Overall Statistics |
Total Trades
29
Average Win
6.43%
Average Loss
-0.96%
Compounding Annual Return
12.087%
Drawdown
33.800%
Expectancy
5.068
Net Profit
493.389%
Sharpe Ratio
0.811
Probabilistic Sharpe Ratio
16.329%
Loss Rate
21%
Win Rate
79%
Profit-Loss Ratio
6.72
Alpha
0.113
Beta
-0.07
Annual Standard Deviation
0.131
Annual Variance
0.017
Information Ratio
0.082
Tracking Error
0.229
Treynor Ratio
-1.518
Total Fees
$256.69
|
# https://quantpedia.com/strategies/fed-model/ # # Each month, the investor conducts a one-month predictive regression (using all available data up to that date) predicting excess stock market # returns using the yield gap as an independent variable. The “Yield gap” is calculated as YG = EY − y, with earnings yield EY ≡ ln (1 ++ E/P) # and y = ln (1 ++ Y) is the log 10 year Treasury bond yield. Then, the strategy allocates 100% in the risky asset if the forecasted excess # returns are positive, and otherwise, it invests 100% in the risk-free rate. from collections import deque import fk_tools import numpy as np from scipy import stats class ReversalYieldChangeFactor(QCAlgorithm): def Initialize(self): self.SetStartDate(2005, 1, 1) self.SetCash(100000) # Monthly price data and yield gap data. self.data = {} self.period = 12 * 21 self.SetWarmUp(self.period) self.market = 'SPY' self.AddEquity(self.market, Resolution.Daily) self.data[self.market] = deque() self.cash = 'SHY' self.AddEquity(self.cash, Resolution.Daily) # Risk free rate. self.risk_free_rate = self.AddData(fk_tools.QuandlValue, 'FRED/DGS3MO', Resolution.Daily).Symbol # 10Y bond yield symbol. self.bond_yield = 'US10YT' self.AddData(fk_tools.QuantpediaBondYield, self.bond_yield, Resolution.Daily) # SP500 earnings yield data. self.sp_earnings_yield = 'MULTPL/SP500_EARNINGS_YIELD_MONTH' self.AddData(fk_tools.QuandlValue, self.sp_earnings_yield, Resolution.Daily) self.data['yield_gap'] = deque() self.last_month = -1 self.Schedule.On(self.DateRules.MonthStart(self.market), self.TimeRules.AfterMarketOpen(self.market), self.Rebalance) def OnData(self, data): # Update only on month change. It allows us to prefetch data with WarmUp period. if self.last_month == self.Time.month: return self.last_month = self.Time.month # Update market price data. if self.Securities.ContainsKey(self.market) and self.Securities.ContainsKey(self.risk_free_rate): market_price = self.Securities[self.market].Price rf_rate = self.Securities[self.risk_free_rate].Price if market_price != 0 and rf_rate != 0: self.data[self.market].append((market_price, rf_rate)) else: # Append previous data as a next one in case there's 0 as price. if len(self.data[self.market]) > 0: last_data = self.data[self.market][-1] self.data[self.market].append(last_data) # Update SP earnings yield. if self.Securities.ContainsKey(self.bond_yield) and self.Securities.ContainsKey(self.sp_earnings_yield): bond_yield = self.Securities[self.bond_yield].Price sp_ey = self.Securities[self.sp_earnings_yield].Price if bond_yield != 0 and sp_ey != 0: yield_gap = np.log(sp_ey) - np.log(bond_yield) self.data['yield_gap'].append(yield_gap) else: # Append previous data as a next one in case there's 0 as price. if len(self.data['yield_gap']) > 0: last_data = self.data['yield_gap'][-1] self.data['yield_gap'].append(last_data) def Rebalance(self): # Ensure minimum data points to calculate regression. min_count = 6 if len(self.data[self.market]) >= min_count and len(self.data['yield_gap']) >= min_count: market_closes = np.array([x[0] for x in self.data[self.market]]) market_returns = (market_closes[1:] - market_closes[:-1]) / market_closes[:-1] rf_rates = np.array([x[1] for x in self.data[self.market]][1:]) excess_returns = market_returns - rf_rates yield_gaps = [x for x in self.data['yield_gap']] # Linear regression calc. # Y = α + (β ∗ X) # intercept = alpha # slope = beta beta, alpha, r_value, p_value, std_err = stats.linregress(yield_gaps[:-1], market_returns[1:]) X = yield_gaps[-1] # Predicted market return. Y = alpha + (beta * X) # Trade execution / rebalance. if Y > 0: if self.Portfolio[self.cash].Invested: self.Liquidate(self.cash) self.SetHoldings(self.market, 1) else: if self.Portfolio[self.market].Invested: self.Liquidate(self.market) self.SetHoldings(self.cash, 1)
import numpy as np from scipy.optimize import minimize import statsmodels.api as sm sp100_stocks = ['AAPL','MSFT','AMZN','FB','BRKB','GOOGL','GOOG','JPM','JNJ','V','PG','XOM','UNH','BAC','MA','T','DIS','INTC','HD','VZ','MRK','PFE','CVX','KO','CMCSA','CSCO','PEP','WFC','C','BA','ADBE','WMT','CRM','MCD','MDT','BMY','ABT','NVDA','NFLX','AMGN','PM','PYPL','TMO','COST','ABBV','ACN','HON','NKE','UNP','UTX','NEE','IBM','TXN','AVGO','LLY','ORCL','LIN','SBUX','AMT','LMT','GE','MMM','DHR','QCOM','CVS','MO','LOW','FIS','AXP','BKNG','UPS','GILD','CHTR','CAT','MDLZ','GS','USB','CI','ANTM','BDX','TJX','ADP','TFC','CME','SPGI','COP','INTU','ISRG','CB','SO','D','FISV','PNC','DUK','SYK','ZTS','MS','RTN','AGN','BLK'] def MonthDiff(d1, d2): return (d1.year - d2.year) * 12 + d1.month - d2.month def Return(values): return (values[-1] - values[0]) / values[0] def Volatility(values): values = np.array(values) returns = (values[1:] - values[:-1]) / values[:-1] return np.std(returns) def MultipleLinearRegresion(x, y): x = np.array(x).T x = sm.add_constant(x) result = sm.OLS(endog=y, exog=x).fit() return result # Custom fee model class CustomFeeModel(FeeModel): def GetOrderFee(self, parameters): fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005 return OrderFee(CashAmount(fee, "USD")) # Quandl free data class QuandlFutures(PythonQuandl): def __init__(self): self.ValueColumnName = "settle" # Quandl "value" data class QuandlValue(PythonQuandl): def __init__(self): self.ValueColumnName = 'Value' # Quandl short interest data. class QuandlFINRA_ShortVolume(PythonQuandl): def __init__(self): self.ValueColumnName = 'SHORTVOLUME' # also 'TOTALVOLUME' is accesible # Commitments of Traders data. # NOTE: IMPORTANT: Data order must be ascending (datewise). # Data source: https://commitmentsoftraders.org/cot-data/ # Data description: https://commitmentsoftraders.org/wp-content/uploads/Static/CoTData/file_key.html class CommitmentsOfTraders(PythonData): def GetSource(self, config, date, isLiveMode): return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/cot/{0}.PRN".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv) # File example. # DATE OPEN HIGH LOW CLOSE VOLUME OI # ---- ---- ---- --- ----- ------ -- # DATE LARGE SPECULATOR COMMERCIAL HEDGER SMALL TRADER # LONG SHORT LONG SHORT LONG SHORT def Reader(self, config, line, date, isLiveMode): data = CommitmentsOfTraders() data.Symbol = config.Symbol if not line[0].isdigit(): return None split = line.split(',') # Prevent lookahead bias. data.Time = datetime.strptime(split[0], "%Y%m%d") + timedelta(days=1) data['LARGE_SPECULATOR_LONG'] = int(split[1]) data['LARGE_SPECULATOR_SHORT'] = int(split[2]) data['COMMERCIAL_HEDGER_LONG'] = int(split[3]) data['COMMERCIAL_HEDGER_SHORT'] = int(split[4]) data['SMALL_TRADER_LONG'] = int(split[5]) data['SMALL_TRADER_SHORT'] = int(split[6]) data['open_interest'] = int(split[1]) + int(split[2]) + int(split[3]) + int(split[4]) + int(split[5]) + int(split[6]) data.Value = int(split[1]) return data # Quantpedia bond yield data. # NOTE: IMPORTANT: Data order must be ascending (datewise) class QuantpediaIndices(PythonData): def GetSource(self, config, date, isLiveMode): return SubscriptionDataSource("data.quantpedia.com/backtesting_data/index/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv) def Reader(self, config, line, date, isLiveMode): data = QuantpediaIndices() data.Symbol = config.Symbol if not line[0].isdigit(): return None split = line.split(',') data.Time = datetime.strptime(split[0], "%Y-%m-%d") + timedelta(days=1) data['close'] = float(split[1]) data.Value = float(split[1]) return data # Quantpedia bond yield data. # NOTE: IMPORTANT: Data order must be ascending (datewise) class QuantpediaBondYield(PythonData): def GetSource(self, config, date, isLiveMode): return SubscriptionDataSource("data.quantpedia.com/backtesting_data/bond_yield/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv) def Reader(self, config, line, date, isLiveMode): data = QuantpediaBondYield() data.Symbol = config.Symbol if not line[0].isdigit(): return None split = line.split(',') data.Time = datetime.strptime(split[0], "%Y-%m-%d") + timedelta(days=1) data['yield'] = float(split[1]) data.Value = float(split[1]) return data # Quantpedia data. # NOTE: IMPORTANT: Data order must be ascending (datewise) class QuantpediaFutures(PythonData): def GetSource(self, config, date, isLiveMode): return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv) def Reader(self, config, line, date, isLiveMode): data = QuantpediaFutures() data.Symbol = config.Symbol if not line[0].isdigit(): return None split = line.split(';') data.Time = datetime.strptime(split[0], "%d.%m.%Y") + timedelta(days=1) data['back_adjusted'] = float(split[1]) data['spliced'] = float(split[2]) data.Value = float(split[1]) return data # Commitments of Traders data. # NOTE: IMPORTANT: Data order must be ascending (datewise). # Data source: https://commitmentsoftraders.org/cot-data/ # Data description: https://commitmentsoftraders.org/wp-content/uploads/Static/CoTData/file_key.html class CommitmentsOfTraders(PythonData): def GetSource(self, config, date, isLiveMode): return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/cot/{0}.PRN".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv) # File example. # DATE OPEN HIGH LOW CLOSE VOLUME OI # ---- ---- ---- --- ----- ------ -- # DATE LARGE SPECULATOR COMMERCIAL HEDGER SMALL TRADER # LONG SHORT LONG SHORT LONG SHORT def Reader(self, config, line, date, isLiveMode): data = CommitmentsOfTraders() data.Symbol = config.Symbol if not line[0].isdigit(): return None split = line.split(',') # Prevent lookahead bias. data.Time = datetime.strptime(split[0], "%Y%m%d") + timedelta(days=1) data['LARGE_SPECULATOR_LONG'] = int(split[1]) data['LARGE_SPECULATOR_SHORT'] = int(split[2]) data['COMMERCIAL_HEDGER_LONG'] = int(split[3]) data['COMMERCIAL_HEDGER_SHORT'] = int(split[4]) data['SMALL_TRADER_LONG'] = int(split[5]) data['SMALL_TRADER_SHORT'] = int(split[6]) data.Value = int(split[1]) return data # NOTE: Manager for new trades. It's represented by certain count of equally weighted brackets for long and short positions. # If there's a place for new trade, it will be managed for time of holding period. class TradeManager(): def __init__(self, algorithm, long_size, short_size, holding_period): self.algorithm = algorithm # algorithm to execute orders in. self.long_size = long_size self.short_size = short_size self.long_len = 0 self.short_len = 0 # Arrays of ManagedSymbols self.symbols = [] self.holding_period = holding_period # Days of holding. # Add stock symbol object def Add(self, symbol, long_flag): # Open new long trade. managed_symbol = ManagedSymbol(symbol, self.holding_period, long_flag) if long_flag: # If there's a place for it. if self.long_len < self.long_size: self.symbols.append(managed_symbol) self.algorithm.SetHoldings(symbol, 1 / self.long_size) self.long_len += 1 else: self.algorithm.Log("There's not place for additional trade.") # Open new short trade. else: # If there's a place for it. if self.short_len < self.short_size: self.symbols.append(managed_symbol) self.algorithm.SetHoldings(symbol, - 1 / self.short_size) self.short_len += 1 else: self.algorithm.Log("There's not place for additional trade.") # Decrement holding period and liquidate symbols. def TryLiquidate(self): symbols_to_delete = [] for managed_symbol in self.symbols: managed_symbol.days_to_liquidate -= 1 # Liquidate. if managed_symbol.days_to_liquidate == 0: symbols_to_delete.append(managed_symbol) self.algorithm.Liquidate(managed_symbol.symbol) if managed_symbol.long_flag: self.long_len -= 1 else: self.short_len -= 1 # Remove symbols from management. for managed_symbol in symbols_to_delete: self.symbols.remove(managed_symbol) def LiquidateTicker(self, ticker): symbol_to_delete = None for managed_symbol in self.symbols: if managed_symbol.symbol.Value == ticker: self.algorithm.Liquidate(managed_symbol.symbol) symbol_to_delete = managed_symbol if managed_symbol.long_flag: self.long_len -= 1 else: self.short_len -= 1 break if symbol_to_delete: self.symbols.remove(symbol_to_delete) else: self.algorithm.Debug("Ticker is not held in portfolio!") class ManagedSymbol(): def __init__(self, symbol, days_to_liquidate, long_flag): self.symbol = symbol self.days_to_liquidate = days_to_liquidate self.long_flag = long_flag class PortfolioOptimization(object): def __init__(self, df_return, risk_free_rate, num_assets): self.daily_return = df_return self.risk_free_rate = risk_free_rate self.n = num_assets # numbers of risk assets in portfolio self.target_vol = 0.05 def annual_port_return(self, weights): # calculate the annual return of portfolio return np.sum(self.daily_return.mean() * weights) * 252 def annual_port_vol(self, weights): # calculate the annual volatility of portfolio return np.sqrt(np.dot(weights.T, np.dot(self.daily_return.cov() * 252, weights))) def min_func(self, weights): # method 1: maximize sharp ratio return - self.annual_port_return(weights) / self.annual_port_vol(weights) # method 2: maximize the return with target volatility #return - self.annual_port_return(weights) / self.target_vol def opt_portfolio(self): # maximize the sharpe ratio to find the optimal weights cons = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1}) bnds = tuple((0, 1) for x in range(2)) + tuple((0, 0.25) for x in range(self.n - 2)) opt = minimize(self.min_func, # object function np.array(self.n * [1. / self.n]), # initial value method='SLSQP', # optimization method bounds=bnds, # bounds for variables constraints=cons) # constraint conditions opt_weights = opt['x'] return opt_weights