Jan

16

One main assumption in statistics is that samples are independent and not correlated. However, it seems apparent to almost every trader that the outcome for one day is related to yesterdays price action.

Andrew McCauley writes:

Your comments reminded me of something that Benoit Mandelbrot mentioned in his book The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence:

Speaking mathematically, markets can exhibit dependence without correlation. The key to this paradox lies in the distinction between the size and the direction of price changes. Suppose that the direction is uncorrelated with the past: The fact that prices fell yesterday does not make them more likely to fall today. It remains possible for the absolute changes to be dependent: A 10 percent fall yesterday may well increase the odds of another 10 percent move today—but provide no advance way of telling whether it will be up or down. If so, the correlation vanishes, in spite of the strong dependence. Large price changes tend to be followed by more large changes, positive or negative. Small changes tend to be followed by more small changes. Volatility clusters.

Big Al offers:

Just felt like doing some tinkering, so here is a chart with two series: The upper series is the moving 20-day C-C % return of SPY adj, calibrated by the right hand axis. The lower series (left hand axis) is the 20-day rolling sum of the absolute value of the daily % changes. As expected, the lower, vol series tends to peak when the upper series is spiking downward, but the chart could provide some interesting trailheads for further research.

May

3

G'Day,

I hope all is well. Just thought I would share this market coincidence with you.

It has been 42 months since the S&P 500 Index reached a monthly closing high of 1,549 in October 2007. The index is currently 12% below that level. I note that 42 months after the December 1972 peak the S&P 500 Index was also trading at approximately 12% below its peak level. Interestingly, both post peak periods were marked by declines in the order of 50% & when plotted together on a monthly interval (common base) look remarkably similar. If this path were to remain compliant then the index would peak just above 1,375 around July 2011. After this the path suggests an 18 month pullback in the order of 15% to 20% followed by new highs sometime in 2015 (approx. 7.5 years after the 07 peak). It appears to me that 42 may be the consistent theme with respect to the above consilience. The number 42, in The Hitchhiker's Guide to the Galaxy, is the answer to the "Ultimate Question of Life, the Universe, and Everything". Perhaps Douglas Adams was right.

Jul

25

The two recent 1% plus declines in the SPY (07/20 and 07/24) were separated by an up day. It turns out there have been no other 1% plus down-up-down combinations like this since October '05. Below, I have charted them back to January '03, with returns for the next one, two and three days:

  Date        1d       3d       5d
10/20/05  0.004  0.017  0.004
05/12/05 -0.002  0.014  0.029
03/15/04  0.005  0.017 -0.010
09/24/03 -0.008 -0.002  0.010
07/21/03  0.009  0.002  0.016
06/27/03  0.000  0.022  0.031
06/25/03  0.013  0.001  0.023
02/26/03  0.013  0.010  0.002
01/24/03 -0.014  0.001 -0.004

avg          0.002   0.009  0.011
sd            0.009   0.009  0.015
z              0.732   3.159  2.299

Andrew McCauley adds:

So far this year there have been seven declines of 20 points or more in S&P 500 futures. On all occasions the next day provided a positive outcome. 

avg 1.00%
n 7
sd 0.71%
t 3 (versus all other one day returns for 2007)

Referring to Dr. Zussman's previous post, a case of "buying the dips before they occur." 

May

18

I note a positive bias for Australian Equity Futures on recent Mondays after falling Fridays.

The average Monday return, for S&P ASX 200 futures, after a negative Friday is 35 basis points versus 5 basis points for all other nonconditional days. The win rate of over 75% is impressive when compared to 53% for all other data. The t stat of 2.2 is suggestive of this phenomena occurring by chance in the order of 1 in 25.

Intuitively, I suspect that these recent phenomena may be the result of market players either unintentionally or subconsciously reducing risk before the weekend. Then come Monday morning, risk is increased & equity prices rise. The Monday open to close data provide some slight evidence that my intuition may have merit. The Monday closing price has been higher than the Monday opening price 70% of the time since September 2005.

Nov

1

In Australia the press dub The Melbourne Cup as the race that stops a nation. It is one of those rare events where almost everyone, gamblers & non-gamblers alike, have a punt on the outcome of Australia’s most famous thoroughbred race. Sadly, like a large percentage of the population, I tend to walk away from the day, happy but out of pocket.

It is truly one of the social events of the year & the mood of the nation tends to be exceedingly upbeat. It is also a very positive period for Australian stocks. Recording all 4 Day % returns including the 1st Tuesday of November (Melbourne Cup Day) from 1992 to 2005, I found that the S&P ASX 200 had a tendency to produce inordinate gains with an average move of 1.78%.

Returns on Melbourne Cup day also tend to be positive.

I posit whether mood is the major influence on these returns, not unlike the better than average returns that accompany stocks at Christmas & New Year. It is probably an area that deserves further study. Other factors may be the perceived investor relief that October is over, 1st week of the month positive bias, November through to the end of January marking the beginning of an historically positive period and thin markets around Melbourne Cup Day.

I hope the markets remain compliant, and if I’m very lucky, I may walk away from Melbourne Cup Day happy and not out of pocket.

Oct

19

A regular tendency of the market is to provide an outcome that is contrary to what was, or might have been, expected. The Anniversary of the October 1987 Crash is a prime example.

The irony of a record close on Crash Anniversary day would not be lost on the long term drift.

Aug

14

Inspired by the postings Sentiment, by Timothy Roe and Pessimism, from Victor Niederhoffer on the Daily Speculations website, I decided to investigate these observations in more detail.General market sentiment tends to lead investors down the wrong path. There exists a negative relationship between the sentiment of the American Association of Individual Investors (AAII) and future Dow Jones Industrial Average returns.

The AAII has been conducting a weekly sentiment survey of its members since July 1987. It asks respondents to categorize themselves as Bullish, Bearish or Neutral. They then assign a percentage to each group from the total sample. (For the purpose of this study, I use the percentage of Bearish individuals as a gauge of investor sentiment.)

Since 1987, the average percentage of Bearish individuals is 28.31% with a standard deviation of 9.25%. For the week ending 21/07/06, the Bearish percentage stood at 58%. That is over three standard deviations from its mean. Indeed, a very high percentage of Bearish individuals. With this in mind I decided to record all the occasions whereby the Bearish Individuals measure, strayed three standard deviations from its mean, to roughly 56%.

There have been 8 occasions when the AAII percentage of Bearish individuals recorded a score of 56% or more and 12 months later the DJIA was up on average by approximately 20%, with a t stat of 2 and a win rate of 100%. The percentage return is almost double that of all other rolling 52 week periods. In reality the data slightly overstate forecast returns and does not approach statistical significance due to some overlapping and clustering of data. However, the data are suggestive of much higher levels for the DJIA 3, 6, 9 and 12 months out.

I also decided to test future returns when the percentage of Bearish Individuals fell between three and two standard deviations from its mean or roughly 56% to 46%. For mine, still a relatively high outcome. The data in this group were consistent with the previous findings that a high level of Bearish sentiment is positive for future returns. I found 33 occasions that produced a 12 month average return in order of 15%, with a t stat of 2 and a win rate of over 85%. Again the data are somewhat overstated due to overlapping and clustering of data, but the general picture appears to be positive.

Interestingly, if we include the reading of 58% recorded on 21/07/06, then 8 times out of 9, three standard deviation observations occurred when military conflict was omnipresent in the mind of investors.

Six readings of greater than or equal to 56%, occurred between August and October 1990, a time when Iraq invaded Kuwait. The DJIA never traded below its October low again.

A reading of 56% was recorded in October 1992. The month’s news was heavily dominated by the US Presidential campaign. Again the DJIA never traded below its October low.

In late February 2003, Bearish sentiment was at 58%, approximately one month before coalition forces invaded Iraq. The first week of March marked the low for the DJIA, a low that till this day has not been breached.

The recent reading of 58%, recorded in late July 2006, coincided with the Israel & Lebanon conflict, & the DJIA trading at 10,868. Perhaps this could be a multi year low. We will find out over time.

The data are consistent with Lord Nathan Rothschild’s musing that he liked “to buy when the cannons are thundering and sell when the trumpets are blowing”, circa 1810.

For Australian investors the data are also suggestive of positive things to come. Of the 8 times that the AAII percentage of Bearish individuals was equal to or above 56%, the All Ordinaries Index gained on average 16.58% over the next 12 months versus all other rolling 12 month returns of 7.03%. Just over double the average, with a t stat in order of 2 and not one negative 12 month period.

Maybe our Bear will not be depressed for too much longer, because he can be associated with an up stock market.

James Tar objects:

The foundation “Bear Sentiment as a Contrarian Indicator” rests on is flawed. Mr. McCauley makes an obvious mistake. What needs to be considered is that everyone is finally looking at Bull/Bear Sentiment Gauges these days to help formulate an opinion on market direction. Present market chatter, and everyone is saying it, is “The Bear Sentiment is so high we cannot go lower.” Everyone is fixated on this, so much so that the herding on the weekly polls and data (AAII releases) for a contrarian indication of market direction should be a clear warning to the speculator that such a method has now become extinct. The market has perhaps outsmarted once again. Meaning, it might be time to look to these polls as confirmation.

I deeply regret writing such bearish commentary. But if we are truly going to advance our study and discussion of the markets, such a reversal in the foundation of such a widepsread utilisation of “contrarian indicators” must clearly be considered.

Andrea Ravano comments:

I have seldom seen so much negative feeling and low expectations in stock markets, than those surrounding me at present. Private bankers from here and there (I will not mention the countries the calls come from, because I am afraid to offend) mention again and again the risks of war in the Middle East, the price of oil, the risk of inflation etc.. The consensus seems so large that I am a bit puzzled by the market show of strength relative to the so many, possibly sidelined, if not straight short investors.

Which, of course, leads me to believe that if nothing unreasonable happens in terms of terrorism, we might see world stock markets rally by year end, if not sooner.

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