Financial Econometrics and Empirical Market Microstructure
S&P 500 (SPY) Case Study
On December 1 ’08 SPY fell 9.6 % (log return), the biggest daily drop since Black Monday in 1987.
Figure 14 shows a super-exponential increase in (Normal Distribution Implied) PStress leading up to the December 1, 2008 stress event. Note the log scale, so any increase above linear is super-exponential.
The following is noteworthy:
|
юс seal* |
 |
 |
1. On February 27, PStress jumped by 170x from extremely low levels. It was a Black Swan. PStress (i. e., equity market volatility) had no predictive power. However, the extremely low level of volatility/implied stress could be viewed
as a contrarian signal of high hidden risk and risk myopia/overconfldence as discussed earlier.
2. From that point on PStress spiked over 1300x, implying super-exponential increase of tail risk leading up to the December 1, 2008 drop. PStress picks up well escalating endogenous risk signals.
Figure 15 shows SPY DStress during the same time period. Pre-crisis, a drop of 9.6 % would have represented a distant —24 sd event. After the February 27 outlier DStress jumped to —10 sd, and then further contracted to —2 sd as we approach December 1, 2008. In other words, the actual drop of 9.6 % on 1 December was not much of a surprise by then.
|
Early warning 27 Feb *07 |
 |
 |
 |
 |
stress S&P 500 DStress vs Daily Returns calibrated to -9.6% scenario loss % price change
o4» & У # & & jy ол £ o' $ o* & & jP & & o°* # jS> <£ - si
У/ V У У j? УУ V v* У у Уу У У У У у У У У У У У
Fig. 15 S&P 500 DStress
|
Systemic risk broadly converges and declines from early *09, |
 |
 |
 |
 |
PStress for major asset classes in bps, log scale
FebO/ equity risk jump especially financials
Fig. 16 PStress for major asset classes
