“该策略涉及根据大型股距离其52周高点和最大月度回报的接近程度进行排序，然后做多低NH和低MAX的股票，做空高MAX的股票。”
资产类别: 股票 | 地区: 美国 | 周期: 每月 | 市场: 股票 | 关键词: 彩票
I. 策略概要
投资范围包括在纽约证券交易所、美国证券交易所或纳斯达克上市的普通股，股票代码为10或11，不包括股价低于5美元的股票。股票被分为三个市值组，其中最大组占前30%，且仅使用最大组。这些股票根据其与52周高点的接近程度（NH）和一个月内的最大日回报（MAX）进行双重排序。MAX计算为该月最高的日回报，NH是当前股价与52周高点的比率。在最低NH五分位中，采用一种策略，即做空MAX五分位最高的股票，做多MAX五分位最低的股票。该策略采用等权重，并每月重新平衡。
II. 策略合理性
过去的研究表明，投资者会高估具有正偏度的股票，特别是那些具有彩票特征的股票，因为他们被极端正回报的潜力所吸引。然而，接近52周高点的股票并未表现出这种异常现象，因为投资者将52周高点视为一个心理障碍，认为价格不会超过该水平。这种认知导致投资者对接近52周高点的彩票型股票缺乏兴趣。相反，远离52周高点的股票往往具有更强的彩票相关异常，因为投资者预期价格上涨并高估极端正回报的可能性。这种偏好在机构持股比例较低的股票中更为强烈，因为散户投资者更容易受到行为偏差的影响。该策略适用于各种股票特征，包括流动性、规模和价格，使其稳健且不限于非流动性、小盘股或低价股。
III. 来源论文
The Role of Psychological Barriers in Lottery-Related Anomalies [点击查看论文]
边锡俊（Byun, Suk-Joon），韩国科学技术院（KAIST）金融工程专业；高志勋（Goh, Jihoon），韩国科学技术院（KAIST）商学院
<摘要>
先前的研究发现，具有彩票特征的股票被高估。我们表明，由投资者彩票偏好引起的异常现象主要存在于远离其52周高价的股票中。结果表明，如果股票接近其52周高点，投资者不再偏好彩票股票，因为他们将52周高点视为心理障碍或价格上限。我们发现，彩票相关异常与接近52周高点之间的依赖性在机构持股比例较低的股票中尤为明显。套利限制和资本利得等替代解释无法解释我们的结果。
IV. 回测表现
| 年化回报 | 18.58% |
| 波动率 | 19.25% |
| β值 | 0.438 |
| 夏普比率 | 0.76 |
| 索提诺比率 | -0.278 |
| 最大回撤 | N/A |
| 胜率 | 47% |
V. 完整的 Python 代码
import numpy as np
from AlgorithmImports import *
from typing import List, Dict
class LotteryStocks52WeekHigh(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2010, 1, 1)
self.SetCash(100000)
self.exchange_codes: List[str] = ['NYS', 'NAS', 'ASE']
self.period: int = 52 * 5
self.month_period: int = 21
self.leverage: int = 10
self.min_share_price: int = 5
self.quantile: int = 10
self.data: Dict[Symbol, RollingWindow] = {}
self.long: List[Symbol] = []
self.short: List[Symbol] = []
market: Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
self.fundamental_count: int = 1_000
self.fundamental_sorting_key = lambda x: x.DollarVolume
self.selection_flag: bool = True
self.settings.daily_precise_end_time = False
self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse(self.FundamentalSelectionFunction)
self.Schedule.On(self.DateRules.MonthStart(market), self.TimeRules.AfterMarketOpen(market), self.Selection)
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:
self.data[symbol].Add(stock.AdjustedPrice)
if not self.selection_flag:
return Universe.Unchanged
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]]
MAX: Dict[Symbol, float] = {}
NH: Dict[Symbol, float] = {}
for stock in selected:
symbol: Symbol = stock.Symbol
# warmup price rolling windows
if symbol not in self.data:
self.data[symbol] = RollingWindow[float](self.period)
history:dataframe = self.History(symbol, self.period, Resolution.Daily)
if history.empty:
self.Log(f"Not enough data for {symbol} yet")
continue
closes:Series = history.loc[symbol].close
for time, close in closes.items():
self.data[symbol].Add(close)
if not self.data[symbol].IsReady:
continue
closes: List[float] = list(self.data[symbol])
last_month_closes: np.ndarray = np.array(closes[:self.month_period])
last_close: float = closes[0]
daily_returns: np.ndarray = (last_month_closes[:-1] - last_month_closes[1:]) / last_month_closes[1:]
MAX[symbol] = max(daily_returns)
# NH calc
if last_close != 0:
local_highest_close: float = max(closes)
NH[symbol] = last_close / local_highest_close
if len(MAX) < self.quantile or len(NH) < self.quantile:
return Universe.Unchanged
# NH sorting
sorted_by_NH: List[Tuple[Symbol, float]] = sorted(NH.items(), key = lambda x: x[1], reverse = True)
quintile:int = int(len(sorted_by_NH) / self.quantile)
low_NH: List[Symbol] = [x[0] for x in sorted_by_NH[-quintile:]]
# MAX sorting
sorted_by_MAX: List[Tuple[Symbol, float]] = sorted(low_NH, key = lambda x: MAX[x], reverse = True)
quintile: int = int(len(sorted_by_MAX) / self.quantile)
self.long = [x for x in sorted_by_MAX[:quintile]]
self.short = [x for x in sorted_by_MAX[-quintile:]]
return self.long + self.short
def OnData(self, slice: Slice) -> None:
if not self.selection_flag:
return
self.selection_flag = False
# Trade execution
targets:List[PortfolioTarget] = []
for i, portfolio in enumerate([self.long, self.short]):
for symbol in portfolio:
if symbol in slice and slice[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 CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))