import backtrader as bt
import numpy as np
import pandas as pd
from scipy.stats import norm

class DispersionTradingStrategy(bt.Strategy):
    def __init__(self):
        self.sorted_data = None

    def next(self):
        if self.data.datetime.date(ago=0).month != self.data.datetime.date(ago=1).month:
            self.sorted_data = self.sort_quintiles_by_disagreement()
            self.adjust_positions()

    def sort_quintiles_by_disagreement(self):
        stocks_data = pd.DataFrame()
        for d in self.datas:
            if "SP100" not in d._name:
                stocks_data[d._name] = d.array("eps_forecasts")
        stocks_data['belief_disagreement'] = self.calculate_belief_disagreement(stocks_data)
        sorted_stocks = stocks_data.sort_values(by='belief_disagreement', ascending=False)
        return sorted_stocks

    def calculate_belief_disagreement(self, stocks_data):
        # Implement the methodology to calculate the mean absolute difference for each firm,        
        # scaled by earnings uncertainty as per the source paper.
        return belief_disagreement

    def adjust_positions(self):
        highest_disagreement_stocks = self.sorted_data.head(int(len(self.sorted_data) / 5))
        for d in self.datas:
            if "SP100" in d._name:
                self.sell_index_put(d)
            elif d._name in highest_disagreement_stocks.index:
                self.buy_stock(d)

    def buy_stock(self, data):
        size = self.broker.getvalue() * 0.2 / data.close[0]
        self.order_target_size(data, size)

    def sell_index_put(self, data):
        # Implement the logic for selling index put options using Black-Scholes deltas ranging from -0.8 to -0.2.

class DispersionTrading(bt.Cerebro):
    def __init__(self):
        super().__init__()

    def run_strategy(self):
        # Load and preprocess data, including options and EPS forecasts from I/B/E/S database.        
        # Add stocks and index data to the strategy.
        self.addstrategy(DispersionTradingStrategy)
        self.run()

if __name__ == '__main__':
    dispersion_trading = DispersionTrading()
    dispersion_trading.run_strategy()