“BAB策略涉及做多低贝塔股票，做空高贝塔股票，投资组合每月重新平衡。使用过去的收益来预测波动率，目标波动率为12%。”
资产类别: 股票 | 地区: 美国 | 周期: 每月 | 市场: 股票 | 关键词: 择时、贝塔
I. 策略概要
BAB（反贝塔）策略涉及基于低贝塔和高贝塔股票构建投资组合，遵循Frazini和Pedersen的原则。买入低贝塔股票，卖空高贝塔股票。证券按其贝塔值排名，投资组合由贝塔值低于或高于中位数的股票组成。BAB投资组合是自筹资金的零贝塔投资组合，需要短期国库券的空头头寸来平衡投资组合。投资组合中的证券按其贝塔值加权。过去21天的已实现波动率用于预测未来波动率，并调整回报以维持12%的目标波动率。投资组合每月重新平衡，根据上个月的波动率调整其权重。该策略旨在通过瞄准稳定的波动率水平来利用风险回报权衡。
II. 策略合理性
将BAB的风险分解为市场风险和特定风险的学术论文发现，可预测的部分是特定的风险。此外，仅按特定风险调整的策略的业绩与使用总风险调整的策略非常相似。因此，学术论文得出结论，特定风险是风险管理收益的来源。
III. 来源论文
Managing the risk of the “betting-against-beta” anomaly: does it pay to bet against beta? [点击查看论文]
- Barroso, Maio
<摘要>
我们研究了反贝塔异常的风险动态。该策略显示出风险的强烈且可预测的时间变化，并且没有风险回报权衡。利用这一点的风险管理策略实现了1.28的年化夏普比率，相对于原始策略，信息比率高达0.94。市场、规模、价值、盈利能力和投资因素的类似策略平均仅实现了0.15的较低信息比率。风险调整带来的巨大经济效益与动量策略相似，并将这两个异常与其他股票因素区分开来。将风险分解为市场和特定成分，我们发现特定成分驱动了我们的结果。
IV. 回测表现
| 年化回报 | 22.35% |
| 波动率 | 16.99% |
| β值 | 0.782 |
| 夏普比率 | 1.32 |
| 索提诺比率 | 0.187 |
| 最大回撤 | -66.14% |
| 胜率 | 49% |
V. 完整的 Python 代码
from AlgorithmImports import *
import numpy as np
from math import sqrt
import pandas as pd
from scipy import stats
from typing import Dict, List
class TimingBettingAgainstBetaAnomaly(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
self.exchange_codes:List[str] = ['NYS']
# Daily price data.
self.data:Dict[Symbol, RollingWindow] = {}
self.period:int = 21
self.leverage:int = 10
self.min_share_price:int = 5
# Warmup market daily data.
self.symbol:Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
self.data[self.symbol] = RollingWindow[float](self.period)
history:dataframe = self.History(self.symbol, self.period, Resolution.Daily)
if history.empty:
self.Log(f"Not enough data for {self.symbol} yet")
else:
closes:Series = history.loc[self.symbol].close
for time, close in closes.items():
self.data[self.symbol].Add(close)
self.target_volatility:float = 0.12
self.weight:Dict[Symbol, float] = {}
self.fundamental_sorting_key = lambda x: x.DollarVolume
self.fundamental_count:int = 250
self.selection_flag = 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:
security.SetFeeModel(CustomFeeModel())
security.SetLeverage(self.leverage)
def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
# Update the rolling window every day.
for stock in fundamental:
symbol:Symbol = stock.Symbol
if symbol in self.data:
# Store daily price.
self.data[symbol].Add(stock.AdjustedPrice)
# Selection once a month.
if not self.selection_flag:
return Universe.Unchanged
# selected = [x.Symbol for x in fundamental if x.HasFundamentalData and x.Market == 'usa']
selected:List[Fundamental] = [
x for x in fundamental if x.HasFundamentalData and x.Price > self.min_share_price and x.Market == 'usa' \
and x.MarketCap != 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]]
# Warmup price rolling windows.
for stock in selected:
symbol:Symbol = stock.Symbol
if symbol not in self.data:
self.data[symbol] = RollingWindow[float](self.period)
history = self.History(symbol, self.period, Resolution.Daily)
if history.empty:
self.Log(f"Not enough data for {symbol} yet")
continue
closes = history.loc[symbol].close
for time, close in closes.items():
self.data[symbol].Add(close)
if not self.data[self.symbol].IsReady:
return Universe.Unchanged
market_returns:List[float] = []
market_closes:np.ndarray = np.array([x for x in self.data[self.symbol]])
market_returns = (market_closes[:-1] - market_closes[1:]) / market_closes[1:]
beta:Dict[Symbol, float] = {}
for stock in selected:
symbol:Symbol = stock.Symbol
# Data is ready.
if self.data[symbol].IsReady and len(market_returns) != 0:
stock_closes:np.ndarray = np.array([x for x in self.data[symbol]])
stock_returns:np.ndarray = (stock_closes[:-1] - stock_closes[1:]) / stock_closes[1:]
# cov = np.cov(market_returns, stock_returns)[0][1]
# market_variance = np.std(market_returns) ** 2
# beta[symbol] = cov / market_variance
slope, intercept, r_value, p_value, std_err = stats.linregress(market_returns, stock_returns)
beta[symbol] = slope
# Beta diff calc.
beta_median:float = np.median([x[1] for x in beta.items()])
long_diff:List[Tuple[Symbol, float]] = [(x[0], x[1] - beta_median) for x in beta.items() if x[1] >= beta_median]
short_diff:List[Tuple[Symbol, float]] = [(x[0], beta_median - x[1]) for x in beta.items() if x[1] < beta_median]
# Beta diff weighting.
for i, portfolio in enumerate([long_diff, short_diff]):
total_diff:float = sum(list(map(lambda x: x[1], portfolio)))
for symbol, diff in portfolio:
self.weight[symbol] = ((-1)**i) * diff / total_diff
return [x[0] for x in self.weight.items()]
def OnData(self, data: Slice) -> None:
# Market daily data is stored in fundamental.
if not self.selection_flag:
return
self.selection_flag = False
# Portfolio volatility calc.
df:dataframe = pd.dataframe()
weights:List[float] = []
for symbol, w in self.weight.items():
df[str(symbol)] = [x for x in self.data[symbol]]
weights.append(w)
weights = np.array(weights)
daily_returns:dataframe = df.pct_change()
portfolio_vol:flaot = np.sqrt(np.dot(weights.T, np.dot(daily_returns.cov() * 21, weights.T)))
leverage:float = self.target_volatility / portfolio_vol
# trade execution
portfolio:List[PortfolioTarget] = [PortfolioTarget(symbol, w * leverage) for symbol, w in self.weight.items() if symbol in data and data[symbol]]
self.SetHoldings(portfolio, True)
self.weight.clear()
def Selection(self) -> None:
self.selection_flag = True
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))