The Value Uncertainty Premium

1from AlgorithmImports import *
2from numpy import isnan
3from typing import List, Dict
4class TheValueUncertaintyPremium(QCAlgorithm):
5def Initialize(self) -> None:
6self.SetStartDate(2010, 1, 1)
7self.SetCash(100_000)
8self.exchange_codes: List[str] = ['NYS']
9self.weight: Dict[Symbol, float] = {}
10self.quantile: int = 10
11self.leverage: int = 10
12self.bm_by_symbol: Dict[Symbol, RollingWindow] = {}
13
14self.m_period: int = 12
15self.required_estimate_quarter: int = 4
16self.universe_selection_period: int = 12
17self.recent_EPS_estimate: Dict[Symbol, Dict[int, List[float]]] = {}
18
19market: Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
20self.already_subscribed:list[Symbol] = []
21self.last_fundamental: List[Symbol] = []
22self.fundamental_count: int = 500
23self.fundamental_sorting_key = lambda x: x.DollarVolume
24self.selection_flag: bool = False
25self.rebalance_flag: bool = False
26self.UniverseSettings.Leverage = self.leverage
27self.UniverseSettings.Resolution = Resolution.Daily
28self.AddUniverse(self.FundamentalSelectionFunction)
29self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
30self.Schedule.On(self.DateRules.MonthStart(market), self.TimeRules.AfterMarketOpen(market), self.Selection)
31def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
32for security in changes.AddedSecurities:
33    security.SetFeeModel(CustomFeeModel())
34
35def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
36if not self.selection_flag:
37    return Universe.Unchanged
38self.selection_flag = False
39
40# select new universe once a period
41if self.Time.month % self.universe_selection_period == 0:
42    selected: List[Fundamental] = [
43        x for x in fundamental 
44        if x.HasFundamentalData 
45        and x.Market == 'usa' 
46        and x.MarketCap != 0 
47        and x.SecurityReference.ExchangeId in self.exchange_codes 
48        and not isnan(x.ValuationRatios.ForwardDividend) and x.ValuationRatios.ForwardDividend
49        and not isnan(x.FinancialStatements.BalanceSheet.TotalAssets.ThreeMonths) and x.FinancialStatements.BalanceSheet.TotalAssets.ThreeMonths != 0 
50        and not isnan(x.EarningReports.BasicAverageShares.ThreeMonths) and x.EarningReports.BasicAverageShares.ThreeMonths != 0 
51        and not isnan(x.FinancialStatements.BalanceSheet.CurrentLiabilities.ThreeMonths) and x.FinancialStatements.BalanceSheet.CurrentLiabilities.ThreeMonths
52    ]
53    if len(selected) > self.fundamental_count:
54        selected = [x for x in sorted(selected, key=self.fundamental_sorting_key, reverse=True)[:self.fundamental_count]]
55    for stock in selected:
56        symbol: Symbol = stock.Symbol
57        if symbol not in self.already_subscribed:
58            self.AddData(EstimizeEstimate, symbol)
59            self.already_subscribed.append(symbol)
60    
61    self.last_fundamental = selected
62self.rebalance_flag = True
63UNC: Dict[Symbol, float] = {}
64for stock in self.last_fundamental:
65    symbol: Symbol = stock.Symbol
66    
67    # store pb value
68    if symbol not in self.bm_by_symbol:
69        self.bm_by_symbol[symbol] = RollingWindow[float](self.m_period)
70    # calculate UNC
71    if self.bm_by_symbol[symbol].IsReady:
72        bm_values: List[float] = [x for x in self.bm_by_symbol[symbol]]
73        bm_std: float = np.std(bm_values)
74        pb_mean: float = np.mean(bm_values)
75        UNC[stock] = bm_std / pb_mean
76    # get net income estimate
77    if symbol.Value in self.recent_EPS_estimate and self.Time.year in self.recent_EPS_estimate[symbol.Value]:
78        current_be: float = stock.FinancialStatements.BalanceSheet.TotalAssets.ThreeMonths - stock.FinancialStatements.BalanceSheet.CurrentLiabilities.ThreeMonths
79        
80        # NOTE Expected net income for the end of fiscal year y, given the information available up to day d, is estimated as the product of expected earnings per share given by the mean of analysts’ forecasts up to day d and the total number of shares outstanding.
81        estimated_net_income: float = np.mean(self.recent_EPS_estimate[symbol.Value][self.Time.year]) * stock.EarningReports.BasicAverageShares.ThreeMonths
82        
83        expected_dividend: float = stock.ValuationRatios.ForwardDividend
84        expected_be: float = current_be + estimated_net_income - expected_dividend
85        bm: float = expected_be / stock.MarketCap
86        self.bm_by_symbol[symbol].Add(bm)
87    else:
88        if self.bm_by_symbol[symbol].Count != 0:
89            self.bm_by_symbol[symbol].Reset()
90if len(UNC) >= self.quantile:
91    sorted_by_perf: List[Tuple[Symbol, float]] = sorted(UNC.items(), key = lambda x:x[1], reverse=True)
92    quantile: int = int(len(sorted_by_perf) / self.quantile)
93    long: List[Fundamental] = [x[0] for x in sorted_by_perf[:quantile]]
94    short: List[Fundamental] = [x[0] for x in sorted_by_perf[-quantile:]]
95    # market cap weighting
96    for i, portfolio in enumerate([long, short]):
97        mc_sum: float = sum(list(map(lambda stock: stock.MarketCap, portfolio)))
98        for stock in portfolio:
99            self.weight[stock.Symbol] = ((-1)**i) * stock.MarketCap / mc_sum
100return list(self.weight.keys())
101
102def OnData(self, slice: Slice) -> None:
103# store latest EPS Estimize estimate
104estimize: Dict[Symbol, float] = slice.Get(EstimizeEstimate)
105for symbol, value in estimize.items():
106    ticker: str = symbol.Value
107    # store eond of the year estimates indexed by fiscal year
108    if value.FiscalQuarter == self.required_estimate_quarter:
109        if ticker not in self.recent_EPS_estimate:
110            self.recent_EPS_estimate[ticker] = {}
111        if value.FiscalYear not in self.recent_EPS_estimate[ticker]:
112            self.recent_EPS_estimate[ticker][value.FiscalYear] = []
113        self.recent_EPS_estimate[ticker][value.FiscalYear].append(value.Eps)
114if not self.rebalance_flag:
115    return
116self.rebalance_flag = False
117# trade execution
118portfolio: List[PortfolioTarget] = [PortfolioTarget(symbol, w) for symbol, w in self.weight.items() if slice.contains_key(symbol) and slice[symbol]]
119self.SetHoldings(portfolio, True)
120self.weight.clear()
121
122def Selection(self) -> None:
123self.selection_flag = True
124# Custom fee model.
125class CustomFeeModel(FeeModel):
126def GetOrderFee(self, parameters: OrderFeeParameters) -> OrderFee:
127fee: float = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
128return OrderFee(CashAmount(fee, "USD"))