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A Mean Reverting Stock Market With Increasing Risk

The daily returns of the S&P 500 exhibit mean-reverting behavior since the late 1990s but the index reached new all-time highs recently. I show in this article that this has been accomplished at increasing risk, despite beliefs that volatility is low. In other words, new highs have come at higher risk.

Many technical analysts and quants are infatuated with VIX when in reality that volatility index has no predictive power and follows the inverse of S&P 500 price in a non-liner fashion, as I have shown in previous articles. In fact, anyone trading ETFs based on VIX is playing with fire since this index has a power law distribution with unknown expectation and variance. As a result, trading strategies involving VIX and its various ETFs have unknown expectation and variance. When someone finds out, it is always too late but ETF providers are happy to make the management fees.

In addition to the statistical uncertainty, VIX is not predictive of future price volatility despite claims by both technical analysts and some academics that involve data-mining bias and conclusions based on limited samples. Causality between VIX and S&P 500 is “stretched”, in the sense that it does not exist. The non-linear behavior of VIX near all time highs, with the low values, has created a false sense that one can forecast future moves by forecasting volatility. As already mentioned, due to the power law distribution of VIX, expectation and variance are unknown: there is no way of forecasting anything.

How has a mean-reverting stock market after the late 1990s been able to climb to new highs even after two major bear markets in 2001-2003 and 2008? While this phenomenon unfolds, risks in the market are slowly but steadily rising. In other words, new highs have been accomplished at increasing risk despite accounts based on VIX that this has occurred at low risk.

The daily S&P 500 chart below shows the 0-lag autocorrelation of log returns, the number of returns greater that +1% and the standard deviation of long returns for rolling periods of 1000 days.

Below are some observations from the above chart:

  1. The autocorrelation of daily log returns peaked in the early 1970s and then declined steadily. After about 1998, negative autocorrelation increased to significant levels (horizontal lower line.) Since about August 2015, the autocorrelation as returned in neutral territory.
  2. As autocorrelation decreased from highly positive (momentum) to highly negative (mean-reversion), the number of returns greater that +1% in a rolling 1000-day period increased steadily, as shown in the second indicator pane of the above chart. This is the price action mechanism that has enabled the market to reach new highs. In essence, low positive or negative returns are now more frequently followed +1% surges than in the past and that facilitate development of uptrends.
  3. While autocorrelation decreased (first pane) and number of +1% returns increased, the standard deviation also increased, as shown in the third pane. Note that all three peaked near the bottom of the dot com bear market and after the 2011 correction. In fact, risk rose while the market was recovering from severe stress after the dot com crash and the financial crisis.

The conclusion is that despite what VIX allegedly shows, risks are increasing in the market because of a need of occasional bursts to maintain the uptrend. These bursts are followed by mean-reversion and this process repeats. When this feedback mechanism will fail, and it will at some point, a downtrend will start. However, the timing of this failure is unknown. But the statement that the “fear index” (VIX) decreases at higher risk is more accurate based on empirical evidence. In other words, fear decreases while risk rises. Is this a paradox? Probably it is.

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Charting and backtesting program: Amibroker


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