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Initial Conclusions/Theories Regarding Run Frequency

September 21, 2009

1) The market is operating in compressed time: runs are getting shorter as information flow is accessible more rapidly, commissions are lower, and participants react and synthesize information faster. High frequency, program, and algorithmic trading makes up most of the trading volume. This is what is responsible for what is perceived as mean-reversion: runs rarely last more than 3 days . Imagine a roulette wheel that rarely if even landed on red more than 3 times in a row—it would be very easy to make money using a martingale strategy. As a consequence fading generates much higher winning percentages than in the past which makes it a profitable strategy, in contrast 40% or fewer runs lasted only 1 day in the past gradually moving into the mid 50s this decade. The winning percentage for daily follow-through prior to this decade (ie a trending strategy) was lower than the inverse MR system in this decade– and made its money like most  trend systems via a higher W/L ratio.

2) The market is becoming more efficient: for many of the reasons above. The Sharpe Ratio for all combinations of profitable run strategies is declining over time. Traders are confusing the high profitability of mean-reversion strategies in recent years on an absolute rather than risk-adjusted basis. Volatility was higher in 2008 than it has ever been over long periods. The Sharpe Ratio for trending and countertrending strategies prior to this decade was higher–partially this reflects poor market returns for this decade, but the trend across decades is lower. 

3) Run Frequency Is Also Dictated by Auto-Correlation and  Market Breadth:  A lesser known fact is that autocorrelation (ie the tendency to follow through) in the index used to be driven by a lead/lag effect where the larger stocks moved first and the smaller stocks followed in sequence (See a Non-Random Walk Down Wall Street). With electronic trading and the acceleration of market time, this lead/lag effect is gradually becomind smaller and smaller. The correlation of the Russell 2000 and the S&P500 is becoming higher for example. Breadth and increasing breadth is the only observable clue of this lead/lag effect happening in real-time. Thus when breadth starts from a lower base and starts accelerating in conjunction with price my theory is that auto-correlation or follow through is more likely than mean-reversion. For a a complete review of the effect of market breadth, Quantifiable Edges has an entire archive here that is well worth reading . Some additional breadth research came out today The opposite is true if breadth is absent–ie if prices are falling/rising and breadth is low then MR is more likely. The other contingency is that when breadth is extreme and prices and volumes are extreme this should lead to mean reversion as well. The current abscence of mean-reversion after the spectacular performance in 2008 is largely due to breadth factors—-in 2008 we saw a massive withdrawal of capital, and a gradual decline in market breadth which based on my theory would dictate heavy mean-reversion under most contingencies. In contrast in 2009 since the beginning of the rally we are seeing a return of money to the market and heavy and accelerating  breadth as noted by Rob Hanna at Quantifiable Edges   Thus it should not be surprising that MR has weakened substantially and has not been the dominant regime. Nonetheless at a macro-level the same principles apply as dictated by the theory: when prices and breadth reach extremes such as they have now, mean-reversion should be likely to set in again quite soon.

4 Comments leave one →
  1. September 22, 2009 10:21 am

    The market is operating in compressed time…

    Very astute observation. Mandelbrot would probably agree that as markets lean towards dislocation and mis-pricing, market time speeds up. Or maybe he wouldn’t agree. He would certainly want to discuss it.

    • david varadi permalink*
      September 22, 2009 12:19 pm

      thanks wood…..although one thing that systematically affects fractal structure both in natural phenomena and market phenomena is the changing nature of the underlying generator. Frequencies can permanently change or move in long cycles……my argument is for the former. This does not mean magnitude cannot evolve to make daily follow through profitable again in the future.


  2. September 23, 2009 1:11 am

    Have you considering the relationship between “compressed market time” and high-frequency upsilon time from Olsen et al (§ 6.3) of An Introduction to High-Frequency Finance?


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