
Fig. 7 analyses the VIX index by fitting it with our simple log-periodic
formula. The VIX index is one of the world's most popular measures
of investors' expectations about future stock market volatility
(that is, risk). See http://www.cboe.com/micro/vixvxn/introduction.asp.
For historical data, see http://www.cboe.com/micro/vixvxn/specifications.asp.
The VIX time series is shown as the red wiggly curve. We have followed
the same procedure as for figures 4-6: (i) we fit the real VIX
data with our simple log-periodic formula; (ii) we then generate
10 synthetic time series by adding white noise to the fit; (iii)
we redo a fit of each of the 10 synthetic time series by the simple
log-periodic formula and thus obtain the bundle of 10 predictions
shown as the magenta lines. Strikingly, we first observe that our
log-periodic formula is able to account quite well for the behavior
of the VIX index, strengthening the evidence that the market is
presently in a strong herding (anti-bubble) phase. Note also the
rather good stability of the predictions, suggesting a reasonable
reliability. Last, note that the VIX is predicted to continue to
decrease (smaller expected risks) well in the regime when the price
have started their descent, with a bottom in the last quarter of
2003. The VIX is expected to turn up and increase significanly
only later in 2004. This dephasing of the log-periodic fits of
the S&P500 and of the VIX is reminiscent of the well-known
stock market proverb: "Bear markets decline on a slope of
hope".
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