Original paper
Abstract
A dispersion trade is entered into when a trader believes that the constituents of an index will be more volatile than the index itself. The South African derivatives market is fairly advanced, however it still experiences inefficiencies and dispersion trades have been known to perform well in inefficient markets. This paper tests the South African market for dispersion opportunities and explores various methods of executing these trades. The South African market shows positive results for dispersion trading; namely short-term reverse dispersion trading. Call options and Cross-Sectional Volatility (CSV) swaps are also tested. CSV swaps performed poorly whereas call options experienced annual returns well above the market.
Keywords:Â dispersion trading, volatility arbitrage, cross-sectional volatility, reverse dispersion trade
Trading rules
- Target investment: S&P 100 stocks.
- Engage in options related to both individual stocks and the entire index.
- Employ earnings per share predictions from the I/B/E/S database.
- For each company, determine the average absolute variation, adjusting for unpredictability in earnings (see the referenced research for the approach).
- On a monthly basis, categorize stocks into five groups based on the variance in opinions.
- Buy stocks with highest belief disagreement.
- Sell index put as an equally-weighted portfolio of 1-month index put options.
- Use Black-Scholes deltas within the range of -0.8 to -0.2 for index put options.
Python code
Backtrader
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()Note: This code provides a template for implementing the Dispersion Trading strategy using Backtrader. You’ll need to fill in the actual calculations for belief disagreement and selling index put options based on the paper’s methodology, as well as loading and preprocessing the necessary data.