“该策略涉及使用琼斯模型估算应计项目，并根据可自由支配的应计项目将公司分为四分位数。该策略做多低动量公司，做空高动量公司。”
资产类别: 股票 | 地区: 美国 | 周期: 每年 | 市场: 股票 | 关键词: 应计项目、动量
I. 策略概要
投资范围包括纽约证券交易所、美国证券交易所和纳斯达克所有上市的普通股。该策略涉及使用琼斯模型估算总应计项目，然后计算非自由支配和自由支配应计项目。公司每年根据自由支配应计项目分为四分位数。应计项目动量低的（连续四年处于最低四分位数）公司被归类为低动量，而应计项目动量高的（连续四年处于最高四分位数）公司被归类为高动量。该策略做多应计项目动量低的公司，做空应计项目动量高的公司。
II. 策略合理性
该论文指出，源自可自由支配应计项目的应计项目动量提供了超出近期应计项目的市场相关额外信息，投资者对此有所反应。对应计项目动量与未来股票回报之间的负相关关系提出了两种解释。第一种解释认为，应计项目动量预示着高盈余管理，表明未来盈余将反转并导致较低的回报。第二种解释将其视为增长的替代指标，与众所周知的增长异象相关。分析结果（使用市净率、资产和员工增长等增长替代指标）发现，应计项目动量与盈余操纵相关，而非公司增长。进一步的测试证实，高应计项目动量与随后的回报之间存在稳健的负相关关系，这提供了超出可自由支配应计项目的额外信息。研究还表明，盈余动量在反映盈余管理方面不能替代应计项目动量。最后，结果在不同子样本中保持一致，并且不受监管变化的影响，这表明市场对应计项目动量高的反应不受披露政策变化的影响。
III. 来源论文
Accruals Momentum [点击查看论文]
- Hao, Xiaoting (郝晓婷) 和 Jang, Juwon (张柱元) 和 Lee, Eunju (李恩珠). 威斯康星大学密尔沃基分校 – 谢尔登·B·卢巴商学院；德克萨斯A&M大学；马萨诸塞大学洛厄尔分校。
<摘要>
我们研究了高应计项目动量的信息含量，其定义为连续四年高自由裁量应计项目。我们发现，持续报告高水平自由裁量应计项目的公司，其随后的回报较低。在控制了高应计项目动量估计期内的年度自由裁量应计项目水平后，结果依然稳健。此外，即使现有应计项目异常现象消失后，高应计项目动量对未来回报的预测能力仍然非常持久。我们的结果还表明，高应计项目动量对低增长公司的影响更为显著，这表明高应计项目动量股票的定价过高是由管理层操纵盈利的自由裁量权驱动的。
IV. 回测表现
| 年化回报 | 9.94% |
| 波动率 | 11.1% |
| β值 | -0.057 |
| 夏普比率 | 0.54 |
| 索提诺比率 | -0.014 |
| 最大回撤 | N/A |
| 胜率 | 52% |
V. 完整的 Python 代码
from AlgorithmImports import *
from collections import deque
import numpy as np
import statsmodels.api as sm
from typing import List, Dict, Deque, Tuple
from numpy import isnan
class AccrualsMomentum(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
self.exchange_codes:List[str] = ['NYS', 'NAS', 'ASE']
# Latest accruals data.
self.accruals_data:Dict[Symbol, StockData] = {}
self.min_share_price:int = 5
self.period:int = 5
self.leverage:int = 15
self.quantile:int = 4
# Accruals value for last year.
self.latest_accruals:Dict[Symbol, StockData] = {}
self.fundamental_count:int = 1000
self.fundamental_sorting_key = lambda x: x.DollarVolume
self.long:List[Symbol] = []
self.short:List[Symbol] = []
self.consecutive_period:int = 4
self.low_residual_portfolios:Deque = deque(maxlen = self.consecutive_period)
self.high_residual_portfolios:Deque = deque(maxlen = self.consecutive_period)
self.symbol:Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
self.regression_period:int = 5
self.regression_data:Dict[Symbol, Tuple[float]] = {}
self.months:int = 12
self.selection_flag:bool = False
self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse(self.FundamentalSelectionFunction)
self.Schedule.On(self.DateRules.MonthEnd(self.symbol), self.TimeRules.AfterMarketOpen(self.symbol), self.Selection)
self.settings.daily_precise_end_time = False
def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
for security in changes.AddedSecurities:
symbol = security.Symbol
security.SetFeeModel(CustomFeeModel())
security.SetLeverage(self.leverage)
self.regression_data[symbol] = deque(maxlen = self.regression_period)
def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
if not self.selection_flag:
return Universe.Unchanged
selected:List[Fundamental] = [
x for x in fundamental if x.HasFundamentalData and x.Market == 'usa' and x.Price >= self.min_share_price \
and not isnan(x.FinancialStatements.BalanceSheet.CurrentAssets.Value) and x.FinancialStatements.BalanceSheet.CurrentAssets.Value > 0 \
and not isnan(x.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value) and x.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value > 0 \
and not isnan(x.FinancialStatements.BalanceSheet.CurrentLiabilities.Value) and x.FinancialStatements.BalanceSheet.CurrentLiabilities.Value > 0 \
and not isnan(x.FinancialStatements.BalanceSheet.CurrentDebt.Value) and x.FinancialStatements.BalanceSheet.CurrentDebt.Value > 0 \
and not isnan(x.FinancialStatements.IncomeStatement.DepreciationAndAmortization.Value) and x.FinancialStatements.IncomeStatement.DepreciationAndAmortization.Value > 0 \
and not isnan(x.FinancialStatements.BalanceSheet.GrossPPE.Value) and x.FinancialStatements.BalanceSheet.GrossPPE.Value > 0 \
and not isnan(x.FinancialStatements.IncomeStatement.TotalRevenueAsReported.Value) and x.FinancialStatements.IncomeStatement.TotalRevenueAsReported.Value > 0 \
and x.SecurityReference.ExchangeId in self.exchange_codes
]
if len(selected) > self.fundamental_count:
selected = [x for x in sorted(selected, key=self.fundamental_sorting_key, reverse=True)[:self.fundamental_count]]
updated:List[Symbol] = []
residual:Dict[Symbol, float] = {}
for stock in selected:
symbol:Symbol = stock.Symbol
if symbol not in self.accruals_data:
# Data for previous year.
self.accruals_data[symbol] = None
if symbol not in self.latest_accruals:
# Previous year's accruals.
self.latest_accruals[symbol] = None
# Accrual calc.
current_accruals_data:StockData = StockData(stock.FinancialStatements.BalanceSheet.CurrentAssets.Value, stock.FinancialStatements.BalanceSheet.CashAndCashEquivalents.Value,
stock.FinancialStatements.BalanceSheet.CurrentLiabilities.Value, stock.FinancialStatements.BalanceSheet.CurrentDebt.Value, stock.FinancialStatements.BalanceSheet.IncomeTaxPayable.Value,
stock.FinancialStatements.IncomeStatement.DepreciationAndAmortization.Value, stock.FinancialStatements.BalanceSheet.TotalAssets.Value,
stock.FinancialStatements.IncomeStatement.TotalRevenueAsReported.Value)
# There is not previous accruals data.
if not self.accruals_data[symbol]:
self.accruals_data[symbol] = current_accruals_data
updated.append(symbol)
continue
current_accruals:float = self.CalculateAccruals(current_accruals_data, self.accruals_data[symbol])
delta_sales:float = (current_accruals_data.Sales - self.accruals_data[symbol].Sales) / self.accruals_data[symbol].TotalAssets
ppe:float = stock.FinancialStatements.BalanceSheet.GrossPPE.Value / self.accruals_data[symbol].TotalAssets
# There is not previous accruals value.
if not self.latest_accruals[symbol]:
self.latest_accruals[symbol] = current_accruals
updated.append(symbol)
continue
# Regression data.
accruals_factor:float = 1 / self.latest_accruals[symbol]
reg_data:Tuple[float] = (current_accruals, accruals_factor, delta_sales, ppe)
if symbol not in self.regression_data:
self.regression_data[symbol] = deque(maxlen = self.regression_period)
self.regression_data[symbol].append(reg_data)
if len(self.regression_data[symbol]) == self.regression_data[symbol].maxlen:
total_accruals:List[float] = [x[0] for x in self.regression_data[symbol]]
accruals_factors:List[float] = [x[1] for x in self.regression_data[symbol]]
sales_deltas:List[float] = [x[2] for x in self.regression_data[symbol]]
ppes:List[float] = [x[3] for x in self.regression_data[symbol]]
# Regression.
x:List[List[float]] = [accruals_factors, sales_deltas, ppes]
regression_model = MultipleLinearRegression(x, total_accruals)
# x = [accruals_factors[:-1], sales_deltas[:-1], ppes[:-1]]
# regression_model = MultipleLinearRegression(x, total_accruals[1:])
alpha:float = regression_model.params[0]
residual[symbol] = alpha
# Update accruals data and value.
self.accruals_data[symbol] = current_accruals_data
self.latest_accruals[symbol] = current_accruals
updated.append(symbol)
# Make sure we ahve consecutive accruals data.
symbols_to_remove:List[Symbol] = []
for symbol in self.accruals_data:
if symbol not in updated:
symbols_to_remove.append(symbol)
for symbol in symbols_to_remove:
del self.accruals_data[symbol]
del self.latest_accruals[symbol]
sorted_by_residual:List[Tuple[Symbol, float]] = sorted(residual.items(), key = lambda x : x[1], reverse = True)
quartile:int = int(len(sorted_by_residual) / self.quantile)
high_by_residual:List[Symbol] = [x[0] for x in sorted_by_residual[:quartile]]
low_by_residual:List[Symbol] = [x[0] for x in sorted_by_residual[-quartile:]]
self.high_residual_portfolios.append(high_by_residual)
self.low_residual_portfolios.append(low_by_residual)
if len(self.high_residual_portfolios) == self.high_residual_portfolios.maxlen and len(self.low_residual_portfolios) == self.low_residual_portfolios.maxlen:
self.long = [x[0] for x in residual.items() if x[0] in self.high_residual_portfolios[0] and x[0] in self.high_residual_portfolios[1]
and x[0] in self.high_residual_portfolios[2] and x[0] in self.high_residual_portfolios[3]]
self.short = [x[0] for x in residual.items() if x[0] in self.low_residual_portfolios[0] and x[0] in self.low_residual_portfolios[1]
and x[0] in self.low_residual_portfolios[2] and x[0] in self.low_residual_portfolios[3]]
return self.long + self.short
# Source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3188172
def CalculateAccruals(self, current_accrual_data, prev_accrual_data) -> float:
delta_assets:float = current_accrual_data.CurrentAssets - prev_accrual_data.CurrentAssets
delta_cash:float = current_accrual_data.CashAndCashEquivalents - prev_accrual_data.CashAndCashEquivalents
delta_liabilities:float = current_accrual_data.CurrentLiabilities - prev_accrual_data.CurrentLiabilities
delta_debt:float = current_accrual_data.CurrentDebt - prev_accrual_data.CurrentDebt
dep:float = current_accrual_data.DepreciationAndAmortization
total_assets_prev_year:float = prev_accrual_data.TotalAssets
acc:float = (delta_assets - delta_liabilities - delta_cash + delta_debt - dep) / total_assets_prev_year
return acc
def OnData(self, data: Slice) -> None:
if not self.selection_flag:
return
self.selection_flag = False
# order execution
targets:List[PortfolioTarget] = []
for i, portfolio in enumerate([self.long, self.short]):
for symbol in portfolio:
if symbol in data and data[symbol]:
targets.append(PortfolioTarget(symbol, ((-1) ** i) / len(portfolio)))
self.SetHoldings(targets, True)
self.long.clear()
self.short.clear()
def Selection(self) -> None:
self.selection_flag = True
class StockData():
def __init__(self, current_assets:float, cash_and_cash_equivalents:float, current_liabilities:float, current_debt:float, income_tax_payable:float,
depreciation_and_amortization:float, total_assets:float, sales:float):
self.CurrentAssets:float = current_assets
self.CashAndCashEquivalents:float = cash_and_cash_equivalents
self.CurrentLiabilities:float = current_liabilities
self.CurrentDebt:float = current_debt
self.IncomeTaxPayable:float = income_tax_payable
self.DepreciationAndAmortization:float = depreciation_and_amortization
self.TotalAssets:float = total_assets
self.Sales:float = sales
def MultipleLinearRegression(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"))