Why might the "four-year cycle theory" be wrong? Using Bayes' theorem to calculate market risk at the end of 2025.

This analysis challenges the reliability of the "four-year cycle theory" for predicting market risk due to its small sample size. Using Bayesian probability, it calculates the likelihood of a bear market occurring in late 2025 to early 2026.

Core Argument: Conclusions based on only three complete four-year cycles are statistically unreliable. Bayesian methods offer a more robust alternative.
Bayesian Calculation: Estimates a 13.2% probability of a bear market given a stagflation-to-recession scenario, based on historical data.
Key Probabilities:
- Prior probability of a bear market: ~18%
- Probability of stagflation leading to recession: ~45%
- Probability of stagflation→recession during a bear market: ~33%
Final Risk Assessment: The overall probability of a bear market in 25Q4-26Q1 is estimated at 15-20%, with a range of 12% (optimistic) to 25% (pessimistic).
Recommended Strategy: Advocates for tactical defense rather than a full strategic retreat, emphasizing preparedness without overreaction.

Author: NingNing

By 2025, we had experienced less than four complete four-year cycles. However, basic statistical knowledge tells us that any conclusions drawn from extremely small statistical sample sizes (only three valid data points) require careful verification, rather than simple blind faith.

In predicting large market cycles with small samples, the Bayesian probability method for deriving the correlation between 25Q4 and 19Q4 is more valuable than the four-year cycle theory.

The 25Q4 criterion for 19Q4 can be converted into Bayesian formula notation: P(Bear Market | Merrill Lynch Clock Stagflation) = [P(Bear Market) / P(Merrill Lynch Clock Stagflation)] * (P(Merrill Lynch Clock Stagflation | Bear Market))

Bayesian probability parameter estimation

P (Bear Market) - Prior Probability

Since 1929: The S&P 500 has experienced 27 bear markets.

Average frequency: once every 3.5 years

Annual probability: Approximately 28.6%

Quarterly probability (Q4-Q1 span): Approximately 15-20%

Conservative estimate: P (bear market) ≈ 18%

P(Stagflation → Recession) - Merrill Lynch Clock Transition Probability

Historical probability of transition from stagflation to recession:

The stagflation of the 1970s ultimately led to three recessions in 1973-74, 1980, and 1981-82.

2000-2001: The bursting of the tech bubble and a mild recession

2007-2008: Financial crisis, deep recession

2011-2012: European debt crisis, not fully recovered (avoided)

2018-2019: Trade war concerns, successful soft landing

Statistical estimation:

There have been approximately six "stagflation → recession" scenarios in the past 50 years.

Four of them turned into a recession (66%).

Two soft landings (34%)

Current environment adjustments:

The Federal Reserve actively cut interest rates (vs. passively raised interest rates in the 1970s).

Labor market resilience (vs. 2008 financial systemic risk)

Tariff policy uncertainty

Global pressure to de-dollarize

Estimated: P(stagflation → recession) ≈ 40-50% (median 45%)

P(Stagflation → Recession | Bear Market) - Likelihood Probability

Under the condition of a bear market, the probability of experiencing "stagflation → recession":

Historical bear market classification:

Recession-type bear markets (12 times): 1929, 1937, 1973-74, 1980, 1981-82, 1990, 2000-02, 2007-09, 2020, 2022

Non-recessionary bear markets (15 times): Other technical corrections

In 12 recession-type bear markets:

Periods that experienced stagflation: 1973-74, 1980, 1981-82, 2007-08 (approximately 4 times).

Those that did not experience stagflation: 1929 (deflation), 2020 (pandemic impact), 2022 (pure inflation).

Estimated: P(Stagflation → Recession | Bear Market) ≈ 33%

Bayesian computation

Standard formula:

P(Bear Market | Stagflation → Recession) = P(Stagflation → Recession | Bear Market) × P(Bear Market) / P(Stagflation → Recession)

= 0.33 × 0.18 / 0.45

= 0.0594 / 0.45

= 0.132 = 13.2%

Scenario Analysis Matrix

Key Difference Analysis: Why is the probability low?

Overall Conclusion

P(25Q4-26Q1 Bear Market) ≈ 15-20%

Confidence interval:

Lower limit (optimistic): 12%

Median (benchmark): 17%

Upper limit (pessimistic): 25%

Strategy

Tactical defense is needed, not strategic retreat.