Original paper
Abstract
This paper investigates the role of realized and implied and their risk premia (variance and skewness) for commodities’ future returns. We estimate these moments from high frequency and commodity futures option data that results in forward-looking measures. Risk premia are computed as the difference between implied and realized moments. We highlight, from a cross-sectional and time series perspective, the strong positive relation between commodity returns and implied skewness. Moreover, we emphasize the high performance of skewness risk premium. Additionally, we show that their portfolios exhibit the best risk-return tradeoff. Most of our results are robust to other factors such as the momentum and roll yield.
Keywords:Â Commodity Forecast, Implied Volatility, Implied Skewness, Risk Premium
Trading rules
- Scope for investments: 8 commodities (agricultural: corn, soybeans, wheat; metal: copper, silver, gold; energy: oil, natural gas).
- Estimate implied skewness: Use Bakshi’s model-free approach with one-month options on futures contracts.
- Design portfolios with both long and short positions:
- Go long: Commodities in the top quartile (25%) based on implied skewness.
- Go short: Commodities in the bottom quartile (25%) based on implied skewness.
- Portfolio structure: 2 long and 2 short commodity futures contracts, equal weights.
- Duration and frequency of portfolio construction: Set up daily and held for an equivalent of 21 consecutive business days (approximately a month).
- Rebalancing: On a daily basis, sticking to 1/21 of the total portfolio weight.
Python code
Backtrader
import backtrader as bt
import numpy as np
class ImpliedSkewnessStrategy(bt.Strategy):
params = (
('lookback', 21),
('rebalance_days', 1),
)
def __init__(self):
self.rebalance_counter = 0
def next(self):
if self.rebalance_counter % self.params.rebalance_days == 0:
self.rebalance_portfolio()
self.rebalance_counter += 1
def rebalance_portfolio(self):
implied_skewness = []
for d in self.getdatanames():
skewness = self.calculate_implied_skewness(d)
implied_skewness.append((d, skewness))
implied_skewness.sort(key=lambda x: x[1], reverse=True)
long_positions = implied_skewness[:2]
short_positions = implied_skewness[-2:]
target_weight = 1 / (2 * self.params.lookback)
for data_name, _ in long_positions:
data = self.getdatabyname(data_name)
position_size = target_weight * self.broker.getvalue() / data.close[0]
self.order_target_size(data, position_size)
for data_name, _ in short_positions:
data = self.getdatabyname(data_name)
position_size = -target_weight * self.broker.getvalue() / data.close[0]
self.order_target_size(data, position_size)
def calculate_implied_skewness(self, data_name):
# Implement Bakshi's model-free approach here
# This function should return the implied skewness of the given data
pass
if __name__ == '__main__':
cerebro = bt.Cerebro()
# Add data feeds for the 8 commodities here
# ...
cerebro.adddata(data_feed, name='corn')
cerebro.adddata(data_feed, name='soybeans')
cerebro.adddata(data_feed, name='wheat')
cerebro.adddata(data_feed, name='copper')
cerebro.adddata(data_feed, name='silver')
cerebro.adddata(data_feed, name='gold')
cerebro.adddata(data_feed, name='oil')
cerebro.adddata(data_feed, name='natural_gas')
cerebro.addstrategy(ImpliedSkewnessStrategy)
cerebro.broker.setcash(100000.0)
cerebro.broker.setcommission(commission=0.001)
print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue())
cerebro.run()
print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue())This is a basic template for the Implied Skewness Strategy in Backtrader. Note that you will need to implement the Bakshi’s model-free approach to calculate implied skewness and add the data feeds for the 8 commodities.