This study derives optimal trend-following rules using a two-state regime-switching model.
EMA is the optimal rule in a Markov model, while a MACD-like strategy is optimal in a semi-Markov model.
Empirical results confirm that the optimal rules outperform traditional 10-month SMA and 12-month momentum strategies in historical market data.
Opinion
Unlike previous studies that simply compare different trend-following strategies, this paper provides a theoretical basis for selecting the best strategy based on market conditions.
Markov models favor EMA because they assume fixed transition probabilities, making it optimal to gradually adjust to new price trends.
Semi-Markov models favor MACD-like rules, as market state durations affect trend strength, making it beneficial to combine short-term momentum and long-term mean reversion.
The empirical validation of these theoretical rules enhances their credibility, suggesting that practitioners can use them for more effective trend-following strategies.
Core Sell Point
This study provides a mathematical foundation for EMA and MACD-like rules as optimal trend-following strategies in regime-switching markets. Empirical tests confirm their superior performance compared to traditional SMA and momentum strategies.
A recent study, Optimal Trend Following Rules in Two-State Regime-Switching Models, analyzes trend-following investment strategies and provides a theoretical foundation for identifying optimal trading rules. Unlike previous research, which primarily focused on empirical backtesting of various trading rules, this paper derives the optimal trend-following strategy using a regime-switching framework with two market states: bull and bear markets.
Key findings include:
In a Markov Switching Model (MSM) with fixed transition probabilities, the Exponential Moving Average (EMA) rule is the optimal trend-following strategy.
In a semi-Markov Switching Model (ESMSM) where state durations influence transition probabilities, the optimal strategy resembles the Moving Average Convergence/Divergence (MACD) rule.
Empirical analysis confirms that the theoretically derived optimal rules outperform traditional 10-month Simple Moving Average (SMA) and 12-month momentum strategies in real-world data.
Methodology
Return Modeling: Uses a two-state regime-switching model to capture bull and bear market dynamics.
Markov vs. Semi-Markov Models:
Markov Model (MSM): Transition probabilities between states are fixed.
Semi-Markov Model (ESMSM): Transition probabilities depend on how long the market has remained in a given state.
Deriving the Optimal Trend-Following Rules: Theoretically derives the optimal trading strategy for each model using mathematical and numerical analysis.
Empirical Testing: Applies the optimal trading rules to international stock market data, including the U.S. and 16 other countries, and compares their performance with existing trend-following strategies.
Key Findings
1. Optimal Trend-Following Strategies Depend on the Market Model
Markov Model (MSM):
The Exponential Moving Average (EMA) rule is optimal.
EMA assigns exponentially decaying weights to past prices, allowing it to react efficiently to regime changes.
Semi-Markov Model (ESMSM):
The optimal rule resembles MACD (Moving Average Convergence/Divergence).
Like MACD, this rule incorporates both short-term momentum and long-term mean reversion, making it well-suited for markets where state duration affects trend strength.
2. Empirical Analysis: U.S. Market Performance
The study analyzes U.S. market data (1875–2020) and evaluates the performance of:
Results: The optimal rules consistently outperform traditional SMA and momentum-based strategies across different market regimes.
3. Global Market Performance
Using out-of-sample testing on 16 international stock markets, the study finds that:
Trend-following strategies outperform buy-and-hold in most markets.
The optimal rules derived from theory often outperform traditional SMA and momentum rules.
However, in some markets, SMA and momentum strategies perform better, suggesting market structure variations influence strategy effectiveness.
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