bonds, equities · United States · bonds, ETFs, funds · Monthly · United States Free

Stock Trading Rule that Produces Higher Returns with Lower Risk

Academic paper

Paper linkhttps://papers.ssrn.com/sol3/papers.cfm?abstract_id=3949604

Strategy in a nutshell

The investment universe consists of the S&P 500 (via mutual funds or ETFs) and 3-month Treasury bills. The strategy involves selling the index at relative maxima and buying at relative minima. At the close of the last trading day each month, calculate the nine-month simple moving average (SMA) trend line and its first derivative.

Sell Signal: Triggered if the derivative is negative, the nine-month SMA slope ≤ tangent of 355°, the two-month SMA slope ≤ tangent of 353°, and either the S&P 500 opening or closing price is below the nine-month SMA. On the first trading day of the next month, close the S&P 500 position and invest in 3-month Treasury bills. This allocation remains for the following two months regardless of a new buy signal.

Buy Signal: Triggered if the derivative is positive and the nine-month SMA slope ≥ tangent of 5°. On the first trading day of the next month, close the bill position and buy the S&P 500. Allocation decisions are made monthly.

Economic rationale

The strategy is a risk-on/risk-off trend-following system, aiming to capture upward equity trends while switching to safe Treasury bills at market peaks. Conversely, it re-enters equities at market troughs. The underlying logic is not fully transparent, and the paper does not justify why it should work. There is a risk that the strategy is overfitted, so a thorough out-of-sample analysis is recommended to validate its effectiveness.

Backtest performance

Annualised return6.78%

Beta0.369

Sharpe ratio0.251

Sortino ratio0.189

Win rate96%

Full Python code

1from AlgorithmImports import *
2import math
3# endregion
4
5class StockTradingRuleThatProducesHigherReturnsWithLowerRisk(QCAlgorithm):
6
7def Initialize(self):
8self.SetStartDate(2000, 1, 1)
9self.SetCash(100000)
10
11self.curr_month:int = -1
12self.long_period:int = 9 * 21
13self.short_period:int = 2 * 21
14
15# market data
16security:Equity = self.AddEquity("SPY", Resolution.Minute)
17security.SetFeeModel(CustomFeeModel())
18security.SetLeverage(5)
19self.spy_symbol:Symbol = security.Symbol
20
21# bills data
22security:Equity = self.AddEquity("BIL", Resolution.Minute)
23security.SetFeeModel(CustomFeeModel())
24security.SetLeverage(5)
25self.bil_symbol:Symbol = security.Symbol
26
27# sma data objects
28self.long_SMA_data:SMAData = SMAData(self, self.spy_symbol, self.long_period)
29self.short_SMA_data:SMAData = SMAData(self, self.spy_symbol, self.short_period)
30
31self.SetWarmup(self.long_period, Resolution.Daily)
32
33# placing MOC orders is allowed 15,5 minutes before market close
34self.Schedule.On(self.DateRules.EveryDay(self.spy_symbol), self.TimeRules.BeforeMarketClose(self.spy_symbol, 16), self.EveryDayBeforeMarketClose)
35
36def EveryDayBeforeMarketClose(self):
37# update sma each day
38if self.long_SMA_data.sma_is_ready() and self.short_SMA_data.sma_is_ready():
39    # store sma values to internal list
40    self.long_SMA_data.update_values()
41    self.short_SMA_data.update_values()
42
43# wait until warmup is done and rebalance monthly
44if self.IsWarmingUp or (self.curr_month == self.Time.month):
45    return
46self.curr_month = self.Time.month
47
48# storage of SMA values is ready
49if self.long_SMA_data.is_ready() and self.short_SMA_data.is_ready():
50    long_SMA_slope:float = self.long_SMA_data.calc_slope()
51    short_SMA_slope:float = self.short_SMA_data.calc_slope()
52
53    long_SMA_value:float = self.long_SMA_data.SMA.Current.Value
54    short_SMA_value:float = self.short_SMA_data.SMA.Current.Value
55
56    # tangent
57    tan_353:float = math.tan(math.pi * (353 / 180))
58    tan_355:float = math.tan(math.pi * (355 / 180))
59    tan_5:float = math.tan(math.pi * (5 / 180))
60
61    # if the derivative is negative, the slope of the nine-month SMA is lower or equal to the tangent of 355°, the slope of the two-month SMA is lower or equal to the tangent of 353°
62    if long_SMA_slope < 0 and (long_SMA_slope <= tan_355) and (short_SMA_slope <= tan_353):
63        # s&p one day history
64        history = self.History(self.spy_symbol, 1, Resolution.Daily)
65        if history.empty:
66            return
67
68        close_price:float = history.loc[self.spy_symbol].close[0]
69        open_price:float = history.loc[self.spy_symbol].open[0]
70        
71        # either (or both) opening price of the S&P 500 or closing price of the S&P 500 is below the nine-month SMA
72        if (close_price < long_SMA_value) or (open_price < long_SMA_value):
73            # close S&P and buy BIL
74            if self.Portfolio[self.spy_symbol].Invested:
75                self.MarketOnCloseOrder(self.spy_symbol, -self.Portfolio[self.spy_symbol].Quantity)
76
77            if self.Securities.ContainsKey(self.bil_symbol) and self.Securities[self.bil_symbol].Price != 0:
78                q:int = int(self.Portfolio.MarginRemaining / self.Securities[self.bil_symbol].Price)
79                # q = self.CalculateOrderQuantity(self.bil_symbol, 1)
80                self.MarketOnCloseOrder(self.bil_symbol, q - self.Portfolio[self.bil_symbol].Quantity)
81    
82    # if the derivative is positive and the slope of the nine-month SMA is higher or equal to the tangent of 5°
83    elif long_SMA_slope > 0 and (long_SMA_slope >= tan_5):
84        # buy signal close BIL and buy S&P
85        if self.Portfolio[self.bil_symbol].Invested:
86            self.MarketOnCloseOrder(self.bil_symbol, -self.Portfolio[self.bil_symbol].Quantity)
87
88        # self.SetHoldings(self.spy_symbol, 1)
89        if self.Securities.ContainsKey(self.spy_symbol) and self.Securities[self.spy_symbol].Price != 0:
90            q:int = int(self.Portfolio.MarginRemaining / self.Securities[self.spy_symbol].Price)
91            # q = self.CalculateOrderQuantity(self.spy_symbol, 1)
92            self.MarketOnCloseOrder(self.spy_symbol, q - self.Portfolio[self.spy_symbol].Quantity)
93
94class SMAData:
95def __init__(self, algorithm:QCAlgorithm, symbol:Symbol, period:float) -> None:
96self.SMA_period:float = period
97self.SMA:SimpleMovingAverage = algorithm.SMA(symbol, period, Resolution.Daily)
98self.SMA_values:RollingWindow = RollingWindow[float](period)
99
100def update_values(self) -> None:
101self.SMA_values.Add(self.SMA.Current.Value)
102
103def sma_is_ready(self) -> bool:
104return self.SMA.IsReady
105
106def is_ready(self) -> bool:
107return self.SMA_values.IsReady
108
109def calc_slope(self) -> float:
110delta_SMA:float = self.SMA_values[0] - self.SMA_values[self.SMA_period-1]
111
112# return slope
113return delta_SMA / self.SMA_period
114
115# Custom fee model
116class CustomFeeModel(FeeModel):
117def GetOrderFee(self, parameters):
118fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
119return OrderFee(CashAmount(fee, "USD"))