{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# A First Neural Network\n",
        "\n",
        "*Last modified: November 11, 2026*\n",
        "\n",
        "This notebook trains neural networks on two problems. In the first, a\n",
        "strong signal is hidden in noisy data, and the network finds it easily.\n",
        "In the second, we try to predict the stock market’s return from the\n",
        "variables Welch and Goyal (2008) study, and the network does badly on\n",
        "data it was not trained on. The second problem is the one finance\n",
        "actually poses, and seeing why the network fails is the point of the\n",
        "exercise.\n",
        "\n",
        "## Packages\n",
        "\n",
        "PyTorch is the library we use to build and train networks. Fixing the\n",
        "random seed makes the results reproducible: training starts from random\n",
        "weights, and a different seed gives a somewhat different network."
      ],
      "id": "72834000-352a-4789-9ec0-7da6a94994ca"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "from pathlib import Path\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "\n",
        "torch.manual_seed(0)\n",
        "rng = np.random.default_rng(0)"
      ],
      "id": "76590401"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## An easy problem: learning a call payoff\n",
        "\n",
        "We generate 1,000 stock prices and the payoff of a call option with\n",
        "strike 100 on each, plus noise. A linear regression cannot fit the kink\n",
        "at the strike; a network with a few hidden units can."
      ],
      "id": "791875cc-b122-4885-90d7-953a8ebc5d63"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "S = rng.uniform(60, 140, size=1000)\n",
        "payoff = np.maximum(S - 100, 0) + rng.normal(scale=3, size=1000)\n",
        "\n",
        "# Networks train best when inputs are of order one, so we rescale the price\n",
        "X = torch.tensor((S[:, None] - 100) / 20, dtype=torch.float32)\n",
        "Y = torch.tensor(payoff[:, None], dtype=torch.float32)"
      ],
      "id": "af60e4ab"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "A network in PyTorch is a sequence of layers. This one takes one input,\n",
        "has a hidden layer of eight units with the ReLU activation, and produces\n",
        "one output."
      ],
      "id": "58749313-636e-471f-a976-eb1fccaded75"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "net = nn.Sequential(\n",
        "    nn.Linear(1, 8),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(8, 1),\n",
        ")"
      ],
      "id": "15e82403"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Training is gradient descent on the mean squared error. Each pass\n",
        "computes the loss, computes its gradient with `backward()`, and lets the\n",
        "optimizer take a step."
      ],
      "id": "dc17ab94-b456-4f61-81b2-9e4b88213a10"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final training loss: 9.46"
          ]
        }
      ],
      "source": [
        "opt = torch.optim.Adam(net.parameters(), lr=0.05)\n",
        "for epoch in range(2000):\n",
        "    opt.zero_grad()\n",
        "    loss = ((net(X) - Y) ** 2).mean()\n",
        "    loss.backward()\n",
        "    opt.step()\n",
        "print(f\"Final training loss: {loss.item():.2f}\")"
      ],
      "id": "be69108a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The noise we added has a variance of $3^2 = 9$, so a loss close to 9\n",
        "means the network has found the payoff and is left with the noise only."
      ],
      "id": "3ad85be5-9b3b-497b-80dd-9dd40bb5c905"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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pp/HMM8/02pwJgiAAx6Tt6upqp+OlRExdXZ3da5PJxAkvH3MHMo4+j8Dv7gaM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\nENV1p5hEAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "grid = np.linspace(60, 140, 200)\n",
        "with torch.no_grad():\n",
        "    fit = net(torch.tensor((grid[:, None] - 100) / 20, dtype=torch.float32)).numpy().ravel()\n",
        "b1, b0 = np.polyfit(S, payoff, 1)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
        "ax.scatter(S, payoff, s=4, color=\"0.75\", label=\"Data\")\n",
        "ax.plot(grid, b0 + b1 * grid, label=\"Linear regression\")\n",
        "ax.plot(grid, fit, label=\"Neural network\")\n",
        "ax.set_xlabel(\"Stock price\")\n",
        "ax.set_ylabel(\"Payoff\")\n",
        "ax.legend(frameon=False)\n",
        "plt.show()"
      ],
      "id": "d38ad28a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## A hard problem: predicting the stock market\n",
        "\n",
        "### The data\n",
        "\n",
        "Amit Goyal keeps the data of Welch and Goyal (2008) up to date on [his\n",
        "website](https://sites.google.com/view/agoyal145). The monthly file has\n",
        "the S&P 500, its dividends and earnings, interest rates, and other\n",
        "variables proposed as predictors of the market’s return. We download it\n",
        "once and save it."
      ],
      "id": "8d6fa287-bd6a-4699-92b7-df5dbdcbf391"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "DATA = Path(\"../_data\") if Path(\"../_data\").exists() else Path(\"data\")\n",
        "file = DATA / \"goyal_welch_monthly_2025.parquet\"\n",
        "if not file.exists():\n",
        "    url = (\"https://docs.google.com/spreadsheets/d/\"\n",
        "           \"1qwpl2R_DNujpU5YUkk8lacP1tTeMb9iJ/export?format=csv\")\n",
        "    DATA.mkdir(exist_ok=True)\n",
        "    pd.read_csv(url, thousands=\",\").to_parquet(file)\n",
        "raw = pd.read_parquet(file)\n",
        "raw.index = pd.PeriodIndex(raw.pop(\"yyyymm\").astype(str), freq=\"M\")\n",
        "raw.tail(3)"
      ],
      "id": "78322766"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We build nine predictors as Welch and Goyal (2008) do: the\n",
        "dividend-price and earnings-price ratios of the S&P 500 (in logs), the\n",
        "book-to-market ratio of the Dow Jones, the Treasury bill rate, the term\n",
        "spread, the default spread, net equity issuance, stock variance, and\n",
        "inflation. Inflation is published with a delay, so we lag it one more\n",
        "month. The outcome is the next month’s equity premium: the return on the\n",
        "value-weighted CRSP index of S&P 500 stocks minus the Treasury bill\n",
        "rate."
      ],
      "id": "0bc2429d-5219-4adc-99cc-037184779d47"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1926-12 to 2025-11 (1188 months)"
          ]
        }
      ],
      "source": [
        "X = pd.DataFrame({\n",
        "    \"dp\": np.log(raw[\"D12\"]) - np.log(raw[\"Index\"]),\n",
        "    \"ep\": np.log(raw[\"E12\"]) - np.log(raw[\"Index\"]),\n",
        "    \"bm\": raw[\"b/m\"],\n",
        "    \"tbl\": raw[\"tbl\"],\n",
        "    \"tms\": raw[\"lty\"] - raw[\"tbl\"],\n",
        "    \"dfy\": raw[\"BAA\"] - raw[\"AAA\"],\n",
        "    \"ntis\": raw[\"ntis\"],\n",
        "    \"svar\": raw[\"svar\"],\n",
        "    \"infl\": raw[\"infl\"].shift(1),\n",
        "})\n",
        "premium = (raw[\"CRSP_SPvw\"] - raw[\"Rfree\"]).shift(-1).rename(\"premium\")\n",
        "data = pd.concat([X, premium], axis=1).dropna()\n",
        "predictors = list(X.columns)\n",
        "print(data.index.min(), \"to\", data.index.max(), f\"({len(data)} months)\")"
      ],
      "id": "e1f3cc81"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Training, validation and test samples\n",
        "\n",
        "We train on the months up to 1979, use 1980 to 1999 to decide when to\n",
        "stop training the network, and keep 2000 to 2025 for the final test. The\n",
        "test sample is never used to make any choice."
      ],
      "id": "a52995b0-50b5-4db9-bb07-1e43430dc901"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "train = data.loc[:\"1979-12\"]\n",
        "valid = data.loc[\"1980-01\":\"1999-12\"]\n",
        "test = data.loc[\"2000-01\":]\n",
        "\n",
        "# Standardize with the training sample's means and standard deviations only\n",
        "mu, sd = train[predictors].mean(), train[predictors].std()\n",
        "z = lambda df: ((df[predictors] - mu) / sd).to_numpy(dtype=\"float32\")"
      ],
      "id": "ec0e149a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The benchmark is the simplest forecast: the average premium in the\n",
        "training sample. A model is worth something only if it beats that. We\n",
        "measure this with the out-of-sample $R^2$, which compares a model’s\n",
        "squared forecast errors with the benchmark’s and is negative when the\n",
        "model does worse."
      ],
      "id": "a52e7564-a5a0-4a8f-8b50-bdbad3c6866f"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "benchmark = train[\"premium\"].mean()\n",
        "\n",
        "def r2_oos(actual, forecast):\n",
        "    return 1 - ((actual - forecast) ** 2).sum() / ((actual - benchmark) ** 2).sum()"
      ],
      "id": "59af302c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Linear regressions\n",
        "\n",
        "First, one predictor at a time, then all nine together, the “kitchen\n",
        "sink.”"
      ],
      "id": "2789edd8-63d7-472e-9256-902807d27cb2"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "def linear_forecasts(cols):\n",
        "    A = np.c_[np.ones(len(train)), ((train[cols] - mu[cols]) / sd[cols])]\n",
        "    beta = np.linalg.lstsq(A, train[\"premium\"], rcond=None)[0]\n",
        "    predict = lambda df: np.c_[np.ones(len(df)), ((df[cols] - mu[cols]) / sd[cols])] @ beta\n",
        "    return predict\n",
        "\n",
        "rows = []\n",
        "for col in predictors + [\"all nine\"]:\n",
        "    cols = predictors if col == \"all nine\" else [col]\n",
        "    predict = linear_forecasts(cols)\n",
        "    rows.append({\"predictors\": col,\n",
        "                 \"R2 train\": 1 - ((train[\"premium\"] - predict(train)) ** 2).sum()\n",
        "                                 / ((train[\"premium\"] - benchmark) ** 2).sum(),\n",
        "                 \"R2 test (2000-2025)\": r2_oos(test[\"premium\"], predict(test))})\n",
        "pd.DataFrame(rows).set_index(\"predictors\").round(3)"
      ],
      "id": "806c42bc"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### A neural network\n",
        "\n",
        "The network has one hidden layer of 16 units. We train it on the\n",
        "training sample and, after every epoch, compute its loss on the\n",
        "validation sample. We keep the weights from the epoch with the lowest\n",
        "validation loss: this is early stopping. The `weight_decay` argument\n",
        "penalizes large weights, another guard against overfitting."
      ],
      "id": "4b71c67a-f7a3-4930-93f3-e6d5aadd630b"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Lowest validation loss at epoch 2726"
          ]
        }
      ],
      "source": [
        "X_train, y_train = torch.tensor(z(train)), torch.tensor(train[[\"premium\"]].to_numpy(dtype=\"float32\"))\n",
        "X_valid, y_valid = torch.tensor(z(valid)), torch.tensor(valid[[\"premium\"]].to_numpy(dtype=\"float32\"))\n",
        "\n",
        "net = nn.Sequential(nn.Linear(len(predictors), 16), nn.ReLU(), nn.Linear(16, 1))\n",
        "opt = torch.optim.Adam(net.parameters(), lr=0.001, weight_decay=1e-3)\n",
        "\n",
        "history, best_loss = [], np.inf\n",
        "for epoch in range(3000):\n",
        "    opt.zero_grad()\n",
        "    loss = ((net(X_train) - y_train) ** 2).mean()\n",
        "    loss.backward()\n",
        "    opt.step()\n",
        "    with torch.no_grad():\n",
        "        valid_loss = ((net(X_valid) - y_valid) ** 2).mean().item()\n",
        "    history.append((loss.item(), valid_loss))\n",
        "    if valid_loss < best_loss:\n",
        "        best_loss, best_epoch = valid_loss, epoch\n",
        "        best_weights = {k: v.clone() for k, v in net.state_dict().items()}\n",
        "\n",
        "net.load_state_dict(best_weights)\n",
        "print(f\"Lowest validation loss at epoch {best_epoch}\")"
      ],
      "id": "52b91630"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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7n1LZeBSIJEktPg+Rh8FgwMiRI+UOI6hwDJZc9BHikQkWkSxmzZoFq9WKhQsXege3A8Cp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\n"
          }
        }
      ],
      "source": [
        "history = pd.DataFrame(history, columns=[\"Training\", \"Validation\"])\n",
        "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
        "history.plot(ax=ax)\n",
        "ax.axvline(best_epoch, color=\"0.5\", ls=\":\", lw=1)\n",
        "ax.set_yscale(\"log\")\n",
        "ax.set_xlabel(\"Epoch\")\n",
        "ax.set_ylabel(\"Mean squared error\")\n",
        "plt.show()"
      ],
      "id": "80dd29d0"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now the comparison that matters, on the test sample:"
      ],
      "id": "91d4260e-0f37-43b0-a274-fd7d4f7480ac"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "with torch.no_grad():\n",
        "    nn_train = net(torch.tensor(z(train))).numpy().ravel()\n",
        "    nn_test = net(torch.tensor(z(test))).numpy().ravel()\n",
        "\n",
        "kitchen_sink = linear_forecasts(predictors)\n",
        "results = pd.DataFrame({\n",
        "    \"R2 train\": [1 - ((train[\"premium\"] - kitchen_sink(train)) ** 2).sum()\n",
        "                     / ((train[\"premium\"] - benchmark) ** 2).sum(),\n",
        "                 1 - ((train[\"premium\"] - nn_train) ** 2).sum()\n",
        "                     / ((train[\"premium\"] - benchmark) ** 2).sum()],\n",
        "    \"R2 test (2000-2025)\": [r2_oos(test[\"premium\"], kitchen_sink(test)),\n",
        "                            r2_oos(test[\"premium\"], nn_test)],\n",
        "}, index=[\"Linear, all nine\", \"Neural network\"])\n",
        "results.round(3)"
      ],
      "id": "ed46fd38"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Both models explain part of the premium in the sample they were trained\n",
        "on and lose badly to the training-sample average after 2000.\n",
        "\n",
        "### Why the models fail\n",
        "\n",
        "A model can only learn the relation in the range of data it has seen.\n",
        "The next figure shows the dividend-price ratio with the range it covered\n",
        "in the training sample shaded. After the 1990s it fell far below\n",
        "anything in that range, so every model trained on data up to 1979 had to\n",
        "extrapolate."
      ],
      "id": "0710c756-7499-4178-862d-95caa3b8b153"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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yy+coc5MZoqQwG6J6t+bbnQyKFoIQO+fCLyeMGN89vD9cb1pSoERjhaTlWidO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          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
        "data[\"dp\"].plot(ax=ax, lw=0.8, label=\"Log dividend-price ratio\")\n",
        "ax.axhspan(train[\"dp\"].min(), train[\"dp\"].max(), color=\"0.85\", label=\"Range in training sample\")\n",
        "ax.axvline(pd.Period(\"2000-01\", \"M\"), color=\"0.5\", ls=\":\", lw=1)\n",
        "ax.set_xlabel(\"\")\n",
        "ax.set_ylabel(\"\")\n",
        "ax.legend(frameon=False, loc=\"lower left\")\n",
        "plt.show()"
      ],
      "id": "b1566482"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "How far outside, in units of the training sample’s standard deviation:"
      ],
      "id": "ea175bea-f093-422b-8b21-f10aa6deedf0"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "((test[predictors] - mu) / sd).agg([\"min\", \"max\"]).round(1)"
      ],
      "id": "5c2845cb"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "A linear model extrapolates along a straight line, and with nine\n",
        "predictors far outside their training range at once, its forecasts swing\n",
        "far more than any plausible expected return. A network extrapolates in\n",
        "ways that depend on its arbitrary weights, so it can do even worse, and\n",
        "how much worse changes with the random seed. Neither problem shows up in\n",
        "the training sample, which is why models are judged on data they have\n",
        "not seen.\n",
        "\n",
        "## Takeaways\n",
        "\n",
        "- A neural network learns a strong, stable relation from plenty of data\n",
        "  with little effort.\n",
        "- Monthly stock returns offer the opposite: a weak signal, short\n",
        "  samples, and predictors whose behavior changes over time. Flexibility\n",
        "  then hurts more than it helps.\n",
        "- Gu et al. (2020) do find gains from machine learning, with tens of\n",
        "  thousands of stocks, many characteristics, and models re-estimated as\n",
        "  new data arrive. Even then the out-of-sample $R^2$ is a percent or two\n",
        "  a month.\n",
        "\n",
        "## Try it\n",
        "\n",
        "1.  Change the seed in `torch.manual_seed(0)` and train the network\n",
        "    again. How much does its test $R^2$ change?\n",
        "2.  Drop `dp`, `ep` and `bm`, the valuation ratios that drifted\n",
        "    furthest, and refit both models. What happens?\n",
        "3.  Re-estimate the linear model every year using all data up to that\n",
        "    point, as Welch and Goyal (2008) do, and compare its test $R^2$ with\n",
        "    the fixed model’s.\n",
        "\n",
        "Gu, Shihao, Bryan Kelly, and Dacheng Xiu. 2020. “Empirical Asset Pricing\n",
        "via Machine Learning.” *Review of Financial Studies* 33 (5): 2223–73.\n",
        "<https://doi.org/10.1093/rfs/hhaa009>.\n",
        "\n",
        "Welch, Ivo, and Amit Goyal. 2008. “A Comprehensive Look at the Empirical\n",
        "Performance of Equity Premium Prediction.” *Review of Financial Studies*\n",
        "21 (4): 1455–508."
      ],
      "id": "2b99a1ca-d47a-4d60-81aa-3008d8441a87"
    }
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