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Modeling can be an efficient link between equity analysis and portfolio management.

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As the outlook for individual stocks improves or deteriorates over time, the portfolio manager only needs to change the weightings of those stocks in the portfolio model to optimize the return of all portfolios in the group or style. As long as the individual portfolio accounts are traded efficiently, the group will perform as a homogeneous element. Risk Management.

Systematic Equities: A Closer Look

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Portfolio Management Passive vs. Active Portfolio Management: What's the Difference? Partner Links. I followed the same logic for performing feature importance over the whole dataset — just the training took longer and results were a little more difficult to read, as compared with just a handful of features. We will use GELU for the autoencoders. It is not the actual implementation as an activation function. For now, we will just use a simple autoencoder made only from Dense layers. Note : One thing that I will explore in a later version is removing the last layer in the decoder.

We want, however, to extract higher level features rather than creating the same input , so we can skip the last layer in the decoder. We achieve this creating the encoder and decoder with the same number of layers during the training, but when we create the output we use the layer next to the only one as it would contain the higher level features. The full code for the autoencoders is available in the accompanying Github — link at top. We created more features from the autoencoder. As we want to only have high level features overall patterns we will create an Eigen portfolio on the newly created features using Principal Component Analysis PCA.

This will reduce the dimension number of columns of the data.

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  • The descriptive capability of the Eigen portfolio will be the same as the original features. Note Once again, this is purely experimental. As everything else in AI and deep learning, this is art and needs experiments. As mentioned before, the purpose of this notebook is not to explain in detail the math behind deep learning but to show its applications. Of course, thorough and very solid understanding from the fundamentals down to the smallest details, in my opinion, is extremely imperative. Hence, we will try to balance and give a high-level overview of how GANs work in order for the reader to fully understand the rationale behind using GANs in predicting stock price movements.

    Feel free to skip this and the next section if you are experienced with GANs and do check section 4. The steps in training a GAN are:. When combined together, D and G as sort of playing a minmax game the Generator is trying to fool the Discriminator making it increase the probability for on fake examples, i.

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    Having separated loss functions, however, it is not clear how both can converge together that is why we use some advancements over the plain GANs, such as Wasserstein GAN. Overall, the combined loss function looks like:. Note : Really useful tips for training GANs can be found here. Note : I will not include the complete code behind the GAN and the Reinforcement learning parts in this notebook — only the results from the execution the cell outputs will be shown.

    Make a pull request or contact me for the code.

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    Generative Adversarial Networks GAN have been recently used mainly in creating realistic images, paintings, and video clips. The main idea, however, should be same — we want to predict future stock movements. So, in theory, it should work. Note: The next couple of sections assume some experience with GANs. Often, after training the GAN we do not use the D any more. The last kept output is the one considered the real output of G. Training GANs is quite difficult. Models may never converge and mode collapse can easily happen. Again, we will not go into details, but the most notable points to make are:.

    RNNs are used for time-series data because they keep track of all previous data points and can capture patterns developing through time. This is called gradient exploding , but the solution to this is quite simple — clip gradients if they start exceeding some constant number, i.

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    LSTMs, however, and much more used. Strictly speaking, the math behind the LSTM cell the gates is:. The LSTM architecture is very simple — one LSTM layer with input units as we have features in the dataset and hidden units, and one Dense layer with 1 output - the price for every day. The initializer is Xavier and we will use L1 loss which is mean absolute error loss with L1 regularization - see section 3. Note — In the code you can see we use Adam with learning rate of.

    Don't pay too much attention on that now - there is a section specially dedicated to explain what hyperparameters we use learning rate is excluded as we have learning rate scheduler - section 3. Then we move the 17 days window with one day and again predict the 18th.

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    We iterate like this over the whole dataset of course in batches. In another post I will explore whether modification over the vanilla LSTM would be more beneficial, such as:.

    One of the most important hyperparameters is the learning rate. Setting the learning rate for almost every optimizer such as SGD , Adam , or RMSProp is crucially important when training neural networks because it controls both the speed of convergence and the ultimate performance of the network. One of the simplest learning rate strategies is to have a fixed learning rate throughout the training process. Choosing a small learning rate allows the optimizer find good solutions, but this comes at the expense of limiting the initial speed of convergence.

    Changing the learning rate over time can overcome this tradeoff. Recent papers, such as this one, show the benefits of changing the global learning rate during training, in terms of both convergence and time.