Qtrader.ipynb

qtrader.ipynb

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        "[View in Colaboratory](https://colab.research.google.com/gist/gjlr2000/15da1e50cebf856cdcea9adfdd655d31/qtrader.ipynb)"
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      "source": [
        "# Teaching a robot to 'buy low, sell high'\n",
        "\n",
        "In AI we are witnessing a variation of the [Argumentum ad lunam](https://rationalwiki.org/wiki/Argumentum_ad_lunam):\n",
        "> *\"If we can put a man on the moon,  we must be able to X\"*.\n",
        "(informal fallacies or false analogies)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "But now it uses Alpha Go or Watson examples:\n",
        "\n",
        "> *If  \"AlphaGo Zero: Google DeepMind supercomputer [can learn] 3,000 years of human knowledge in 40 days\" [[link](https://www.telegraph.co.uk/science/2017/10/18/alphago-zero-google-deepmind-supercomputer-learns-3000-years/)]*\n",
        "\n",
        ">  *Then  \"AI Trading Systems Will Shake Up Wall Street\"  [[link](http://www.itprotoday.com/machine-learning/how-ai-trading-systems-will-shake-wall-street)] *\n",
        "\n",
        "In [AI in Finance: Cutting Through the Hype ](https://medium.com/@gjlr2000/ai-in-finance-cutting-through-the-hype-with-case-studies-f361518b00d4) I explained several examples of the application of AI in Finance, but I left out the 'holy grail': developing an artificial system that finds profitable strategies. Notice that this is different from *predicting* asset prices; what we really want is the trader to *act* on the information and maximize wealth.\n",
        "\n",
        "Luckily, Gordon Ritter from NYU built such a system (as published by Newsweek in [CAN MACHINE LEARNING BE APPLIED TO TRADING?](http://www.newsweek.com/business-technology-trading-684303)) which is very nicely explained in his academic paper:\n",
        "> **[Machine Learning for Trading](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3015609)**\n",
        "\n",
        "Following my practice of using replicable research for case studies in AI, I replicated Ritter's paper in this notebook. As before, I will try to reduce the jargon ('Q-learning' 'MDP' ?) and try to highlight the intuition behind it.\n",
        "\n",
        "**Spoilers**: Yes, the system can *learn* a profitable strategy from scratch *if* you have millions of examples *and* the current price only depends on the previous price. *But* there are ways (in research stage) to improve it.  \n",
        "\n",
        "**Note**: This python code was developed as a didactic tool, and will be painfully slow for commercial applications - Ritter wrote it in Java and it \"completes one million iterations in seconds\". My goal was to use Google Colaboratory in a single file to make sure the result is replicable by anyone. \n",
        "\n",
        "The following section sets the parameters as defined by Ritter:\n",
        "\n"
      ]
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      "source": [
        "(I add the usual python libraries, then I will create the list of possible actions,  portfolios and prices.)\n"
      ]
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      "source": [
        "# -*- coding: utf-8 -*-\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "\n",
        "#Initialize: \n",
        "# True -- will reset Q_space\n",
        "# False -- will try to use Q_space in memory (or reset if there is none)\n",
        "Initialize = True\n",
        "\n",
        "#Parameters from Ritter's paper\n",
        "H = 5\n",
        "Param = {\n",
        "        'epsilon' : 0.1,\n",
        "        'alpha' : 0.001,\n",
        "        'gamma' : 0.999,\n",
        "        'lambda'  : np.log(2)/H,\n",
        "        'kappa'  : 0.0001,\n",
        "        'sigma'  : 0.1,\n",
        "        'P_min'  : 0.1,\n",
        "        'P_max'  : 100,\n",
        "        'P_e'  : 50.0,\n",
        "        'LotSize'  : 100,\n",
        "        'K'  : 5,\n",
        "        'M'  : 10,\n",
        "        'TickSize'  : 0.1,\n",
        "        'N_train' : np.power(10,5)\n",
        "        \n",
        "}\n",
        "# N_train is 10^7 (10mn) for Ritter - \n",
        "# I use 10^5 iterated 10 times so a total of 10^6 (1mn)\n",
        "# (which is better to show the improvement on the strategy)"
      ],
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      "outputs": []
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      "source": [
        "\n",
        "Practitioners will see a few constants that mean something:\n",
        "> P_e: refers to the 'arbitrage' price, or the price around which the price simulator will oscillate. So 'buy low' should happen when the Price is below P_e, and 'sell high' when the price is above P_e\n",
        "\n",
        ">P_min, P_max: are the boundaries of the price (so it can only go from 0.1 to 100). This is a first **red flag** to a practitioner which is used to prices being able to jump. \n",
        "\n",
        ">LotSize: Minimum size of (equities/contracts) that can we trade.\n",
        "\n",
        ">TickSize: is the minimum price movement of a trading instrument.\n",
        "\n",
        ">K: refers to the actions that each trade can take: from -K to +K lot sizes\n",
        " \n",
        ">M: is the multiple of lot Sizes than the total portfolio can hold\n",
        "\n",
        ">$\\gamma$ is the only greek letter that could refer to a financial term: the one period discount factor of future rewards (and could be linked to the risk free rate). \n",
        "\n",
        "The rest of  the greek letters ($\\alpha$, $\\epsilon$,  $\\lambda$, $\\kappa$, $\\sigma$) are the beloved symbols used by academics to refer to constants used within their models. I will explain them further when we see them in the code\n",
        "\n",
        ">$\\sigma$ and $\\lambda$ are parameters used to determine the price bands around the 'arbitrage' level P_2 and the speed of mean reversion\n",
        "\n",
        ">$\\alpha$, $\\epsilon$, and $\\kappa$ are parameters used to tune the Q-learning.\n"
      ]
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      "source": [
        "#python requires the additional +1 to get the full range {-K, -K+1, ..., K}\n",
        "\n",
        "ParamSpace = { \n",
        "    'A_space' : np.arange(-Param['K'] ,Param['K']+1)*Param['LotSize'],\n",
        "    'H_space' : np.arange(-Param['M'],Param['M']+1)*Param['LotSize'],\n",
        "    'P_space' : np.arange(1,Param['P_max']/Param['TickSize']+1)*Param['TickSize'],\n",
        "\n",
        "     }\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
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      "source": [
        "Lets review the list of possible actions. It should go from -K*LotSize = -500 to +500:"
      ]
    },
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      "cell_type": "code",
      "source": [
        "print (ParamSpace['A_space'])"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-500 -400 -300 -200 -100    0  100  200  300  400  500]\n"
          ],
          "name": "stdout"
        }
      ]
    },
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      "source": [
        "And the H space is the set of possible portfolios, going from -M * LotSize = -1000 to +1000\n",
        "\n",
        "Why H space ? Well, Ritter called it $\\mathcal{H}$-space as Holding-space; I guess to differentiate from the P-space which is used for prices. Oh, and space is a legacy from the control theory used to develop the learning algorithms ([State-space](https://en.wikipedia.org/wiki/State-space_representation))."
      ]
    },
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        },
        "outputId": "fe3aabdc-f0c0-482f-9748-3e0f73651bd1"
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      "cell_type": "code",
      "source": [
        "print (ParamSpace['H_space'])\n"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-1000  -900  -800  -700  -600  -500  -400  -300  -200  -100     0   100\n",
            "   200   300   400   500   600   700   800   900  1000]\n"
          ],
          "name": "stdout"
        }
      ]
    },
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      "source": [
        "I will not print the Price-space, but imagine it going from [0.1 to 100] in 0.1 steps.\n",
        "\n",
        "The spaces set up above are very important for the code, and below I define functions that will make sure whenever a price (or holding) is generated. That way I avoid having to deal with prices that fall within ticks. **Note** this part can be optimized if you are a hard-core coder."
      ]
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      "source": [
        "#to make sure we do not get Prices and Holdings outside of\n",
        "#the valid state \n",
        "def find_nearest(array, value):\n",
        "    array = np.asarray(array)\n",
        "    idx = (np.abs(array - value)).argmin()\n",
        "    return array[idx]\n",
        "\n",
        "\n",
        "def Price(d):\n",
        "    return find_nearest(ParamSpace['P_space'], d)\n",
        "\n",
        "def Holding(d):\n",
        "    return find_nearest(ParamSpace['H_space'], d)    "
      ],
      "execution_count": 0,
      "outputs": []
    },
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      "metadata": {
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      "source": [
        "## Price Simulation\n",
        "This is a very important part. Ritter chose \n",
        "\n",
        "> *\"a tradable security with a strictly positive price process $p_t > 0$.  ... $p_t$ tends to revert to its long-run equilibrium level pe with mean-reversion\n",
        "rate $\\lambda$, [volatility $\\sigma$] and is a standard discretization of the Ornstein-Uhlenbeck process.\"*\n",
        "\n",
        "Please refer to the paper for the exact details, but now you can see where the $\\lambda$ and $\\sigma$ parameters are needed - they are not used to 'learn' but to simulate the price action.\n",
        "\n",
        "Let's see an example:\n"
      ]
    },
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        "outputId": "ea7bf974-230f-4cb7-adb8-21bf4257965b"
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      "cell_type": "code",
      "source": [
        "def PriceSampler(sampleSize):\n",
        "    eps_t = np.random.randn(sampleSize)\n",
        "    pe = Param['P_e']\n",
        "    sigma = Param['sigma']\n",
        "    lambda_ = Param['lambda']\n",
        "    p = Price(pe)\n",
        "    \n",
        "    prices = [p]\n",
        "    for i in range(0,sampleSize):\n",
        "        y = np.log(p / pe)\n",
        "        y = y + sigma * eps_t[i] - lambda_ * y\n",
        "        pnew = pe * np.exp(y)\n",
        "        pnew = np.min([pnew, Param['P_max']])\n",
        "        # discretizing to make sure it appear in P_space\n",
        "        prices.append(Price(pnew))\n",
        "        # this one seems missing !\n",
        "        p = pnew\n",
        "    return prices\n",
        "  \n",
        "sample = PriceSampler(500)\n",
        "plt.plot(sample)"
      ],
      "execution_count": 43,
      "outputs": [
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          "output_type": "execute_result",
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            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fe7e86b2b38>]"
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          "execution_count": 43
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xdetWFAoFZDJ+2sjo6CgmJtrbB5HA35yVManqhc2HXQkbDWJyMmICfWR9aCtB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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fe7eb6c5198>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "zWkhv0hyxFC5",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Mmm....\n",
        "\n",
        "You can see that the price action kind of oscillates quite rapidly around 50 (the P_e) we selected\n",
        "\n",
        "Is that a realistic assumption ? That is another discussion, and I have written extensively about Mean Reverting trading in\n",
        "[Trading Mean Reversion: the full series.](https://www.linkedin.com/pulse/trading-mean-reversion-full-series-gerardo-lemus/) \n",
        "\n",
        "**Important**:  the PriceSampler **can** be changed to another Price dynamic, **as long** as the current Price only depends on the previous Price so that we can fit the action into a Markov Decision Process (MDP - read Ritter's piece). \n",
        "\n",
        "For example, in Ritter's code the Price is made to be always positive, but in the examples I mention in my blogs that is not the case (the signals can be also negative). I could change the PriceSampler to reflect this case, as I know the dynamics only depend in the previous prices in both cases.\n",
        "\n",
        "**Note** check both my blog [MeanReversion:definitions](https://medium.com/@gjlr2000/mean-reversion-in-finance-definitions-45242f19526f) and Ritter's paper to see the difference in the mean reverting formula.\n",
        "\n",
        "**Note 2** Instead of using Prices we can use other variables (like returns) that only depend on the previous value - but that requires re-defining the architecture. \n"
      ]
    },
    {
      "metadata": {
        "id": "ehB54TnK0Jy6",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Building the Cheatsheet\n",
        "### (\"How many times have I told you too ...\" or Q-learning)\n",
        "\n",
        "[Q-learning](https://en.wikipedia.org/wiki/Q-learning) is another term borrowed from academia and control -theory, but we can see it as Cheatsheet writing.\n",
        "\n",
        "Once the Cheatsheet is done, all the robot has to do is to follow its instructions to trade. In classical Algorithmic Trading the rules are set up by a coder; in Q-learning the robot will first 'train' in a safe environment (no money needed) - it will perform actions and then will write the reward back in the Cheatsheet (just like an exasperated parent educating a child, to be repeated thousands of times)\n",
        "\n",
        "\n",
        "\n",
        "So lets create the Cheatsheet (or Q-space):"
      ]
    },
    {
      "metadata": {
        "id": "dvih4cprP8Sl",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "\n",
        "#State_space = pd.DataFrame(index = ParamSpace['P_space'], columns = ParamSpace['H_space'])\n",
        "iterables = [ ParamSpace['P_space'], ParamSpace['H_space'] ]\n",
        "State_space = pd.MultiIndex.from_product(iterables)\n",
        "\n",
        "\n",
        "try:\n",
        "    Q_space\n",
        "    if Initialize:\n",
        "      Q_space = pd.DataFrame(index = State_space, columns = ParamSpace['A_space']).fillna(0)\n",
        "  \n",
        "except:\n",
        "    Q_space = pd.DataFrame(index = State_space, columns = ParamSpace['A_space']).fillna(0)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "OXJkVqOH2KxK",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "All the combinations of Prices and Holdings are called the 'State-Space', and Q-space is extended by adding another dimension (actions).\n",
        "\n",
        "Below you can see a glimpse of it.\n",
        "\n",
        "You will notice that the rows represent all possible combinations of Prices and Portfolios, and the columns are the possible actions. All is started with zeros, and eventually it will be filled with positive or negative rewards during training.\n",
        "\n",
        "This Cheatsheet has 21k rows and 11 columns, or 231k cells that need to be filled. Not all of them will be visited during training (as the Price dynamics might not end up in some cells), but now you can start to see why you need millions of training samples (as you cannot rely in a single observation per visit, you need to average a few). \n",
        "\n",
        "\n",
        "\n",
        "**Note**: the definition of State-Space has to be done very carefully and is one of the critical parts of the robot. In this case Prices were directly used as part of the state, but in other dynamics (like a raising stock market) that is not possible - you have to use returns instead (make the process [stationary](https://en.wikipedia.org/wiki/Stationary_process))"
      ]
    },
    {
      "metadata": {
        "id": "siRxLNGcPfaG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1105
        },
        "outputId": "367c6d11-3787-4d17-8bab-0b67eff8dc8b"
      },
      "cell_type": "code",
      "source": [
        "print (Q_space)\n"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "             -500  -400  -300  -200  -100   0     100   200   300   400   500\n",
            "0.1   -1000     0     0     0     0     0     0     0     0     0     0     0\n",
            "      -900      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -800      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -700      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -600      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -500      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -400      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -300      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -200      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -100      0     0     0     0     0     0     0     0     0     0     0\n",
            "       0        0     0     0     0     0     0     0     0     0     0     0\n",
            "       100      0     0     0     0     0     0     0     0     0     0     0\n",
            "       200      0     0     0     0     0     0     0     0     0     0     0\n",
            "       300      0     0     0     0     0     0     0     0     0     0     0\n",
            "       400      0     0     0     0     0     0     0     0     0     0     0\n",
            "       500      0     0     0     0     0     0     0     0     0     0     0\n",
            "       600      0     0     0     0     0     0     0     0     0     0     0\n",
            "       700      0     0     0     0     0     0     0     0     0     0     0\n",
            "       800      0     0     0     0     0     0     0     0     0     0     0\n",
            "       900      0     0     0     0     0     0     0     0     0     0     0\n",
            "       1000     0     0     0     0     0     0     0     0     0     0     0\n",
            "0.2   -1000     0     0     0     0     0     0     0     0     0     0     0\n",
            "      -900      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -800      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -700      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -600      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -500      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -400      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -300      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -200      0     0     0     0     0     0     0     0     0     0     0\n",
            "...           ...   ...   ...   ...   ...   ...   ...   ...   ...   ...   ...\n",
            "99.9   200      0     0     0     0     0     0     0     0     0     0     0\n",
            "       300      0     0     0     0     0     0     0     0     0     0     0\n",
            "       400      0     0     0     0     0     0     0     0     0     0     0\n",
            "       500      0     0     0     0     0     0     0     0     0     0     0\n",
            "       600      0     0     0     0     0     0     0     0     0     0     0\n",
            "       700      0     0     0     0     0     0     0     0     0     0     0\n",
            "       800      0     0     0     0     0     0     0     0     0     0     0\n",
            "       900      0     0     0     0     0     0     0     0     0     0     0\n",
            "       1000     0     0     0     0     0     0     0     0     0     0     0\n",
            "100.0 -1000     0     0     0     0     0     0     0     0     0     0     0\n",
            "      -900      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -800      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -700      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -600      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -500      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -400      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -300      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -200      0     0     0     0     0     0     0     0     0     0     0\n",
            "      -100      0     0     0     0     0     0     0     0     0     0     0\n",
            "       0        0     0     0     0     0     0     0     0     0     0     0\n",
            "       100      0     0     0     0     0     0     0     0     0     0     0\n",
            "       200      0     0     0     0     0     0     0     0     0     0     0\n",
            "       300      0     0     0     0     0     0     0     0     0     0     0\n",
            "       400      0     0     0     0     0     0     0     0     0     0     0\n",
            "       500      0     0     0     0     0     0     0     0     0     0     0\n",
            "       600      0     0     0     0     0     0     0     0     0     0     0\n",
            "       700      0     0     0     0     0     0     0     0     0     0     0\n",
            "       800      0     0     0     0     0     0     0     0     0     0     0\n",
            "       900      0     0     0     0     0     0     0     0     0     0     0\n",
            "       1000     0     0     0     0     0     0     0     0     0     0     0\n",
            "\n",
            "[21000 rows x 11 columns]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "vYjUpo6J4DkX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Later on I'll explain how to use the Cheatsheet - but **note** that as it stands the default action will be the first one (sell -500); instead, we might want to fill the Action = 0 column with a small positive number to make sure our robot does not bet the house after training.\n",
        "\n",
        "Above I mentioned that we need to fill the Q-space by applying rewards each time we train. \n",
        "\n",
        "In case someone mentions '[Bellman equation](https://en.wikipedia.org/wiki/Bellman_equation)', keep in mind that this is the method used to fill the Q-space and that it comes from a methodology called 'dynamic programming'.\n",
        "\n",
        "**Note** Defining a reward that fits the Bellman equation is another critical part. It turns out the Bellman equation requires a 'Markov Decision Process' because the reward is computed recursively but only if the underlyng state process is stationary.\n",
        "\n",
        "### Definition of Reward\n",
        "As a practitioner, I liked that Ritter did not shirk away from transaction costs and risk aversion, and developed a reward function that includes them.\n",
        "\n",
        "Lets start with the costs:\n",
        "> SpreadCost: depends on how many lots you trade,\n",
        "\n",
        "> ImpactCost: includes a simple model of the impact on the market as a function of the size\n",
        "\n",
        "**Note** Most important; here is where you can add more realistic cost (Ritter mentions financing as example). And finally we are seeing advantages of this method over theoretically-derived strategies: many of those require many assumptions that become unrealistic, but using a machine learning approach you can add them to the simulation.\n"
      ]
    },
    {
      "metadata": {
        "id": "WAymm5NA9Eaa",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def SpreadCost(d_n):\n",
        "    return Param['TickSize'] * np.abs(d_n)\n",
        "\n",
        "def ImpactCost(d_n):\n",
        "    return (d_n*d_n)*Param['TickSize']/Param['LotSize']\n",
        "\n",
        "def TotalCost(d_n):\n",
        "    return SpreadCost(d_n) + ImpactCost(d_n)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "RQ8TnmO9-AUX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "As for the reward, Ritter did a very good job of defining it in a form that is intended to maximize the resulting Sharpe Ratio. If you were only maximizing PnL the optimal policy might simply be greedily buying all it can whenever the Price is low.\n",
        "\n",
        "Here is where you you will $\\kappa$ being used: it penalizes the PnL is the variance is too high. Read the paper for more details. \n",
        "\n",
        "**Note**: The fine print when applying this specific reward function specifies that the asset returns should be \"mean-variance equivalent\", which roughly means that the statistics of the resulting simulation only have two parameters. If you believe you need another one (which is the case when people think of adding 'black swans' scenarios happening randomly) then the theory stops working - however, your two parameters can be part of a distribution that uses 'fat tails'."
      ]
    },
    {
      "metadata": {
        "id": "EaPaY94fPZVz",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "'''\n",
        "def PnL(prePrice, nextPrice, totalCost, n):\n",
        "    return n * (nextPrice - prePrice) - totalCost;\n",
        "\n",
        "def Reward(prePrice, nextPrice, totalCost, n):\n",
        "    pnl = PnL(prePrice, nextPrice, totalCost, n)\n",
        "    return pnl - 0.5 * Param['kappa'] * (pnl * pnl)\n",
        "'''\n",
        "\n",
        "def ResultReward(currState, nextState):\n",
        "    currPrice = currState[0]\n",
        "    nextPrice = nextState[0]\n",
        "    currHolding = currState[1]\n",
        "    nextHolding = nextState[1]\n",
        "    dn = nextHolding - currHolding\n",
        "    cost = TotalCost(dn)\n",
        "    pricedif = nextPrice - currPrice\n",
        "    pnl = nextHolding * pricedif - cost\n",
        "    reward = pnl -0.5 * Param['kappa'] * (pnl * pnl)\n",
        "    result = {\n",
        "            'pnl': pnl,\n",
        "            'cost': cost,\n",
        "            'reward' : reward,\n",
        "            'dn' : dn\n",
        "            }\n",
        "    return result\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "MCE1WAMY-8Ss",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "This are the functions that will aid us to fill the Cheatsheet (Q-space).\n",
        "\n",
        "You will notice another one of the parameters we defined above ($\\epsilon$). This one is used to make sure during training that the robot chooses actions that it has not tried before."
      ]
    },
    {
      "metadata": {
        "id": "VWJjvi88-3eW",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "\n",
        "def getQvalue(state):\n",
        "    price = state[0]\n",
        "    holding = state[1]\n",
        "    return Q_space.loc[(price, holding),]\n",
        "\n",
        "def argmaxQ(state):\n",
        "    return getQvalue(state).idxmax()\n",
        "\n",
        "def getMaxQ(state):\n",
        "    return getQvalue(state).max()\n",
        "\n",
        "\n",
        "def chooseAction(state):\n",
        "    random_action = np.random.rand()\n",
        "    if (random_action < Param['epsilon']):\n",
        "        A_space = ParamSpace['A_space'] \n",
        "        dn = A_space[np.random.randint(len(A_space))]\n",
        "    else:\n",
        "        dn = argmaxQ(state)\n",
        "    return dn"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "9AEY_R1D_rth",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "And finally we reach the Q-learning !\n",
        "\n",
        "This part is bases on the 'Bellman equation' I mentioned above:\n",
        "\n",
        "Imagine we start at state (currState: Price = 50, Holding = 0), and we know the next Price is 49.8:\n",
        "\n",
        "\n",
        "\n",
        "1.   Look at the Cheatsheet, row (50, 0). On that row, we will pick either the action with the highest value or a random action (as defined in the chooseAction function).\n",
        "2.   With that action (lets say it was to buy 100 lots) we update the state (nextState: Price = 49.8, Holding = 100), and the reward is negative ! (we lost money - bad robot)\n",
        "3. We update the Cheatsheet on (currState: P= 50, H=0) with a negative number - it is not a good idea to buy if the price is close to 50. Here is where we introduce $\\alpha$ (the rate of learning)\n",
        "\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "-JtehLEE_oPg",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def qLearning():\n",
        "    pricePath = PriceSampler(Param['N_train'])\n",
        "#    plt.plot(pricePath)\n",
        "    # initialize holding at first holding possible\n",
        "    currHolding = Holding(0)\n",
        "    \n",
        "    for i in range(0, Param['N_train']-1):\n",
        "        # indexing\n",
        "        currPrice = pricePath[i]\n",
        "        currState = (currPrice, currHolding)\n",
        "        \n",
        "        # choose action\n",
        "        shares_traded = chooseAction(currState)\n",
        "        \n",
        "        nextHolding = Holding(currHolding + shares_traded)\n",
        "        \n",
        "        nextPrice = pricePath[i+1]\n",
        "        nextState = (nextPrice, nextHolding)\n",
        "        \n",
        "        result = ResultReward(currState, nextState)\n",
        "        q_sa = Q_space.loc[currState, shares_traded]\n",
        "        increment = Param['alpha'] * ( result['reward'] + Param['gamma'] * getMaxQ(nextState) - q_sa)\n",
        "        Q_space.loc[currState, shares_traded] = q_sa + increment\n",
        "        \n",
        "        currHolding = nextHolding\n",
        "        \n",
        "        #if ( i% np.power(10,5) == 0):\n",
        "        #    print(i)            \n",
        "        #Q_space.to_pickle('q_space')\n",
        "    return i\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "cdBg0-JAD2qr",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Let's try it !\n",
        "\n",
        "First, lets define a way to create a Price sequence which is outside the training sample:"
      ]
    },
    {
      "metadata": {
        "id": "zZLl1xdnOl_P",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "            \n",
        " \n",
        "def OutOfSample(nsteps):\n",
        "    pricePath = PriceSampler(nsteps+1)\n",
        "    currHolding = Holding(0)\n",
        "    pnl = []\n",
        "    \n",
        "    for i in range(0, nsteps):\n",
        "        \n",
        "        currPrice = pricePath[i]\n",
        "        currState = (currPrice, currHolding)\n",
        "        shares_traded = chooseAction(currState)\n",
        "        \n",
        "        nextHolding = Holding(currHolding + shares_traded)\n",
        "        \n",
        "        nextPrice = pricePath[i+1]\n",
        "        nextState = (nextPrice, nextHolding)\n",
        "        \n",
        "        result = ResultReward(currState, nextState)\n",
        "        pnl.append(result['pnl'])\n",
        "        \n",
        "        currHolding = nextHolding\n",
        "        \n",
        "    return pd.DataFrame(pnl)\n",
        "    \n",
        " "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "T5BqFdJJEHwN",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Off to the races:\n",
        "\n",
        "I train the robot 10 times, and hopefully you will see how the accumulated PnL improves after each iteration. The first time should see a very poor performance (around -200k after 5k samples), which should improve by the last one (+600k)\n",
        "\n",
        "And if you keep it running around 10mn times, you should replicate Ritter's Figure 4.1 with almost straight line raising to 2.5mn PnL."
      ]
    },
    {
      "metadata": {
        "id": "Zozz1c6KOeyy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "outputId": "0e41bf9e-9c3e-4794-e212-c5d40adf3c72"
      },
      "cell_type": "code",
      "source": [
        "   \n",
        "pnl = OutOfSample(5000)\n",
        "pnl_sum = pnl.cumsum()\n",
        "plt.plot(pnl_sum)\n",
        "\n",
        "for i in range(0,10):\n",
        "  itr = qLearning()\n",
        "  pnl = OutOfSample(5000)\n",
        "  pnl_sum = pnl.cumsum()\n",
        "  plt.plot(pnl_sum)\n",
        "\n",
        "\n",
        "    \n",
        "    "
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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k0ehyA5BkCGJUfCRalYo1729T+E26sA99BkZStvNvAW0kDbgHXXBcgN1+8CCH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\nAynhNSAwdW25AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fe7e85b59e8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "pOPHJwc6-OdZ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "Q_space.to_pickle('Q_space_ritter')\n",
        "from google.colab import files\n",
        "files.download('Q_space_ritter')\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "pISljng7FYMb",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Analyzing the Q-trader\n",
        "\n",
        "Among many reasons, I wanted to replicate the code in Python (instead of a faster language) because I wanted to 'see through' the results.\n",
        "\n",
        "I wanted to see the 'optimal policy' by myself. Doing the coding with Pandas allows us to quickly see the 'buy low, sell high' policy.\n",
        "\n",
        "If I aggregate the Q-space by price and then show the action that has the maximum value - I get the following picture:\n"
      ]
    },
    {
      "metadata": {
        "id": "_WMMRSinRYI1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 364
        },
        "outputId": "e2e1c6d2-8923-420c-9ed5-bc77096f7dde"
      },
      "cell_type": "code",
      "source": [
        "Q_price = Q_space.groupby(level = [0]).sum()\n",
        "Q_action = Q_price.idxmax(axis =1)\n",
        "plt.plot(Q_action)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fe7e8386358>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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95Vm6L6YhQU00DO+L55tHzXn75Rp1SkzfgeM29AYAJQ2NVriEqNMu0z5qoelb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\nmoiISMVY1ERERCr2N55W3TJixKlZAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fe7e83af518>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "iMgqyHLMGMtK",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Unsurprisingly, the optimal policy has a 'buy' bias for prices between 30 and 50, and 'sell' between 50 and 100.\n",
        "\n",
        "Still - it is not very smooth. As the Q-space is large, some states are not visited very often and the first memory (lets say a random profit) remains. Prices below to 20 are also ignored and set up to the default (sell -500).\n",
        "\n",
        "For the full picture, see below the full colour action cheatsheet per state. \n",
        "\n",
        "You can notice that some states (usually prices below 20) remain unvisited. Also, the action will depend not only on the price but on the current holding.\n"
      ]
    },
    {
      "metadata": {
        "id": "mY4C3n0xN1Hn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        },
        "outputId": "a460339e-8d15-42e4-a834-17599dac52dc"
      },
      "cell_type": "code",
      "source": [
        "Q_full_action = (pd.DataFrame(Q_space.idxmax(axis =1))).unstack()\n",
        "\n",
        "import seaborn as sns\n",
        "\n",
        "ax = sns.heatmap(Q_full_action, yticklabels=100)\n",
        "plt.show()"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KTaD9R/+UGyHUjTBgOKchy74W2zDlpsF01PlQjKJrxT7R+tHr5BcPBoy7Y0pHRL8pYhsU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\nIYQQQoyKGh+EEEIIMar/A089G9z8QmITAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fe7e867f240>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "6ix3h8FlsRcL",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Still early, but setting up the foundations:\n",
        "\n",
        "Ritter's paper shows that you can train a robot from scratch under a very limited set of conditions:\n",
        "\n",
        "\n",
        "*   The asset price need to be memoryless (do not depend on the paste beyond the current price)\n",
        "* The reward is tailored to maximize Sharpe Ratio *if* the simulations replicate random numbers generated with only two parameters (notice that even if we have three parameters, P_e, $\\lambda$ and $\\sigma$, they will be combined into 2 in the output of the simulation). The reward uses a variable $\\kappa$ which regulates the risk aversion.\n",
        "* There are many parameters ($\\alpha$, $\\epsilon$) which seem to be 'magically' defined\n",
        "*   And most importantly: you should be able to generate huge amount of simulations.\n",
        "\n",
        "But Ritter did not plan to create a full-fledged Robo-Buffet, instead **he developed the blueprint** and each one of the points above can be improved. For instance:\n",
        "\n",
        "\n",
        "### Changing the reward\n",
        "The reward function can be twisted to favour gains over losses (one of the big bugbears of traders) by changing the line\n",
        "\n",
        "\n",
        "```\n",
        "reward = pnl -0.5 * Param['kappa'] * (pnl * pnl)\n",
        "```\n",
        "to \n",
        "\n",
        "\n",
        "```\n",
        "loss = np.min(0,pnl)\n",
        "reward = pnl -0.5 * Param['kappa'] * ( loss * loss)\n",
        "```\n",
        "\n",
        "so that Robo-Buffet is not penalized when making large gains. \n",
        "\n",
        "While it makes sense to change the reward function, we loose sense of what are we really maximizing, and we have to be careful.\n",
        "\n",
        "### Changing the architecture:\n",
        "The reason why only memoryless prices can be used for training is due to the choice of state architecture. There are many tricks to improve this -- for instance, in gaming:\n",
        "\n",
        "\n",
        "> *\"DQN is trained using an input consisting of the last four game screens\"*\n",
        "> [Deep Q-Learning with Recurrent Neural Networks](http://cs229.stanford.edu/proj2016/report/ChenYingLaird-DeepQLearningWithRecurrentNeuralNetwords-report.pdf)\n",
        "\n",
        "We could copy this trick by adding the last N prices to the state, something like:\n",
        "\n",
        "\n",
        "```\n",
        "currState = (currPrice, prev_1_Price, prev_2_Price, currHolding)\n",
        "```\n",
        "If we do that, the State Space grows dramatically, and using deep learning neural networks *instead* of the big Q-space cheatsheet makes sense (read the above paper)\n",
        "\n",
        "Additionally, instead of prices we can use 'hidden states' that output Prices (to make sure the end up states following the memoryless property that the theory requires)\n",
        "\n",
        "### But we need data, data, data.\n",
        "Having a model of the financial world to develop a model-less robo trader seems like an oxymoron: if you have the model you might as well use it to compute directly the dynamic programming equations without relying on 'Q-learning'\n",
        "\n",
        "Still, with cheap computer power it might be faster just to develop the model and blast the solution away. And in some domains (High Frequency Trading) the data might be available !\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    }
  ]
}