Overview
The Logarithmic Price Mean Reversion Dynamic Stop-Loss Strategy is a quantitative trading approach based on statistical principles, leveraging the tendency of prices to oscillate around their mean. This strategy converts prices into logarithmic form and calculates Z-scores (standard deviation multiples) to measure price deviation from the mean. When the Z-score reaches specific thresholds, the strategy identifies overbought or oversold conditions and executes trades based on the expectation that prices will revert to their mean. What sets this strategy apart is its dynamic stop-loss mechanism, which automatically adjusts stop-loss levels according to changes in market volatility, enhancing risk management efficiency.

Strategy Principles
The core principles of this strategy are based on mean reversion theory and the statistical properties of logarithmic prices. The implementation follows these steps:

1. First, the strategy converts closing prices into logarithmic form (log_price = math.log(close)), which helps transform multiplicative changes into additive changes, making price movements more normally distributed.

2. Then, based on a defined rolling window (default 7 periods), it calculates the moving average (rolling_mean) and standard deviation (rolling_std) of the logarithmic prices.

3. Using these statistics, it calculates the current Z-score of the logarithmic price: rolling_z_score = (log_price - rolling_mean) / rolling_std, which represents how many standard deviations the current price is away from the mean.

4. Entry conditions are set as follows:

When the Z-score falls below the long entry threshold (default -1.825), a long position is opened.
When the Z-score rises above the short entry threshold (default 1.825), a short position is opened.

1. The take-profit target is set at the exponential form of the moving average of logarithmic price: take_profit_price = math.exp(rolling_mean), meaning the strategy aims for price to revert to its statistical mean.

2. The dynamic stop-loss mechanism is the key innovation of this strategy:

Initial stop-loss positions are set based on the Z-score and volatility at entry.
As market volatility changes, stop-loss positions are dynamically adjusted:
When volatility increases, long stop-losses decrease and short stop-losses increase, providing more trading room.
When volatility decreases, long stop-losses increase and short stop-losses decrease, protecting existing profits.

1. Exit logic includes two scenarios:

Price reaches the take-profit level (reverts to the mean).
Price hits the dynamically adjusted stop-loss level.

Strategy Advantages

1. Statistical Foundation: The strategy is based on solid statistical principles, using Z-scores to measure price deviation, providing objective entry and exit signals.

2. Logarithmic Price Transformation: Using logarithmic prices instead of raw prices makes price movements more normally distributed, improving the effectiveness of statistical indicators.

3. Dynamic Risk Management: The strategy's standout feature is its dynamic stop-loss mechanism, which automatically adjusts stop-loss levels based on changes in market volatility, protecting capital while allowing sufficient trading room.

4. Bidirectional Trading: The strategy supports both long and short trades, enabling opportunity seeking in various market environments.

5. Mean as Target: Using the statistical mean as a take-profit target aligns with mean reversion theory, enhancing the rationality of profit-taking.

6. Adjustable Parameters: The strategy offers multiple adjustable parameters, including rolling window, entry Z-scores, and stop-loss Z-scores, allowing traders to adapt to different markets and personal risk preferences.

Strategy Risks

1. Mean Reversion Assumption Risk: The core assumption that prices will revert to their statistical mean may fail in trending markets or during structural changes, leading to sustained losses. Solution: Add trend filters to pause trading in strong trend markets.

2. Overly Sensitive Z-scores: In extremely low volatility markets, even small price movements can generate large Z-score changes, triggering unnecessary trading signals. Solution: Set minimum volatility thresholds or adjust entry thresholds in low volatility environments.

3. Window Length Sensitivity: Strategy performance is highly sensitive to the rolling window length parameter; inappropriate choices may lead to overtrading or missed opportunities. Solution: Find optimal parameters through backtesting different window lengths or use adaptive window lengths.

4. Data Shortage Risk: In the early stages of trading, lack of sufficient historical data to calculate moving averages and standard deviations may lead to unstable signals. Solution: Ensure an adequate warm-up period before calculating indicators.

5. Stop-Loss Adjustment Strategy Risk: While innovative, the dynamic stop-loss mechanism may lead to excessive stop-loss adjustments during rapid volatility changes. Solution: Set maximum adjustment limits to prevent over-adjustment.

Strategy Optimization Directions

1. Adaptive Window Length: The current strategy uses a fixed rolling window length (default 7 periods) to calculate statistical indicators. Consider implementing an adaptive window length that automatically adjusts based on market cyclicality. This can better capture mean reversion opportunities at different time scales, improving strategy adaptability.

2. Trend Filter: Incorporate trend determination mechanisms to pause or adjust strategy parameters in strong trend markets, applying mean reversion strategy only in ranging or reversal markets. This can be implemented by adding long-term moving averages or trend indicators like ADX, avoiding frequent losses in one-sided trend markets.

3. Multi-timeframe Analysis: Integrate Z-score signals from multiple timeframes for more comprehensive entry and exit decisions. For example, confirm mean reversion opportunities in larger timeframes, then seek precise entry points in smaller timeframes, improving win rates and risk-reward ratios.

4. Take-profit Optimization: The current strategy uses a simple mean as the take-profit target. Consider implementing dynamic take-profit mechanisms, such as setting targets based on market structure or risk-reward ratios associated with stop-losses, or implementing partial take-profit strategies to progressively lock in profits as price moves favorably.

5. Volatility Weighting: Consider incorporating volatility weighting when calculating Z-scores, giving higher weight to data from more stable periods. This can reduce the interference of extreme volatility on signal generation, improving signal quality.

6. Machine Learning Integration: Consider introducing machine learning algorithms to optimize entry and exit thresholds. Models can be trained on historical data to predict optimal Z-score thresholds and dynamic stop-loss parameters, enhancing the strategy's adaptability and overall performance.

Conclusion
The Logarithmic Price Mean Reversion Dynamic Stop-Loss Strategy is a quantitative trading approach based on statistical principles, identifying market overbought and oversold conditions through logarithmic price Z-scores and profiting when prices are expected to revert to their mean. The core innovation lies in its dynamic stop-loss mechanism, which automatically adjusts risk parameters based on market volatility changes, providing superior risk management.

While based on solid statistical foundations, the strategy still faces challenges such as potential failure of the mean reversion assumption, parameter sensitivity, and market environment adaptability. By incorporating trend filters, adaptive window lengths, multi-timeframe analysis, and machine learning optimizations, the strategy has the potential to achieve more stable performance across various market environments.

It's worth noting that any quantitative strategy requires thorough backtesting and forward validation, with parameter adjustments based on specific market characteristics and personal risk preferences. This strategy provides a framework that integrates statistical principles and dynamic risk management, which traders can further customize and optimize.

Strategy source code

/*backtest
start: 2024-03-14 00:00:00
end: 2025-03-12 08:00:00
period: 1d
basePeriod: 1d
exchanges: [{"eid":"Futures_Binance","currency":"BTC_USDT"}]
*/

//@version=5
strategy("Mean Reversion Z-Score Strategy with Dynamic SL", overlay=true)

// Input parameters
window = input.int(7, "Rolling Window", minval=1)
z_entry_long = input.float(-1.825, "Z-Score Long Entry", step=0.025)
z_entry_short = input.float(1.825, "Z-Score Short Entry", step=0.025)
z_stop_loss_long = input.float(-2.125, "Z-Score Stop Loss Long", step=0.025)
z_stop_loss_short = input.float(2.125, "Z-Score Stop Loss Short", step=0.025)

// Calculate log price, rolling mean, and rolling standard deviation
log_price = math.log(close)
rolling_mean = ta.sma(log_price, window)
rolling_std = ta.stdev(log_price, window)
rolling_z_score = (log_price - rolling_mean) / rolling_std

// Persistent variables to store entry conditions
var float entry_price = 0.0
var float entry_log_price = 0.0
var float entry_mean = 0.0
var float entry_std = 0.0
var float stop_loss_price = 0.0
var string position = "none"

// Calculate dynamic take-profit
take_profit_price = math.exp(rolling_mean)

// Entry logic
if (rolling_z_score <= z_entry_long and position == "none")
    entry_price := close
    entry_log_price := log_price
    entry_mean := rolling_mean
    entry_std := rolling_std
    stop_loss_price := math.exp(log_price + z_stop_loss_long * rolling_std)
    position := "long"
    strategy.entry("Long", strategy.long)

if (rolling_z_score >= z_entry_short and position == "none")
    entry_price := close
    entry_log_price := log_price
    entry_mean := rolling_mean
    entry_std := rolling_std
    stop_loss_price := math.exp(log_price - z_stop_loss_short * rolling_std)
    position := "short"
    strategy.entry("Short", strategy.short)

// Exit logic with dynamic adjustments
if (position != "none")
    // Calculate new stop-loss based on current volatility
    float new_stop_loss = na
    if (position == "long")
        new_stop_loss := math.exp(log_price + z_stop_loss_long * rolling_std)
        if (rolling_std > entry_std)
            stop_loss_price := math.min(stop_loss_price, new_stop_loss)
        else if (rolling_std < entry_std)
            stop_loss_price := math.max(stop_loss_price, new_stop_loss)
        if (close >= take_profit_price)
            strategy.close("Long", comment="TP")
            position := "none"
        else if (close <= stop_loss_price)
            strategy.close("Long", comment="SL")
            position := "none"
    else if (position == "short")
        new_stop_loss := math.exp(log_price - z_stop_loss_short * rolling_std)
        if (rolling_std > entry_std)
            stop_loss_price := math.max(stop_loss_price, new_stop_loss)
        else if (rolling_std < entry_std)
            stop_loss_price := math.min(stop_loss_price, new_stop_loss)
        if (close <= take_profit_price)
            strategy.close("Short", comment="TP")
            position := "none"
        else if (close >= stop_loss_price)
            strategy.close("Short", comment="SL")
            position := "none"

// Plots
plot(rolling_z_score, title="Z-Score", color=color.blue, linewidth=1)
plot(z_entry_short, title="Z-Score-upper", color=color.rgb(33, 243, 103), linewidth=1)
plot(z_entry_long, title="Z-Score-lower", color=color.rgb(243, 33, 61), linewidth=1)

Strategy parameters

The original address: Logarithmic Price Mean Reversion Dynamic Stop-Loss Strategy