Overall Statistics Total Trades 26 Average Win 1.04% Average Loss -5.41% Compounding Annual Return 6.568% Drawdown 50.300% Expectancy -0.149 Net Profit 316.504% Sharpe Ratio 0.392 Probabilistic Sharpe Ratio 0.023% Loss Rate 29% Win Rate 71% Profit-Loss Ratio 0.19 Alpha 0.01 Beta 0.769 Annual Standard Deviation 0.141 Annual Variance 0.02 Information Ratio -0.047 Tracking Error 0.078 Treynor Ratio 0.072 Total Fees $108.26 Estimated Strategy Capacity$750000000.00 Lowest Capacity Asset SPY R735QTJ8XC9X
# 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 numpy as np
from scipy import stats

class FEDModel(QCAlgorithm):

def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)

# monthly price data and yield gap data
self.data = {}

self.period = 12 * 21
self.SetWarmUp(self.period)

self.market_data = deque()

# risk free rate

# 10Y bond yield symbol

# SP500 earnings yield data

self.yield_gap = deque()

self.recent_month = -1

def OnData(self, data):
rebalance_flag = False

if self.sp_earnings_yield in data and data[self.sp_earnings_yield]:
if self.Time.month != self.recent_month:
self.recent_month = self.Time.month
rebalance_flag = True

if not rebalance_flag:
# earnings yield data is no longer comming in
if self.Securities[self.sp_earnings_yield].GetLastData():
if (self.Time.date() - self.Securities[self.sp_earnings_yield].GetLastData().Time.date()).days > 31:
self.Liquidate()
return

# pdate market price data
if self.market in data and self.risk_free_rate in data and self.bond_yield in data:
if data[self.market] and data[self.risk_free_rate] and data[self.bond_yield]:
market_price = data[self.market].Value
rf_rate = data[self.risk_free_rate].Value
bond_yield = data[self.bond_yield].Value
sp_ey = data[self.sp_earnings_yield].Value
if market_price != 0 and rf_rate != 0 and bond_yield != 0 and sp_ey != 0:
self.market_data.append((market_price, rf_rate))

yield_gap = np.log(sp_ey) - np.log(bond_yield)
self.yield_gap.append(yield_gap)
rebalance_flag = True

# ensure minimum data points to calculate regression
min_count = 6
if len(self.market_data) >= min_count:
market_closes = np.array([x for x in self.market_data])
market_returns = (market_closes[1:] - market_closes[:-1]) / market_closes[:-1]
rf_rates = np.array([x for x in self.market_data][1:])
excess_returns = market_returns - rf_rates

yield_gaps = [x for x in self.yield_gap]

# linear regression
# Y = α + (β ∗ X)
# intercept = alpha
# slope = beta
beta, alpha, r_value, p_value, std_err = stats.linregress(yield_gaps[1:-1], market_returns[1:])
X = yield_gaps[-1]

# predicted market return
Y = alpha + (beta * X)

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)

# 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.isdigit(): return None
split = line.split(',')

data.Time = datetime.strptime(split, "%Y-%m-%d") + timedelta(days=1)
data['yield'] = float(split)
data.Value = float(split)

return data

# Quandl "value" data
class QuandlValue(PythonQuandl):
def __init__(self):
self.ValueColumnName = 'Value'