Hurst Exponent Patterns Across Different Asset Classes

The Hurst exponent varies systematically across asset classes. Equities behave differently from bonds, which behave differently from currencies or commodities. Understanding these patterns helps calibrate expectations, select appropriate strategies, and identify when a particular market is behaving abnormally relative to its typical character.

Equity Markets

Developed market equity indices typically show:

• Typical H range: 0.52-0.60
• Character: Mild persistence, trending tendency
• Time variation: H rises during strong trends, falls during corrections

Individual stocks often show higher Hurst values than indices. Small-cap stocks tend to show more persistence than large-caps. Emerging market equities frequently show higher H (0.55-0.70) than developed markets.

The persistence in equities likely reflects momentum effects—a combination of information diffusion, behavioral factors, and institutional flows that create trend continuation.

Fixed Income

Government bond markets typically show:

• Typical H range: 0.48-0.55
• Character: Near random walk to mild persistence
• Variation: Lower H during stable policy, higher during regime changes

The relatively low Hurst values in bonds reflect the anchoring effect of central bank policy. Interest rates are managed instruments, not pure market prices, which constrains their range of motion. Corporate bonds show more persistence than governments, reflecting credit risk dynamics.

Foreign Exchange

Major currency pairs typically show:

• Typical H range: 0.48-0.55
• Character: Near random walk, occasional trends
• Variation: Higher H during central bank divergence, lower during stability

FX markets are among the most liquid and efficiently arbitraged, contributing to their near-random walk character. However, persistent interest rate differentials and macro trends can create extended periods of trending (higher H).

Emerging market currencies often show higher persistence than majors, reflecting less arbitrage activity and stronger directional flows.

Commodities

Commodities show the widest variation:

• Typical H range: 0.50-0.75 (highly variable)
• Energy: Often H 0.55-0.65 (supply/demand trends)
• Precious metals: Often H 0.55-0.70 (monetary/safe haven flows)
• Agricultural: Variable, influenced by weather cycles and seasons

The high persistence in some commodities reflects fundamental supply/demand imbalances that take time to resolve. A drought affecting wheat takes multiple growing seasons to correct, creating persistent price trends.

Cryptocurrencies

Digital assets typically show:

• Typical H range: 0.55-0.80
• Character: High persistence, strong trends
• Variation: Extremely time-varying, regime-dependent

Cryptocurrencies exhibit some of the highest Hurst values among liquid markets. This reflects narrative-driven adoption cycles, limited institutional arbitrage (historically), and strong reflexivity. As markets mature and institutional participation increases, H may trend toward more conventional levels.

Real Estate and Alternatives

Alternative assets show distinct patterns:

• REITs: H often 0.55-0.65, reflecting real estate cycles
• Private equity indices: Artificially smooth (appraisal-based), unreliable H
• Hedge fund indices: Variable, depends on strategy composition

Be cautious with infrequently-priced assets. Appraisal-based values create artificial smoothness that distorts Hurst estimates.

Summary Table

Cross-Asset Applications

Understanding cross-asset Hurst patterns enables several applications:

Strategy allocation: Deploy trend-following in high-H asset classes; mean-reversion in low-H classes.

Anomaly detection: If bonds suddenly show H = 0.70, something unusual is happening (perhaps a policy regime change).

Diversification: Assets with different Hurst characteristics may diversify well across different regimes.

Risk management: Multi-period risk in high-H assets is higher than standard models suggest.

Temporal Variation Within Classes

Within each asset class, H varies over time:

• Crisis periods often show different H than calm periods
• Policy regime changes affect persistence
• Market structure evolution changes typical H over decades

The ranges provided are historical generalizations, not guarantees of future behavior. Monitor rolling Hurst estimates to track current conditions.

Conclusion

Different asset classes exhibit systematically different Hurst characteristics. Equities tend to show mild persistence; bonds and FX are closer to random walks; commodities and crypto show higher persistence. These patterns reflect underlying market dynamics—information diffusion, arbitrage efficiency, supply/demand fundamentals, and participant behavior. Understanding these cross-asset patterns calibrates expectations and informs strategy selection.