Overall Statistics |
Total Trades 4118 Average Win 0.00% Average Loss 0.00% Compounding Annual Return -0.050% Drawdown 0.500% Expectancy -0.078 Net Profit -0.453% Sharpe Ratio -0.158 Probabilistic Sharpe Ratio 0.001% Loss Rate 69% Win Rate 31% Profit-Loss Ratio 1.96 Alpha -0 Beta 0.001 Annual Standard Deviation 0.002 Annual Variance 0 Information Ratio -0.589 Tracking Error 0.149 Treynor Ratio -0.325 Total Fees $4693.25 Estimated Strategy Capacity $1200000.00 Lowest Capacity Asset SCHO UOVIOSUIT3DX |
#region imports from AlgorithmImports import * from arch.unitroot.cointegration import engle_granger from pykalman import KalmanFilter #endregion class PCADemo(QCAlgorithm): def Initialize(self): #1. Required: Five years of backtest history self.SetStartDate(2014, 1, 1) #2. Required: Alpha Streams Models: self.SetBrokerageModel(BrokerageName.AlphaStreams) #3. Required: Significant AUM Capacity self.SetCash(1000000) #4. Required: Benchmark to SPY self.SetBenchmark("SPY") self.assets = ["SCHO", "SHY"] # Add Equity ------------------------------------------------ for i in range(len(self.assets)): self.AddEquity(self.assets[i], Resolution.Minute) # Instantiate our model self.Recalibrate() # Set a variable to indicate the trading bias of the portfolio self.state = 0 # Set Scheduled Event Method For Kalman Filter updating. self.Schedule.On(self.DateRules.WeekStart(), self.TimeRules.At(0, 0), self.Recalibrate) # Set Scheduled Event Method For Kalman Filter updating. self.Schedule.On(self.DateRules.EveryDay(), self.TimeRules.BeforeMarketClose("SHY"), self.EveryDayBeforeMarketClose) def Recalibrate(self): qb = self history = qb.History(self.assets, 252*2, Resolution.Daily) if history.empty: return # Select the close column and then call the unstack method data = history['close'].unstack(level=0) # Convert into log-price series to eliminate compounding effect log_price = np.log(data) ### Get Cointegration Vectors # Get the cointegration vector coint_result = engle_granger(log_price.iloc[:, 0], log_price.iloc[:, 1], trend="c", lags=0) coint_vector = coint_result.cointegrating_vector[:2] # Get the spread spread = log_price @ coint_vector ### Kalman Filter # Initialize a Kalman Filter. Using the first 20 data points to optimize its initial state. We assume the market has no regime change so that the transitional matrix and observation matrix is [1]. self.kalmanFilter = KalmanFilter(transition_matrices = [1], observation_matrices = [1], initial_state_mean = spread.iloc[:20].mean(), observation_covariance = spread.iloc[:20].var(), em_vars=['transition_covariance', 'initial_state_covariance']) self.kalmanFilter = self.kalmanFilter.em(spread.iloc[:20], n_iter=5) (filtered_state_means, filtered_state_covariances) = self.kalmanFilter.filter(spread.iloc[:20]) # Obtain the current Mean and Covariance Matrix expectations. self.currentMean = filtered_state_means[-1, :] self.currentCov = filtered_state_covariances[-1, :] # Initialize a mean series for spread normalization using the Kalman Filter's results. mean_series = np.array([None]*(spread.shape[0]-20)) # Roll over the Kalman Filter to obtain the mean series. for i in range(20, spread.shape[0]): (self.currentMean, self.currentCov) = self.kalmanFilter.filter_update(filtered_state_mean = self.currentMean, filtered_state_covariance = self.currentCov, observation = spread.iloc[i]) mean_series[i-20] = float(self.currentMean) # Obtain the normalized spread series. normalized_spread = (spread.iloc[20:] - mean_series) ### Determine Trading Threshold # Initialize 50 set levels for testing. s0 = np.linspace(0, max(normalized_spread), 50) # Calculate the profit levels using the 50 set levels. f_bar = np.array([None]*50) for i in range(50): f_bar[i] = len(normalized_spread.values[normalized_spread.values > s0[i]]) \ / normalized_spread.shape[0] # Set trading frequency matrix. D = np.zeros((49, 50)) for i in range(D.shape[0]): D[i, i] = 1 D[i, i+1] = -1 # Set level of lambda. l = 1.0 # Obtain the normalized profit level. f_star = np.linalg.inv(np.eye(50) + l * D.T@D) @ f_bar.reshape(-1, 1) s_star = [f_star[i]*s0[i] for i in range(50)] self.threshold = s0[s_star.index(max(s_star))] # Set the trading weight. We would like the portfolio absolute total weight is 1 when trading. self.trading_weight = coint_vector / np.sum(abs(coint_vector)) def EveryDayBeforeMarketClose(self): qb = self # Get the real-time log close price for all assets and store in a Series series = pd.Series() for symbol in qb.Securities.Keys: series[symbol] = np.log(qb.Securities[symbol].Close) # Get the spread spread = np.sum(series * self.trading_weight) # Update the Kalman Filter with the Series (self.currentMean, self.currentCov) = self.kalmanFilter.filter_update(filtered_state_mean = self.currentMean, filtered_state_covariance = self.currentCov, observation = spread) # Obtain the normalized spread. normalized_spread = spread - self.currentMean # ============================== # Mean-reversion if normalized_spread < -self.threshold: orders = [] for i in range(len(self.assets)): orders.append(PortfolioTarget(self.assets[i], self.trading_weight[i])) self.SetHoldings(orders) self.state = 1 elif normalized_spread > self.threshold: orders = [] for i in range(len(self.assets)): orders.append(PortfolioTarget(self.assets[i], -1 * self.trading_weight[i])) self.SetHoldings(orders) self.state = -1 # Out of position if spread recovered elif self.state == 1 and normalized_spread > -self.threshold or self.state == -1 and normalized_spread < self.threshold: self.Liquidate() self.state = 0