Hi everybody,

I threw together an algo that uses PCA to get the component that explains the most variance in the energy sector. It assumes the principle component is a unit portfolio and buys 500 units of the portfolio.

It is really basic, but could be the baseline for more work. Here are a couple references on the idea.

PCA analysis in an Ipython notebook

Stat Arb in the US Equities Market

This is not a duplication of either, but an overly simplified version of the idea. It uses prices instead of returns, and rebalances on a 5 day schedule. I need to do more work to wrap my head around the math, but it looks like there's a strategy in there somewhere.

David

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Backtest from
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initial capital

Cumulative performance:

Algorithm
Benchmark

Custom data:

Total Returns

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Alpha

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Beta

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Sharpe

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Sortino

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Max Drawdown

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Benchmark Returns

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Volatility

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Returns | 1 Month | 3 Month | 6 Month | 12 Month |

Alpha | 1 Month | 3 Month | 6 Month | 12 Month |

Beta | 1 Month | 3 Month | 6 Month | 12 Month |

Sharpe | 1 Month | 3 Month | 6 Month | 12 Month |

Sortino | 1 Month | 3 Month | 6 Month | 12 Month |

Volatility | 1 Month | 3 Month | 6 Month | 12 Month |

Max Drawdown | 1 Month | 3 Month | 6 Month | 12 Month |

''' Principle Component Analysis http://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf http://nbviewer.ipython.org/github/carljv/Will_it_Python/blob/master/MLFH/ch8/ch8.ipynb ''' import numpy as np import pandas as pd from sklearn.decomposition import PCA from zipline.utils import tradingcalendar as calendar def initialize(context): set_symbol_lookup_date('2005-01-01') context.stocks = symbols( 'XOM', 'CVX', 'SLB', 'COP', 'EOG', 'PXD', 'OXY', 'HAL', 'APC', 'WMB', 'APA', 'NOV', 'BHI', 'VLO', 'NBL', 'DVN', 'NFX', 'COG', 'HES', 'MRO', 'FTI', 'TSO', 'RRC', 'CAM', 'CHK', 'SWN', 'CNX', 'EQT', 'MUR', 'RIG', 'OKE', 'NBR', 'DNR', 'ESV', 'HP', 'RDC', 'NE', 'BTU', 'DO', 'XLE' ) set_slippage(slippage.FixedSlippage(spread=0.00)) set_commission(commission.PerShare(cost=0.01, min_trade_cost=1.0)) context.manager = EventManager(period=5, rule_func=lambda x: True) context.leverage = 1.5 def handle_data(context, data): P = context.portfolio pos = P.positions market_value = 0 for i in data: market_value += abs(pos[i].amount * data[i].price) record(leverage=market_value / P.portfolio_value, exposure=P.positions_value / P.portfolio_value) if not context.manager.signal(get_datetime()): return # Drop any stocks with nan values prices = history(60, '1d', 'price').T.dropna().T prices = zscore(np.log(prices)) pca = PCA(n_components=1).fit(prices.corr()) unit_values = -pd.Series(pca.components_[0], index=prices.columns) for i in data: if i in unit_values.index: shares = 500 * unit_values[i] order_target(i, shares) else: order_target(i, 0) zscore = lambda x: (x - x.mean()) / x.std() class EventManager(object): ''' Manager for timing the entry point of periodic events. ''' def __init__(self, period=1, max_daily_hits=1, rule_func=None): ''' :Parameters: period: integer <default=1> number of business days between events max_daily_hits: integer <default=1> upper limit on the number of times per day the event is triggered. (trading controls could work for this too in some cases) rule_func: function (returns a boolean) <default=None> decision function for timimng an intraday entry point ''' self.period = period self.max_daily_hits = max_daily_hits self.remaining_hits = max_daily_hits self._rule_func = rule_func self.next_event_date = None self.market_open = None self.market_close = None @property def todays_index(self): dt = calendar.canonicalize_datetime(get_datetime()) return calendar.trading_days.searchsorted(dt) def open_and_close(self, dt): return calendar.open_and_closes.T[dt] def signal(self, *args, **kwargs): ''' Entry point for the rule_func All arguments are passed to rule_func ''' now = get_datetime() dt = calendar.canonicalize_datetime(now) if self.next_event_date is None: self.next_event_date = dt times = self.open_and_close(dt) self.market_open = times['market_open'] self.market_close = times['market_close'] if now < self.market_open: return False if now == self.market_close: self.set_next_event_date() decision = self._rule_func(*args, **kwargs) if decision: self.remaining_hits -= 1 if self.remaining_hits <= 0: self.set_next_event_date() return decision def set_next_event_date(self): self.remaining_hits = self.max_daily_hits tdays = calendar.trading_days idx = self.todays_index + self.period self.next_event_date = tdays[idx] times = self.open_and_close(self.next_event_date) self.market_open = times['market_open'] self.market_close = times['market_close']