Overall Statistics |
Total Trades 280 Average Win 1.57% Average Loss -2.02% Compounding Annual Return 2.013% Drawdown 42.100% Expectancy 0.053 Net Profit 7.979% Sharpe Ratio 0.181 Probabilistic Sharpe Ratio 3.818% Loss Rate 41% Win Rate 59% Profit-Loss Ratio 0.78 Alpha 0.022 Beta 0.077 Annual Standard Deviation 0.171 Annual Variance 0.029 Information Ratio -0.392 Tracking Error 0.202 Treynor Ratio 0.402 Total Fees $2600.39 |
import numpy as np from math import floor class KalmanFilter: def __init__(self): self.delta = 1e-4 self.wt = self.delta / (1 - self.delta) * np.eye(2) self.vt = 1e-3 self.theta = np.zeros(2) self.P = np.zeros((2, 2)) self.R = None self.qty = 2000 def update(self, price_one, price_two): # Create the observation matrix of the latest prices # of TLT and the intercept value (1.0) F = np.asarray([price_one, 1.0]).reshape((1, 2)) y = price_two # The prior value of the states \theta_t is # distributed as a multivariate Gaussian with # mean a_t and variance-covariance R_t if self.R is not None: self.R = self.C + self.wt else: self.R = np.zeros((2, 2)) # Calculate the Kalman Filter update # ---------------------------------- # Calculate prediction of new observation # as well as forecast error of that prediction yhat = F.dot(self.theta) et = y - yhat # Q_t is the variance of the prediction of # observations and hence \sqrt{Q_t} is the # standard deviation of the predictions Qt = F.dot(self.R).dot(F.T) + self.vt sqrt_Qt = np.sqrt(Qt) # The posterior value of the states \theta_t is # distributed as a multivariate Gaussian with mean # m_t and variance-covariance C_t At = self.R.dot(F.T) / Qt self.theta = self.theta + At.flatten() * et self.C = self.R - At * F.dot(self.R) hedge_quantity = int(floor(self.qty*self.theta[0])) return et, sqrt_Qt, hedge_quantity
import numpy as np from math import floor from KalmanFilter import KalmanFilter class VerticalParticleInterceptor(QCAlgorithm): def Initialize(self): self.SetStartDate(2016, 1, 1) # Set Start Date self.SetCash(100000) # Set Strategy Cash self.SetBrokerageModel(AlphaStreamsBrokerageModel()) self.symbols = [self.AddEquity(x, Resolution.Minute).Symbol for x in ['VIA', 'VIAB']] self.kf = KalmanFilter() self.invested = None self.Schedule.On(self.DateRules.EveryDay('VIA'), self.TimeRules.BeforeMarketClose('VIA', 5), self.UpdateAndTrade) def UpdateAndTrade(self): # Get recent price and holdings information via = self.CurrentSlice[self.symbols[0]].Close viab = self.CurrentSlice[self.symbols[1]].Close holdings = self.Portfolio[self.symbols[0]] forecast_error, prediction_std_dev, hedge_quantity = self.kf.update(via, viab) if not holdings.Invested: # Long the spread if forecast_error < -prediction_std_dev: insights = Insight.Group([Insight(self.symbols[0], timedelta(1), InsightType.Price, InsightDirection.Down), Insight(self.symbols[1], timedelta(1), InsightType.Price, InsightDirection.Up)]) self.EmitInsights(insights) self.MarketOrder(self.symbols[1], self.kf.qty) self.MarketOrder(self.symbols[0], -hedge_quantity) # Short the spread elif forecast_error > prediction_std_dev: insights = Insight.Group([Insight(self.symbols[0], timedelta(1), InsightType.Price, InsightDirection.Up), Insight(self.symbols[1], timedelta(1), InsightType.Price, InsightDirection.Down)]) self.EmitInsights(insights) self.MarketOrder(self.symbols[1], -self.kf.qty) self.MarketOrder(self.symbols[0], hedge_quantity) if holdings.Invested: # Close long position if holdings.IsShort and (forecast_error >= -prediction_std_dev): insights = Insight.Group([Insight(self.symbols[0], timedelta(1), InsightType.Price, InsightDirection.Flat), Insight(self.symbols[1], timedelta(1), InsightType.Price, InsightDirection.Flat)]) self.EmitInsights(insights) self.Liquidate() self.invested = None # Close short position elif holdings.IsLong and (forecast_error <= prediction_std_dev): insights = Insight.Group([Insight(self.symbols[0], timedelta(1), InsightType.Price, InsightDirection.Flat), Insight(self.symbols[1], timedelta(1), InsightType.Price, InsightDirection.Flat)]) self.EmitInsights(insights) self.Liquidate() self.invested = None