# Hybrid Binomial Z-Score Quantitative Strategy

Author: ChaoZhang, Date: 2024-05-28 17:38:08
Tags: SMABB

#### Overview

This strategy employs a hybrid quantitative analysis approach, combining binomial distribution model and regression analysis, to identify different market regimes. The strategy first calculates the Simple Moving Average (SMA) and Bollinger Bands (BB) indicators, then computes the Z-score based on the mean and standard deviation of historical returns. When the Z-score is below the lower threshold and the price is below the lower band, the strategy enters a long position; when the Z-score is above the upper threshold and the price is above the upper band, the strategy closes the position.

#### Strategy Principle

The core principle of this strategy is to use the Z-score to measure the position of current returns relative to the distribution of historical returns. The formula for calculating the Z-score is: (Current Return - Historical Return Mean) / Historical Return Standard Deviation. A higher Z-score indicates that the current return is more extreme and the probability of overbought is higher; a lower Z-score indicates that the current return is more extreme and the probability of oversold is higher. At the same time, the strategy also incorporates the Bollinger Bands indicator, using price breakouts above or below the bands as a secondary confirmation. The strategy generates trading signals only when both the Z-score and Bollinger Bands conditions are met simultaneously. This combination approach can effectively reduce the occurrence of false signals.

1. Quantitative Analysis: The strategy is entirely based on quantitative indicators, with clear rules that are easy to implement and backtest.
2. Dual Confirmation: The strategy employs both the Z-score and Bollinger Bands indicators, forming a dual filtering mechanism to improve signal accuracy.
3. Statistical Foundation: The Z-score originates from the normal distribution theory in statistics, with a solid theoretical foundation, and can objectively measure the extremity of current returns.
4. Parameter Flexibility: Users can adjust parameters such as the SMA period, Bollinger Bands multiplier, and Z-score thresholds according to their needs, flexibly adapting to different markets.

#### Strategy Risks

1. Parameter Sensitivity: Different parameter settings may lead to significant differences in strategy performance, requiring extensive parameter optimization and stability testing.
2. Trend Risk: When the market exhibits strong trends, the Z-score may remain in extreme regions for an extended period, resulting in infrequent or completely absent strategy signals.
3. Overfitting Risk: If the strategy parameters are over-optimized, it may lead to overfitting and poor out-of-sample performance.
4. Black Swan Risk: Under extreme market conditions, historical statistical patterns may fail, exposing the strategy to significant drawdown risks.

#### Strategy Optimization Directions

1. Dynamic Parameters: Consider dynamically adjusting the Z-score thresholds and Bollinger Bands multiplier based on indicators such as market volatility and trend strength to improve adaptability.
2. Trend Filtering: Overlay trend determination indicators, such as MA crossover or DMI, on top of the existing mechanism to avoid excessive invalid signals during strong trends.
3. Portfolio Optimization: Combine this strategy with other quantitative strategies (such as momentum, mean reversion, etc.) to leverage their respective strengths and improve robustness.
4. Stop-Loss and Take-Profit: Introduce reasonable stop-loss and take-profit mechanisms to control risk exposure per trade and improve risk-adjusted returns.

#### Summary

The Hybrid Binomial Z-Score Quantitative Strategy is a quantitative trading strategy based on statistical principles, identifying potential overbought and oversold opportunities by comparing current returns with the distribution of historical returns. Additionally, the strategy employs the Bollinger Bands indicator for secondary confirmation, enhancing signal reliability. The strategy rules are clear and easy to implement and optimize, but it also faces challenges such as parameter sensitivity, trend risk, overfitting risk, etc. In the future, the strategy can be optimized in terms of dynamic parameters, trend filtering, portfolio optimization, stop-loss and take-profit mechanisms, etc., to improve its adaptability and robustness. Overall, this strategy provides a simple yet effective approach for quantitative trading, worthy of further exploration and refinement.

```/*backtest
start: 2023-05-22 00:00:00
end: 2024-05-27 00:00:00
period: 1d
basePeriod: 1h
exchanges: [{"eid":"Futures_Binance","currency":"BTC_USDT"}]
*/

//@version=5
strategy("Estratégia Híbrida Quantitativa", overlay=true)

// Definição de parâmetros
sma_length = input.int(20, title="Período da SMA")
threshold_high = input.float(1.5, title="Threshold Alto")
threshold_low = input.float(-1.5, title="Threshold Baixo")
lookback_period = input.int(252, title="Período de Retorno Histórico (dias)")

// Funções auxiliares
f_sma(source, length) =>
ta.sma(source, length)

f_bollinger_band(source, length, mult) =>
basis = ta.sma(source, length)
dev = mult * ta.stdev(source, length)
[basis + dev, basis - dev]

sma = f_sma(close, sma_length)
[upper_band, lower_band] = f_bollinger_band(close, sma_length, 2)

retornos = ta.change(close, 1)
media_retornos = ta.sma(retornos, lookback_period)

z_score = (retornos - media_retornos) / desvio_padrao_retornos

// Sinal de Compra e Venda
sinal_compra = z_score < threshold_low and close < lower_band
sinal_venda = z_score > threshold_high and close > upper_band

// Execução de Ordem
if (sinal_compra)
strategy.entry("Long", strategy.long)
if (sinal_venda)
strategy.close("Long")