Option Trading and Returns versus the 52-Week High
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Option Trading and Returns versus the 52-Week High and Low
Siu Kai Choy; Jason Zhanshun Wei
- King's College London
- CAUniversity of Toronto
- ?University of Toronto - Rotman School of Management
Strategy in a nutshell
The investment universe consists of all stocks from the CRSP database and their underlying options contracts. First, apply the following screening procedure to the options universe and retain only those which meet the following criteria: trading volume is non-zero, maturity is between 30 and 60 days (i.e., only options maturing in the month following the next), moneyness (defined as the exercise price over the stock price) is in the range of (0.8, 1.2), the bid quote and bid-ask spread are positive, and the percentage bid-ask spread (i.e., bid-ask spread divided by the midpoint) is less than 100%. Second, on the last trading day of each month, calculate the price-to-high (PTH) ratio for each stock, defined as the stock price divided by its 52-week high. Third, sort the stocks into quintiles based on their PTH ratio, where the highest quintile consists of the highest PTH stocks, and the lowest quintile consists of the lowest PTH stocks. Fourth, for each stock in the highest quintile, buy one call option and delta-hedge in the next month with daily rebalancing. Conversely, for each stock in the lowest quintile, sell one call option and delta-hedge in the next month with daily rebalancing. Invest/borrow the net balance at the risk-free rate. Positions are value-weighted based on the dollar value of open interest and rebalanced monthly.
Economic rationale
Driessen, Lin, and Van Hemert (2012) found that the implied volatility in both call and put options decreases when the stock price approaches the 52-week extremes, which indicates anchoring-induced sluggish incorporation of news into stock prices. Consequently, this downward-biased volatility forecast leads to the undervaluation of both calls and puts when the stock price is at its 52-week high and low. However, the demand-pressure theory of Garleanu, Pedersen, and Poteshman (2009) implies mispricing of calls and puts in the opposite direction. More specifically, calls (puts) become undervalued and puts (calls) overvalued when the stock price approaches its 52-week high (low). The demand-pressure effect and the volatility effect reinforce each other for calls (puts) when the stock price approaches its 52-week high (low), but they offset each other for calls (puts) when the stock price approaches its 52-week low (high). Translating prices into returns, when the stock price approaches its 52-week high (low), the subsequent delta-hedged returns are unambiguously higher for calls (puts).
Backtest performance
Full Python code
from AlgorithmImports import *
import data_tools
# endregion
class OptionTradingandReturnsversusthe52WeekHigh(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2010, 1, 1)
self.SetCash(100000)
self.leverage:int = 5
self.quantile:int = 5
self.portfolio_percentage:float = 1
self.high_period:int = 52 * 5
self.exchanges:list[str] = ['NYS', 'NAS', 'ASE']
self.data:dict[Symbol, data_tools.SymbolData] = {}
self.selected_symbols:list[Symbol] = []
self.highest_PTH:List[Symbol] = []
self.lowest_PTH:List[Symbol] = []
self.market_symbol:Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
# options storage
self.min_expiry:int = 30
self.max_expiry:int = 60
self.subscribed_contracts:dict = {} # subscribed option universe
self.coarse_count:int = 500
self.selection_flag:bool = False
self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse(self.CoarseSelectionFunction)
self.SetSecurityInitializer(lambda x: x.SetDataNormalizationMode(DataNormalizationMode.Raw))
self.UniverseSettings.DataNormalizationMode = DataNormalizationMode.Raw
self.Schedule.On(self.DateRules.MonthStart(self.market_symbol), self.TimeRules.BeforeMarketClose(self.market_symbol, 0), self.Selection)
def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
for security in changes.AddedSecurities:
security.SetFeeModel(data_tools.CustomFeeModel())
security.SetLeverage(self.leverage)
symbol:Symbol = security.Symbol
if symbol not in self.data:
self.data[symbol] = data_tools.SymbolData(self.high_period)
for security in changes.RemovedSecurities:
symbol:Symbol = security.Symbol
if symbol in self.data:
del self.data[symbol]
def CoarseSelectionFunction(self, coarse:List[CoarseFundamental]) -> List[Symbol]:
if not self.selection_flag:
return Universe.Unchanged
selected:list = sorted([x for x in coarse if x.HasFundamentalData and x.Market == 'usa' and x.Price > 5],
key=lambda x: x.DollarVolume, reverse=True)[:self.coarse_count]
self.selected_symbols = list(map(lambda stock: stock.Symbol, selected))
return self.selected_symbols
def OnData(self, data:Slice) -> None:
if self.highest_PTH and self.lowest_PTH:
oi_by_symbol:dict[Symobl, float] = {}
# for each stock in the highest quintile, buy one call option and delta-hedge in the next month with daily rebalancing. Conversely, for each stock in the lowest quintile, sell one call option and delta-hedge in the next month.
if self.subscribed_contracts:
# store OI values
if data.OptionChains.Count != 0:
for kvp in data.OptionChains:
contract = list(kvp.Value)[0]
symbol:Symbol = contract.UnderlyingSymbol
open_interest:float = contract.OpenInterest
if open_interest != 0:
oi_by_symbol[symbol] = open_interest
# trade options and hedge
total_oi:float = sum([oi_by_symbol[x] for x in self.highest_PTH if x in oi_by_symbol])
for symbol in self.highest_PTH:
if symbol in data and data[symbol]:
if symbol in self.subscribed_contracts:
if symbol in oi_by_symbol:
price:float = data[symbol].Value
weight:float = oi_by_symbol[symbol] / total_oi
equity:float = self.Portfolio.TotalPortfolioValue * weight
options_q:int = int(equity / (price * 100))
self.Buy(self.subscribed_contracts[symbol], options_q)
total_oi:float = sum([oi_by_symbol[x] for x in self.lowest_PTH if x in oi_by_symbol])
for symbol in self.lowest_PTH:
if symbol in data and data[symbol]:
if symbol in self.subscribed_contracts:
if symbol in oi_by_symbol:
price:float = data[symbol].Value
weight:float = oi_by_symbol[symbol] / total_oi
equity:float = self.Portfolio.TotalPortfolioValue * weight
options_q:int = int(equity / (price * 100))
self.Sell(self.subscribed_contracts[symbol], options_q)
self.subscribed_contracts.clear()
self.highest_PTH.clear()
self.lowest_PTH.clear()
# store daily prices
for symbol in self.selected_symbols:
if symbol in self.data:
if symbol in data and data[symbol] and data[symbol].High != 0 and data[symbol].Value != 0:
price:float = data[symbol].Value
high:float = data[symbol].High
self.data[symbol].update(price, high)
# rebalance monthly
if not self.selection_flag:
return
self.selection_flag = False
# calculate PTH
PTH:dict[Symbol, float] = { symbol : self.data[symbol].PTH() for symbol in self.selected_symbols if symbol in self.data and self.data[symbol].PTH_data_ready() }
if len(PTH) < self.quantile:
self.Liquidate()
return
# sorting
quantile:int = int(len(PTH) / self.quantile)
sorted_by_PTH:List[Symbol] = [x[0] for x in sorted(PTH.items(), key=lambda item: item[1])]
self.highest_PTH = sorted_by_PTH[-quantile:]
self.lowest_PTH = sorted_by_PTH[:quantile]
for symbol in self.highest_PTH + self.lowest_PTH:
if symbol in data and data[symbol]:
# get all contracts for current stock symbol
contracts:List = self.OptionChainProvider.GetOptionContractList(symbol, self.Time)
# get current price for stock
underlying_price:float = data[symbol].Value
# get strikes from commodity future contracts
strikes:List[float] = [c.ID.StrikePrice for c in contracts]
# can't filter contracts, if there isn't any strike price
if len(strikes) <= 0 or underlying_price == 0:
continue
atm_strike:float = min(strikes, key=lambda x: abs(x-underlying_price))
# filter calls contracts with one month expiry
atm_calls:List = [ contract for contract in contracts if self.min_expiry < (contract.ID.Date - self.Time).days < self.max_expiry and contract.ID.OptionRight == OptionRight.Call and contract.ID.StrikePrice == atm_strike ]
# make sure, there is at least one call contract
if len(atm_calls) > 0:
# sort by expiry
atm_call = sorted(atm_calls, key = lambda x: x.ID.Date, reverse=True)[0]
atm_call_subscriptions = self.SubscriptionManager.SubscriptionDataConfigService.GetSubscriptionDataConfigs(atm_call.Underlying)
# check if stock's call contract was successfully subscribed
if atm_call_subscriptions:
# add contract
option = self.AddOptionContract(atm_call, Resolution.Daily)
option.PriceModel = OptionPriceModels.CrankNicolsonFD()
# store contracts by stock's symbol
self.subscribed_contracts[symbol] = atm_call
def Selection(self) -> None:
self.selection_flag = True
self.Liquidate()