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Hello Ray,
Thank you for an article.
I just only want to make a comment that Hurst Exponent of .78 for
S&P-500 is true for monthly data and I came to this number also. But
for daily S&P-500 data it is much less, i.e. daily is less persistent.
It is likely due to short term noise in markets. And if you look at
monthly chart it is often looks more trending and smoother than
shorter time frames.
Best regards,
Alex mailto:alex_bell@xxxxxxx
Tuesday, August 13, 2002, 7:25:28 PM, you wrote:
RR> Hi all RT's,
RR> This is a copy of an article sent to me re. the relationship between Hurst and the VIX. Interesting reading.
RR> Good luck and good trading,
RR> Ray Raffurty
RR> H.E. Hurst became intrigued with the Nile River while a civil servant in Cairo in 1908. Actually, it was more like obsessed: His mathematically curious mind led him to examine 800 years of flood
RR> data on the Nile River basin. He was surprised when he noticed in the data that good flood years were generally followed by good flood years, and bad years begat more bad years.
RR> Hurst knew that he was onto something, so he dug in even deeper. In an effort to quantify and predict these flood characteristics for reservoir planning, Hurst developed his "Hurst exponent",
RR> which is an elegant and precise method of measuring whether or not there is persistence in a data series. Hurst noticed that most natural phenomenon that most thought were random -- like
RR> rainfall, flooding, sunspots, etc -- were actually persistent, and exhibited a "memory effect." In other words, what just happened had a tendency to influence what was about to happen.
RR> We all know from first-hand experience that financial markets are persistent in just this way. The old truism that "the trend is your friend" turns out to be exactly right. Studies on S&P 500
RR> historical data show it to have a Hurst Exponent of .78, which means it is highly persistent in its trends, and not random at all, as some misguided academics would argue. A Hurst Exponent of .50
RR> equates to random price movement.
RR> Interestingly, studies have also shown that this memory effect in the S&P 500 lasts about 48 months, after which this effect completely diminishes. This fits in well with the regular 4 year cycle
RR> in the markets.
RR> All markets show varying degrees of persistence. Currency markets are the most persistent. Futures traders know this very well, as currency markets often show amazing trendiness. This persistence
RR> of price is the main reason it's generally not a good idea to fight the trend, but much better to just "go with the flow."
RR> Interestingly, the rarest thing in financial markets is a trait that is anti-persistent -- that is, it tends to do exactly the opposite of whatever it just did. It doesn't trend. It oscillates.
RR> Volatility is anti-persistent, and this is why it's so useful.
RR> Volatility has a strong tendency to revert to the mean. A period of high volatility is followed by a period of low volatility. A period of low volatility is followed by a period of high
RR> volatility.
RR> Here's how this looks on the chart of the S&P 500:
RR> The VIX also moves back and forth, anti-persistently:
RR> This anti-persistence gives us a nice oscillatory path to anticipate for the VIX. A technical indicator is only valuable if you have a pretty good idea of what it is going to do in the future.
RR> With the VIX, we always know that its tendency will be to revert back to the mean, and do the opposite of what it just did.
RR> This also works so well because high volatility is very much associated with price bottoms, and low volatility with price tops. This is not a hard-and-fast rule, mind you, but it's definitely an
RR> idea that will make you money time and time again.
RR> So when we examine the motion of the VIX in real-time, we look for these anti-persistent, mean-reverting swings. It's a constant back-and-forth cycle on the VIX -- just as the market is
RR> constantly in a process of oscillating between advance phases and decline phases. Watching these oscillations lets us know exactly where we are with the market, in whatever time frame we want to
RR> examine.
RR> Since price is persistent and trendy, then often a "decline phase" as signaled by the VIX won't actually see prices decline, or an "advance phase" won't see prices go up. During the bear market,
RR> there were often short-term advance phases where the market actually declined in price. That's a sign of a very persistent downtrend, and a very weak market, by the way. Such divergences in price
RR> and sentiment are some of the most valuable clues that we can observe.
RR> There's obviously more to it than just this, but in a sense it's not necessarily beneficial to stray too far away from this picture of the markets I just outlined. Sentiment oscillates back and
RR> forth between fear and greed, and by closely studying the VIX and price we have a way to catalog and examine this.
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