Summary  
Implementing percentage-based threshold classification on sequential data to identify and label different event types (e.g., corrections, bear markets, bull markets) and computing summary statistics for each category.

General domain of usage  
Financial market analysis

Financial media throws around "bull market," "bear market," and "correction" constantly – often interchangeably. They aren't the same thing, and confusing them leads to bad decisions.

Each term has a specific, widely accepted definition based on price movement from a recent peak or trough:

Corrections are common – the S&P 500 experiences one roughly every 1–2 years on average. Bear markets are rarer but far more painful. Bull markets are longer than bear markets historically, which is why long-term investors tend to come out ahead.

## The Numbers Behind the Labels

Definitions matter less than the underlying data. Since 1950, the S&P 500 has experienced:

- **27 corrections** of −10% or more;
- **13 bear markets** of −20% or more;
- Average bear market decline: **−36%**;
- Average bear market duration: **~14 months**;
- Average bull market gain: **+180%**;
- Average bull market duration: **~60 months**.

Bull markets last roughly four times longer than bear markets and produce far larger gains than bear markets erase. This asymmetry is the core argument for staying invested rather than trying to time your exit.

A **bear market** is a decline of 20% or more from a recent peak, typically accompanied by widespread pessimism and economic contraction. A **bull market** is a rise of 20% or more from a recent trough, typically accompanied by economic expansion and investor optimism. A **correction** is a decline of 10–20% – a normal, frequent reset that does not qualify as a bear market.

Definition

These thresholds are conventions, not laws. A market that drops 19.9% is not fundamentally different from one that drops 20.1% – but only one gets labeled a bear market. The labels are useful for communication and historical comparison, not for making buy or sell decisions.

Note

The S&P 500 drops 18% from its recent peak over three months. How should this be classified?

Historically, which statement best describes the relationship between bull and bear markets in the S&P 500?

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Bull vs Bear vs Correction

The Numbers Behind the Labels

1. The S&P 500 drops 18% from its recent peak over three months. How should this be classified?

2. Historically, which statement best describes the relationship between bull and bear markets in the S&P 500?