Equity · United States · ETFs, stocks · Monthly · United States Free

Timing the Small Cap Effect ver. 3

Academic paper

Realized Semibetas: Signs of Things to Come

AuthorsTim Bollerslev; Andrew J. Patton; Rogier Quaedvlieg

Institute

Duke University
National Bureau of Economic Research
?Duke University - Department of Economics
?Duke University - Finance
?National Bureau of Economic Research (NBER)
DEEuropean Central Bank
?European Central Bank (ECB)

Paper linkhttps://ssrn.com/abstract=3528276

Strategy in a nutshell

After high-volatility months, go long small-cap and short large-cap stocks or ETFs; hold for 6 months, adjusting monthly based on volatility.

Economic rationale

Small-cap stocks earn higher returns after high-risk periods due to greater exposure to volatility, default, and illiquidity risks.

Backtest performance

Annualised return5.42%

Volatility7.81%

Beta0.094

Sharpe ratio0.69

Sortino ratio-0.095

Win rate52%

Full Python code

1import numpy as np
2from AlgorithmImports import *
3
4class TimingtheSmallCapEffect(QCAlgorithm):
5
6def Initialize(self):
7self.SetStartDate(2000, 1, 1)
8self.SetCash(100000)
9
10self.period = 21
11self.SetWarmUp(self.period, Resolution.DAILY)
12
13self.market = self.AddEquity('SPY', Resolution.Daily).Symbol
14self.data = RollingWindow[float](self.period)   # spy history
15self.historical_volatility = []
16self.min_vol_history_period = 12
17self.was_high_risk_month = False
18
19self.trade_month_count = 0
20
21data = self.AddEquity("DIA", Resolution.Daily)
22data.SetLeverage(5)
23self.large_cap = data.Symbol
24
25data = self.AddEquity("IWM", Resolution.Daily)
26data.SetLeverage(5)
27self.small_cap = data.Symbol
28
29self.Schedule.On(self.DateRules.MonthEnd(self.market), self.TimeRules.BeforeMarketClose(self.market), self.Rebalance)
30
31def OnData(self, data):
32# store market prices
33if self.market in data and data[self.market]:
34    price = data[self.market].Value
35    self.data.Add(price)
36
37def Rebalance(self):
38if self.IsWarmingUp: return
39if not self.data.IsReady: return
40
41if self.time.year == 2023 and self.time.month == 8:
42    foo=3
43
44self.trade_month_count += 1
45if self.trade_month_count == 6:
46    self.trade_month_count = 0
47    self.Liquidate()
48
49if self.was_high_risk_month:
50    self.was_high_risk_month = False
51    self.trade_month_count = 0
52
53    # One month after high risk month.
54    self.SetHoldings(self.small_cap, 1)
55    self.SetHoldings(self.large_cap, -1)            
56
57market_prices = np.array([x for x in self.data])
58market_returns = market_prices[:-1] / market_prices[1:] - 1
59market_volatility = np.std(market_returns) * np.sqrt(252)
60
61self.historical_volatility.append(market_volatility)
62if len(self.historical_volatility) >= self.min_vol_history_period:
63    top_quintile = np.percentile(self.historical_volatility[1:], 80)
64    
65    if market_volatility > top_quintile:
66        # one month lag
67        self.was_high_risk_month = True