 (snp500 : -0.233713)
- You can see the cumulative return plot in result folder
numpy==1.20.0
pandas==1.3.4
torch==1.7.1+cu110
yfinance==0.1.67
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