## Online Annex 3.1. Identifying Idiosyncratic Jumps in Stock Returns

## Source details

**Canonical URL:** [Online Annex 3.1. Identifying Idiosyncratic Jumps in Stock Returns](https://www.imf.org/-/media/files/publications/gfsr/2024/october/english/ch3annex.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/gfsr/2024/october/english/ch3annex.pdf.md)
- [Structured JSON version](/-/media/files/publications/gfsr/2024/october/english/ch3annex.pdf.json)

---

### Methodology: thresholding technique and time-of-day adjustment
- Technique: thresholding technique initially proposed by Mancini (2001) and popularized by Bollerslev et al. (2013).  
- Core principle: compute a time-varying threshold and classify any intraday return whose absolute value exceeds this threshold as a jump.  
- Time-of-day (TOD) indicator: calculated for each stock following Bollerzev et al. (2013); accounts for U-shaped intraday volatility (higher at the beginning and end of the trading day).  
- Threshold construction: daily, time-varying thresholds computed using the bipower variation.  
- Alternative idiosyncratic-jump identification:
  - Technique 1: label a stock jump as idiosyncratic when it does not coincide with jumps in large, liquid passive ETFs tracking the S&P 500 index (SPY).  
  - Technique 2: regress each stock's returns against SPY returns; apply the thresholding technique to regression residuals to obtain idiosyncratic jumps.  
- Both idiosyncratic identification techniques yield similar results.

### Data and notable events
- Sample: intraday returns on selected dates between 2007 and 2024 for a sample of securities.  
- Example event: March 12, 2020 (“Black Thursday”) — thresholding technique identifies two jumps for SPY over that day.  
- TOD example: the TOD for the largest ETF tracking the S&P 500 index (SPY) reflects a typical U-shaped pattern.

### Definitions and measurement concepts
- Bipower variation: an empirical estimate of the integrated volatility of a financial asset over a period, excluding the effects of jumps.  
- Realized variation: an empirical estimate of the total variance of a financial asset over a period; captures both the continuous and jumps components of price movements.

### Key empirical findings and statistics
- Annual jump frequency (sample period 2007–2024):
  - Decreasing trend in jump frequency from approximately 0.9 percent for 2007 to 0.5 percent for 2024 (Online Annex Figure 3.1, panel 3, solid blue line).  
- Contribution of jumps to realized variation:
  - Jumps account for approximately 10 percent of realized variation (Online Annex Figure 3.1, panel 4, solid orange line).  
- Relative rarity and importance:
  - Less than 1 percent of price movements qualify as jumps, yet they account for a disproportionately significant share of realized variation.  
- Consistency across identification methods:
  - Results for overall jumps and idiosyncratic jumps produce similar frequency and variation-share patterns when using the two idiosyncratic identification techniques (panels 3 and 4, dotted and dashed lines).

### Implications for analysis of stock price dynamics
- Time-varying thresholds that incorporate intraday TOD patterns and bipower variation are effective for distinguishing jumps from continuous price movements.  
- Even though jumps are infrequent, their large contribution to realized variation makes them critical for understanding total volatility and tail events in asset returns.  
- Distinguishing systematic from idiosyncratic jumps can be implemented via (i) co-jump filtering with market ETFs (SPY) and (ii) residual-based thresholding after regression on SPY; both approaches yield comparable outcomes.

*Sources: Bloomberg Finance L.P.; and IMF staff calculations.*

---


_Source: https://www.imf.org/-/media/files/publications/gfsr/2024/october/english/ch3annex.pdf_