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:

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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

Fig. 14 S&P 500 PStress

image219as 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.

10 DStress

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

Подпись: (2S> image221 image222 image223

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,

Подпись: lOY -17%

image225 image226 image227 image228

image229PStress for major asset classes in bps, log scale

FebO/ equity risk jump especially financials

Fig. 16 PStress for major asset classes

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