Volatility clustering is the tendency for large return changes to follow large changes, while small changes follow small changes. It matters because historical variances and covariances can miss current volatility conditions. section 3.2.2 section 3.3
The 1987 crash
The S&P 500 fell approximately 20% on October 19, 1987. The following trading days included moves of about +5%, +9%, −4%, 0%, and −8%, illustrating that unusually large changes persisted after the crash. section 3.2.2
A practical test uses the autocorrelation of squared returns, Corr(r²t−1, r²t). For the S&P 500, the measured autocorrelation is 0.2228, with a standard error of 0.0106 and a t-statistic of 21.03, providing strong evidence of clustering. section 3.2.2
Volatility clustering also supports forecasting and crisis interpretation:
- Volatility can spike during crises and later return toward its earlier level; VIX implied volatility rose to about 80% during the 2008 crisis and later declined to 21%. section 3.2.2
- A GARCH model can forecast future volatility from return data; a 63-day AAPL forecast produces a volatility estimate of 0.4810 after annualization. section 3.2.2
Table 3.9 S&P500 returns around the stock market crash of 1987
| Date | Close | % Change |
| 1987-10-08 | 314.160004 | -1.375025 |
| 1987-10-09 | 311.070007 | -0.983574 |
| 1987-10-12 | 309.390015 | -0.540069 |
| 1987-10-13 | 314.519989 | 1.658093 |
| 1987-10-14 | 305.230011 | -2.9537 |
| 1987-10-15 | 298.079987 | -2.342504 |
| 1987-10-16 | 282.700012 | -5.15968 |
| 1987-10-19 | 224.839996 | -20.466931 |
| 1987-10-20 | 236.830002 | 5.332684 |
| 1987-10-21 | 258.380005 | 9.099355 |
| 1987-10-22 | 248.250000 | -3.920584 |
| 1987-10-23 | 248.220001 | -0.012084 |
| 1987-10-26 | 227.669998 | -8.278947 |
| 1987-10-27 | 233.190002 | 2.424564 |
| 1987-10-28 | 233.279999 | 0.038594 |
| 1987-10-29 | 244.770004 | 4.925414 |
| 1987-10-30 | 251.789993 | 2.867994 |
Browse the S&P 500 return table to inspect the crash and the unusually large movements that followed it. section 3.2.2
