2004 Noteworthy

12/31/04 - What a coincidence? The closing price for the SP500 index for last year was 1111.92 and the 2004 closing price is magically 1211.92. That's precisely 100.0 points. It's a great number to end the year, don't you think? However, I can't help but wonder about the odds of that happening?

12/30/04 - New All highs except for the most widely invested indices: DJIA, OEX, SP500, and NASDAQ. Interestingly, the NYSE composite index broke the all time high 12/21/04 (highest close) and 12/23/04 (highest high), set on 9/11/00, which had both the highest high and the highest close (interesting coincidence for the twin tower catastrophe - one year later). The volume was also higher but not by much. On 12/21/04, the volume was 2.5% more than on 9/11/00 and on 12/23/04 the NYSE volume was 6.6% stronger. So despite the light holiday trading, the trading volume is still slightly greater than that set on the day of the previous all-time high. This slight increase in the amount of trading activity isn't a resounding endorsement of these higher prices.

PS - In case you weren't aware of this, the AMEX composite, the S&P Small Cap 600 and the Russell 2000 are also making all-time highs, but the trading volume is declining above the previous highs.

12/27/04 - Did you know that the week of Dec. 13-17 had the largest weekly trading volume for 2004? Trading volume on the NYSE for Dec. 13-17 was 9.34 Billion. So far for 2004, there have been only 4 weeks that have surpassed 2003's largest trading volume of 8.39 Billion shares. Also for comparison's sake 2002's record week was 11.9 Billion and 2001's was 10.5 Billion.

12/22/04 - China's Textile industry is for sure to win free for all! Jan. 1, 2005 marks the beginning of a new set of rules for the textile industry. Quotas for US and European company's will be lifted and they are free to make clothing anywhere they wish. Of course, China is expected to be the big winner. And again, China will dominate yet another manufacturing sector while company's pursue greater profit margins. The few workers that are still left in the home country will of course suffer the consequences as unfettered global capitalism continues to shift jobs.

12/9/04 - Eureka! It all makes sense now. The stock market won't go down because "they" know demand is coming. Those in the "loop" have been buying and holding.

The National Center for Policy Analysis (ncpa.org) gave the "thumbs up" to the Bush plan for changing Social Security. It released the "howto" reform Social Security yesterday. The NCPA says it best. "The NCPA unveiled yesterday a groundbreaking new plan to reform Social Security that for the first time explicitly spells out how to fund the transition from the current pay-as-you-go system to a retirement program that is fully funded."

Why else would stock prices be rising despite declining trading volume, record increases in energy costs, and decreases in future corporate projections? Every one on Wall Street knows that this is "huge" for them. The NCPA is proposing that individuals should use broad index instruments such as the SP500 and Russell 3000 to park their individual social security money. It's a no brainer. Wall Street created ETFs, HOLDRs, and iShares in preparation for this monumental change. The stage has been set for individuals to purchase equities rather than purchasing bonds when deciding how to invest their social security money.( Just look at the returns of bonds versus stocks). Since 1985, stocks have outperformed bonds every year using 10 year returns as the benchmark. WOW! what a complete turnaround from a hundred years ago when nobody would dare give their hard earned money to Wall Street!

Now we know why the NYSE specialists have been hoarding stock over the past year! It's as good as done now with the ncpa.org's approval. Second, when this plan is approved it reduces the federal government's liability to fund social security to less than 15% of it current obligations as the new plan becomes fully funded by working individuals' contributions over the next 34 years. But first the phase of the changeover requires the Government to pre-fund everyone's account. So the government will be the biggest purchaser of stock in history! The second major impact of the changeover will be in the Insurance industry. When individuals start to withdraw funds they will more than likely opt to annuatize these funds. This will create a whole new annuity market which will benefit the insurance industry as the miniscule annuity market grows 1000%. This estimate is derived from studying the Chilean social security plan over the last 23 years. Employees in other countries have overwhelming chosen this avenue of dibursement when they retire.

In summary, Wall Street will now be "King of the hill" as the national savings rate increases by virtue of the fact that every working individual in the USA will now be responsible for their own social security. Buying Stocks clearly will be the vehicle of choice. Company fundementals will be pushed aside as the main driving force behind price movement. They will now be dictated by their popularity and prominence in the broad indices and by how much money flows into everyone's social security accounts.

The biggest winners will be established broad indices and those within the industry who can deliver the lowest transactional fees or expense ratios.

PS - Those that still are under the poverty level will still be cared for by the Goverment as they are now. But that obligation pales in comparison to the financial burden that the current Social Security program imposes on the Government.

12/7/04 - There's a first for everything. This is the first time in 10 years that this site was "hacked". Please accept our apologies as we cleanup the mess. Fortunately, for those of you that have bookmarked our other pages, these pages were unaffected.

12/3/04 - Who's bidding up prices? The latest data from the Mutual Fund industry's cash flow shows that retail investors are increasing their purchases of equity funds. However, the amount of money flowing into stocks is still less than last year. So whose buying and why are prices being bid up higher than last year? 

December 2003, the SP500 index was around 1070 versus today's 1190. Even the trading volume of the last 3 months (during this rally) is less than last year's trading volume over the same period.

11/18/04 - When will the fireworks commence? The following table shows you how often the SP500 index experienced daily ranges 2% or greater. Notice how infrequently these have occurred in 2004. In addition, notice on what day they occur. (They're evenly divided across the week.) When things return to normal, expect 2% ranges to return to the markets. The question is are you prepared for them? In the past, you could expect a "wild day" at least once every three days.

BTW, a 2% daily range at current levels equates to 24 SP points.

Weekday occurrences of  >= 2% daily ranges in the SP500
	Mon	Tues	Wed	Thu	Fri	Total
2004	0	1	2	0	0	3
2003	11	8	7	4	10	40
2002	26	20	25	20	21	112
2001	12	15	17	13	18	75
2000	11	17	17	17	21	83
1999	7	12	14	9	13	55
1998	12	11	9	12	12	67

11/18/04 - NYSE Buying Climax. There's only been two other occasions when the amount of up volume has reached such climatic levels in relative terms. In one case, prices moved higher and in the other case, prices dropped sharply. Not much help is it... So much for buying climaxes as tops. But generally, prices are lower 3 months later. Currently, investors have spent a great deal of money in a short period of time and unless the madness continues, demand or trading activity to buy will wane and prices will drop. In the past, the market hasn't been able to sustain these levels of buying for too long. Investors eventually run out of money to spend.

11/18/04 - Gold moves. Seasonally gold has moved higher from August to December. In 2002, it rose $85. In 2003, it rose $80 and so far in 2004 Gold has risen $59! As always, you can read the glass half full or empty, and if gold stays on track it should rise another $20. Last year, gold moved $48 from Aug. to mid- Nov. and then shot straight up another $32 by 1/12/04. Should investors count on this seasonal play again?

11/16/04 - Yesterday's high matched exactly to 1998's price this time of year. Could 1998 be resistance for the market?

11/16/04 9:48AM - The third Tuesday in November. The odds for today aren't outstanding. 6 out of the last 12 years were up days. However, prices moved high enough throughout the day for day traders to play the buy side in 5 out of the last 6 years. Interestingly, 23 of the last 30 Tuesday's were up days. This unusually high statistic defies randomness and the chi squared value is significant. Will this observed behaviour continue or will this streak end?.

11/12/04 - The last time we were here was 8/27/01. The SP500 hasn't seen 1180 for 3 years.

11/11/04 - The SP500 takes out a multi-year high today. The SP500 index reached a high of 1174.82 with trading volume of 1.66 Bil.. Here's a listing of the previous highs:

Date	Highs	Volume
3/20/02	1170.19	1.77 Bil.
3/19/02	1173.94	1.71 Bil.
3/18/02	1172.73	1.62 Bil.
3/11/02	1172.95	1.76 Bil.
3/8/02	1172.72	2.17 Bil.
1/9/02	1174.26	2.12 Bil.
1/7/02	1176.78	1.89 Bil.
1/4/02	1176.39	2.17 Bil.

10/28/04 - ISO weekly calendar. Working with dates is tricky business using financial data. So to make life easier for businesses and the scientific community, the International Organization of Standardization (ISO) created the definition for the weekly numbering scheme. Essentially, an ISO year and the Gregorian calendar can have either have 52 or 53 weeks depending on how many Thursdays exist in the year (as Thursday represents midweek using Monday as the start of the week). As an extension of the monthly work disclosed below, here is a table listing the ISO week numbers and the number of occurrences of high-low and low-high that each week exhibited in the past.

First, notice that the last line contains the total number of weeks and that the Chi value is 15.8. This high value of Chi Squared says that the frequency of occurrence of these two patterns (high-low to low-high) isn't random to a level of certainty more than 99.9% and yet the probability that the week will yield a pattern of low-high is only 55.8% (662/1187).

(As a caveat, notice the high degree of confidence that the frequency of occurrence isn't random 99.9% and yet the probability of occurrence is low 55.8%. The point here is that these two values represent two distinct attributes. As a matter of fact there are several weeks cited above with probabilities of occurrence of 65.2%, which at seem to be better odds than 55.8%. But if the underlying probability of occurrence can't be demonstrated to be due to a non-random process then regardless of the higher probabilities; the statistic represents a random process.

As an anology, think about the bell curve. The area under the bell curve implies that there is variability in measuring something. Well, if we flipped a coin, we wouldn't get precisely 10 heads and 10 tails after 20 tosses. This outcome is one of many that are possible which still represent the same random process. However, if we got  15 heads and 5 tails then the odds that this is still a random process is remote and the person flipping the coin has found a way to reliably create a non-random process.  But what if we got 13 heads and 7 tails? The probability of occurrence is 65% (13/20), but this doesn't mean that we will reliably and repetively continue to yield 65% when the underlying process is random. As a matter of fact, the probabably of occurrence will eventually fall back to 50% and this sample of observations merely represent a "run or streak". So if the underlying process is random then the outcome is uncertain regardless of the fact that it has a 65% probaility of occurrence. The goal is to find processes that aren't random and develop strategies to maximize the benefit of these reliable behaviours. The next step would be to find high probabilities of occurrence that exhibit non-random behaviour which increase the odds of success.)

Second, scanning the list you'll discover that the highest Chi value is only half of the value from the summary of all weeks (7.3 versus 15.8). The light green values represent 99% confidence while the lightblue values indicate 95%. In addition, all of these weeks highlighted also coincidentally were weeks that demonstrated a pattern of setting the low first then marching to the high. Also worth noting is how just few weeks in the year exhibit non-random behaviour. Only 4 weeks were highlighted, but an additional two weeks could be included if the confidence criteria were relaxed to just 90%.

Interestingly, the highlighted weeks that probably aren't due to random behaviour don't coincide with any future or option expiration week. This is surprising as one would assume that the amount of money at stake during those weeks is exceptionally greater than other weeks. Second, if you were to compute the odds of the week with the greatest degree of confidence that it isn't due to randomness, it would still only be 78.3% reliable (18 out of 23). So don't bet the farm based on these statistics. Having an 80% probability that something will occur are good odds, but not great odds. However, the fact that Chi Squared says that some process is at work, and that it isn't random, indicates that developing a strategy to maximize the benefit of this process is warranted.

 Lastly, it's fascinating how frequently the ordered pattern of highs and lows occur each week. Surprisingly, there are only a few weeks in the year that demonstrate a pattern reliable enough to trade with confidence. The fact that this market ineffieciency still exists begs the question as to when it will be nullified? In the mean time, the week after Federal Income Taxes are due; the last week in August; the first week in November; and the Christmas week are weeks that continue to present investors with an opportunity.

Now let's find out if any runs or streaks appear in the sequence in the order of weekly highs and lows.

10/27/04 - Heads it's up. Tails it's down. What month has the most reliable record of making either a high then low, or a low then a high? In other words, which month has the most predictable sequence of making its high and low? The answer to this question lies in tracking the order of when each month's high or low occurred. Then counting how many times each month had the same order. The table below presents the data as recorded by the SP500 cash index since 1982.

First, notice the last line of the table. It simply classifies each month as going from low to high or high to low. Expectedly, the number of months making their lows first outnumbers the months that make their highs first. Of course since the market has been in an uptrend since 1982, this is expected, but what is interesting is that the Chi Squared value is only 4.22. This statistical value means that the number of occurrences of HL and LH didn't occur by chance. More specifically, this statistic says that we are 95% sure that this is so. Surprisingly this isn't 99% certain. A value greater than 6.64 would give us more confidence that the order of monthly highs and lows wasn't due to chance.

Second, notice that the highest Chi for any specific month was 3.52 for October. Unfortunately, this value only gives us 92.5% certainty that this isn't just a random observation. So, these statistics state that October generally starts out low and ends up high. This isn't reassuring when you align yourself with these statistics and prices drop throughout the month of October. So despite being 92.5% sure that October would put in its low before its high, this October defied historical evidence to the contrary.

Third, the remaining 11 months show that the order of highs to lows versus lows to highs is unfortunately by chance. August is the next month with the record of 2:1 that it will make a low before the high, but even with 2:1 one odds, notice that chi squared is only 2.13 which says that we're only 80% sure that it isn't due to chance. Unfortunately, all of this means is that we can't anticipate the re-occurrence of any monthly pattern with respect to monthly highs and lows.

In summary, although the trend has been up since 1982 we're only 95% sure that the order of the monthly HLs isn't random. However, there are only two months in which you would be likely to say that the order of its HLs is reasonably certain. Unexpectedly, the two months are August and October which are months that aren't on anyone's radar screen. And if you took a survey that asked which months are most likely to trend up, December and January would be the most likely candidates. Unfortunately, these data show otherwise: the order of highs and lows for Dec. and Jan are just a "flip of a coin". Whereas August is traditionally the month that Wall Street views as its vaction month and October is notoriously known as the "Black" month. These hardly bring to mind upward trending months.As a matter of fact, October is known to be the most volatile and is infamously known for the 1929 Crash and Black Monday. So who can blame an investor for not wanting to go long during the month that traditionally caused the worst losses in history.

10/24/04 - Let's check the odds in the SP500 index. Did you know that out of the 204 trading days to date in 2004 only 110 closed higher? And out of those 110 up days only 89 of them had price ranges that were consistent with the expectation that prices deviated more to the up side than to the down side relative to the previous close. In other words, you'd expect prices to rise more than drop on up days, but that didn't happen for 21 out of 110 days. Another anomaly is that if you tried to make just 2 points the following day by going long on the close of these these 89 up days, you would have only won 2 points 55 times out of 89 days. Unfortunately had you followed this plan, the total for 2004 would have resulted in losses of more than 200 points. So the fact is that the market doesn't provide any consistent follow-through for short term traders banking on up days yielding higher prices tomorrow. Interestingly, the day that produced the least amount of losses was Thursday, So Thursday's close has the greatest liklihood of producing follow through. Also worth noting is that if you think large price ranges between the open and close make a difference, then the odds are this. There were only 15 up days in 2004 which had the open to close range greater than 90% of the total daily range. Out of these days only 8 days produced 2 points and the total for the 15 days netted a loss of -55 points. So the expectation of there being a greater likelihood of follow through on up days producing large bodies in the candlestick pattern doesn't pan out. Once again, logic doesn't work on Wall Street.

10/22/04 - The Committment of Traders report shows that the professionals bought more futures contracts in the SP500 than they sold during the week ending 10/19/04. In fact they are still net short, but by only 8100 contracts. This is considered a neutral stance as compared to their substantial positions at market turns.

10/22/04 - The supply of stock issued by those companies in the SP500 increased 2.7 times above the amount issued last year. So supply increased and the flow money into equities slowed down. That is not a combination that causes higher prices. But thank goodness program trading volume is rising along with short interest. These factors are certainly conducive to higher prices. NOT.

10/22/04 - The monthly Money Market Funds (MMF) cash flow shows another hemorrhage. This marks the twentieth month out of the last 22 months that Americans are withdrawing cash from Money Market funds. An analysis of the outflows shows that 65% appears to have gone into equity funds and 30% went into bond funds. The remaining 5% is presumed to used for personal use - spending. Interestingly, the flow rate for equities has decelerated over the last six months while the bond flow rate is steady.

10/20/04 - It's official the Government has run out of money - USA is broke . Of course, our legislators will not act until after the election to vote to raise the treasury's debt ceiling again. The current debt ceiling is $7.384 Trillion and we're above that. Interestingly, receipts by the Government are higher than the previous year by 5%, but despite this, the deficit grew by 16.7%. As a footnote, the SP500 at its highest level for 2004 rose 4.6% above 12/31/2003 price. Coincidence, maybe?

10/20/04 - Joseph Granville is in vogue again, so a review of his theories seems appropriate. Back in May 1999, The Technical Analysis of Stock & Commodities Magazine tested one of his strategies and concluded it doesn't consistently beat the market. Second, Hulbert's Financial Digest which independently tracks and fact checks popular market timers, showed that Granville over a 15 year period underperformed the market. Granville earned an average of 11.9% versus the DJIA's 14.1% over a 15 year period (from 1998 to 2002). So using the spreadsheet as described in the Technical Analysis of Stocks & Commodities Magazine, two graphs were created to show how one of Joseph Granville's methods would have worked for investors. The point here is that trading with an emphasis on volume didn't make investors richer than those that don't use volume.

Interestingly, the chart below doesn't look any different than a plot of OBV.

10/15/04 - The New York Attorney General Elliot Spitzer rocks the Insurance sector. Some of the largest insurance companies are alledged to have restricted business to those companies that provide kickbacks. The news also hints that the health insurance sector is next on his radar.

10/10/04 -  More tax related changes that affect Corporate America are being passed this weekend. $76.5 Billion for the Manufacturing sector, and a repeal of an illegal annual $5 Billion export tax break as determined by the World Trade Organization (WTO) to stop the retaliatory rising rate of Euopean tariffs against products exported to the US. However, to counter this repeal, a new 10 year tax relief plan was passed which is valued at $136 billion.

10/8/04 - Which countries over the previous five years had the best growth rate in Mutual Fund Assets? Here is a list of the major players and how the Mutual Fund's Assets have grown. There were four countries that saw their Mutual Funds Assets decline while the others rose. The annual growth rate in Mutual Fund Assets for the World was 7.87% over the past five years. This figure is encouraging as it is dependent upon two factors. The first factor is that stock market prices are higher and the second implies that investors the world over have cash to invest. As long as the world is awash with money, Mutual Fund Assets should continue to rise. In addition, those countries with the highest annual growth rates in Mutual Fund Assets are also indicative of where investors are putting their money. However, those countries with the highest annual growth rates are also represent the riskiest investments in the world.

Another interesting caveat is that despite the Russian crisis of 1998 and the Asian Meltdown of 1997-98, these two corners of the world showed the highest annual growth ratesin mutual fund assets. Investors that moved funds into these arenas after these crises saw their portfolios grow the most. "Buy low, Sell High" comes to mind. Even those investors that bought the Mexican Stock Market after the 1994-95 Peso crisis saw Mexican stock prices rise from 1,500 to 11,000 and while the Peso devalued from 5.6780 to 11.313. However, investing $10,000 back in Feb. 1995 would have grown to $36,800 in Oct. 2004. versus the DJIA's growing to $25,820 (excluding dividends for both) over the same period. That's almost 50% more capital appreciation! Or how about the Thailand currency crisis during the summer of 1998. Investing $10,000 then would put between $26,956 and $30,983 in your account this year.

So the question is which countries do you believe will be the best performers from 2004-2009? Which country will experience the next currency crisis? What if the USA's currency went into a freefall? How would you protect your yourself?

One research paper outlines the variables for such an event ( Currency crisis). In summary, countries that experience a decrease in exports along with a decrease in savings coupled with a decrease in investment demand, along with interest rates rising above the world's interest rate triggers the avalanche. Currently, two of these factors are in place. When investment demand wanes, the third factor will align itself to present the catastrophic signs of a currency collapse. Once a country loses its competitive advantage, it is forced to devalue its currency.

When China allows the Yuan to float freely, who do you think will be more adversely affected - the Americans or the Chinese? This dislocation of capital will transfer wealth so quickly that investors the world over will feel the shock quickly. Our only hope is that the leaders on both sides of the Pacific will mitagate the potential damage and engineer a smooth transition. This is possible, but ask yourself this, which Presidential Candidate do you have more confidence in containing this potential global economic crisis?

Annual Growth Rate in Mutual Fund Assets
	1998-2003
World	0.078676
Americas	0.061217
Argentina	-0.25712
Brazil	0.073731
Canada	0.092146
Chile	0.215602
Costa Rica	0.161592
Mexico	0.123873
United States	0.058812
Europe	0.098213
Austria	0.085254
Belgium	0.112188
Czech Republic	0.398764
Denmark	0.18623
Finland	0.250898
France	0.121314
Germany	0.07436
Greece	0.035672
Hungary	0.196166
Ireland	0.393709
Italy	0.01701
Liechtenstein+	0.842794
Luxembourg	0.155089
Netherlands	0.01245
Norway	0.135902
Poland	0.566037
Portugal	0.035696
Romania
Russia	0.675823
Spain	-0.08609
Sweden	0.093703
Switzerland	0.054412
Turkey+	0.858611
United Kingdom	0.071346
Asia and Pacific	0.127195
Australia	0.492753
Hong Kong	0.190335
India	0.246582
Japan	-0.0151
Korea, Rep. Of	-0.06126
New Zealand	0.057005
Philippines	0.478097
Taiwan	0.264463
Africa	0.208329
South Africa	0.208329
Note: + indicates change from 2002-2003 due to insufficent data ©2004, The Small Investor's Software Co.

10/7/04 - Oops! Forgot to include the passage of the new tax cuts signed by President Bush on Oct. 4. It's interesting to note that the recent runup in prices was correlated to the news released the last week of Sept. So Corporate America got two bits of good news: lower taxes for consumers, and China will conform with all of the other Fiat Nations (G10). It will allow a floating currency that could help American Business compete against "China, Inc".

10/7/04 - An hypothesis regarding China's floating currency - why now?

Although, the market is looking forward to this event, one has to be mindful of the fact that China's history teaches us that their is a catch and China never does anything unless it is in their interest to do so ( they are masters at manipulating the rest of the world). So, we will have to wait and see why they have agreed to float their currency.

An educated guess is that they plan to change the balance of imports to exports. The Chinese administration has been mainly interested in exporting in an effort to maintain its growing population's standard of living (which isn't very high). Now, China has agreed in principle to import more as they allow an increasing number of foreigners to do more business in China. The big money will come from foreigners assisting China in attracting foreign capital (Wall Street Brokerage firms and Huge Multinational Banks) to help rebuild the country's intrastructure. In the energy sector alone, China has begun the most ambitious Nuclear Energy program on the face of the Earth. Other massive infrastructural plans are in the works and they will be using talent from around the globe to accomplish their goals. So while it was in their interest to protect their currency's low value up until now, so that they could remain one of the world's lowest cost producers of anything, they are still protecting their interests by sacrificing their currency's value. This seemingly contradictory statement isn't contradictory, because China knows that they will need to import more. And if their currency increases in value, they will in effect pay less for those goods and services that they import. So China gets to keep more of what it took from the rest of the world over the last 50 years - captial. Now that they have taken our money, and manufacturing from us, over that last 50 years, they are now willing to reciprocate but at lower rate to us, so that they can "sock it" to us again, by buying our goods and services at a discount.

The problem is Corporate America is happy to accept these terms because they see "Red" when they look at a potential market of 1.6 Billion consumers. Plus, our leaders know that we as a Nation don't have real money anyway. Our Dollar is worthless as is any other Fiat currency, so our leaders don't need to worry about getting the money back from China. Our Treasury will just print more Dollars, which devalues our currency and makes the Chinese Yuan value relatively greater in value.

So China is expecting to pay less for their increased need to buy more energy and other services, and everybody's happy because it will mean initially that Corporate America and Europe can make real money in China. However, the social cost here at home, of this net exporting of capital over the past 50 years on the backs of the American Taxpayer, and the declining demand for American jobs, is threatening our high standard of living. As evidence that Americans are being used, just look at the rising corporate profits amidst the low job growth economy we're in. And according to one source, average wages since 1968 haven't kept pace with "true" inflation, (as compared to the government's lower CPI figures). So our standard of living while still high, is declining using inflation adjusted Dollars.

Life as we know it will change over the next 50 years as the USA drops from the number one "mover and shaker" in the world to being the third or fourth player (burgeoning players: China, India, Russia, Brazil). This change in Chinese policy is another in a string of precedents that shows us who is dictating the terms of these agreements. These changes in policy only occurred because they are in China's best interest and can be viewed as a sign of weakness of the G7 countries as they beg to get into China.

It's all about Jerry Maguire's "show me the money". Corporate America doesn't mind grovelling for China's business because somebody's going to get it so it night as well be us. But how that helps those who live and work in America, remains to be seen. America is predominantly a service based economy. So how many Americans will be outsourced by the Chinese when they have 1.6 billion citizens of their own to employ?

10/1/04 - China announces it will agree in principle to a floating currency. When this will occur hasn't been disclosed, nor has it been negotiated.

9/30/04 - What unusual pattern appeared twice in the last three weeks and gave rise to the same outcome 4 times? For details, click here.

9/26/04 - 2% Stop loss rule: This week an infrequent event occurred. 2% stoploss orders were hit on Thursday. So naturally, the question is how does the market respond when prices fall 2% below the recent highs. The SP500 was used in this survey.

Before the table is presented, let's explain the table's headings. All significant highs are listed along with their 2% stop levels. Then if the 2% stop order was hit within or on the fifth day, the Low and Close were compared to the stop level. In addition, the volume on that day was compared to the volume on the day the high was made. If the stop order wasn't hit within or on the fifth day, then it was noted. The last two columns show the date that the lowest low was made and it the price of the low before the next high appeared.

In all cases when the 2% level was hit within 5 days, the market continued to decline. However, the amount of the declined varied. The largest declined was 7.5% off the high and the lowest was 2.5%. Note that there were only two instances when the volume decreased on the day in which the 2% stop level was hit. The 2/11/04 high saw prices drop to the 2% level and then reversed higher and on 9/21/04 the same circumstances occurred but the outcome as of today hasn't been determined. Also note that there were only 4 instances when the market didn't fall below the 2% stop level. Lastly, there was only one instance in which the 2% stop was hit and reversed 20 points higher (4/5/04). It ultimately went lower, but holding on to a 20 point loss isn't acceptable for most traders.

Here's a summary of the past years 2% stoploss events for the past year. There were 12 events that are displayed below. Four 2% levels didn't get hit so there were really only 8 potential trades this past year. Of the 8 trades, 3 were good for 40+ points below the 2% stop level which equates to 6% below the highs.The remaining 5 were potentially winners from 10 to 20 points which would have turned into breakeven trades or slightly positive depending upon your style. So waiting for these events brought in 120 points during the past year on 8 trades. 

However, notice that the 2% event that occurred last week is different than all the rest. While it did reach the 2% level within the 5 days, the volume didn't increase as compare to the volume on the day that the high was made. So far the market traded two days below the 2% level, but on the second day, the close was above that level and volume was lower.  Including volume in this instance indicates a BUY at these levels for higher prices to come.

Another confounding detail is that on a weekly basis, the best scenario for buying is when prices fall from week to week and volume decreases (read the next section below for more details). Last week, prices dropped from the previous week, however volume increased. Perhaps the fact that it was a future and option expiration week, skews these results, but as the weekly trend data below illustrates, perhaps volume is a confounding factor which shouldn't be used in evaluating the direction of a longer term trade. Therefore, if you exclude volume from the scenario, then SELLING at these levels should at least produce a 10 point trade with the potential for 40 points in the subsequent 20 trading days.

Now put this together with the current Double Repenetration pattern that exists in the SPX, then all sellers need to do is wait for the last price of September and determine if it less than 1122.94. If it is, the monthly price pattern is intact and prices should drop. Stops should be placed at September's highs in October as October should not make a higher high based on this pattern! For more information on Double Repenetration, click here. However, if prices are above 1122.94 then the Bulls win and close all short, or sell,  trades as the "Double Repo" becomes invalid.

Date	High	2% stop level	First Date Hit	Low	Close	Vol	Trading Days	Not hit within 5 days	Date	Lowest Low
10/15/03	1053.79	1032.71							10/24/04	1018.32
			10/23/03	<	>	=+	5
			10/24/03	<	<	<	6
11/14/03	1063.65	1042.38							11/21/03	1031.2
			11/17/03	<	>	=+	1
			11/18/03	<	<	>	2
12/3/03	1074.3	1052.81						X	12/10/03	1053.41
1/26/04	1155.38	1132.27							1/29/04	1122.38
			1/28/04	<	<	>	2
			1/29/04	<	>	>	3
2/11/04	1158.89	1135.71						X	2/24/04	1134.43
			2/24/04	<	>	<	8
3/5/04	1163.23	1139.97							3/24/04	1087.06
			3/9/04	<	>	>	2
			3/10/04	<	<	>	3
4/5/04	1150.87	1127.56							5/12/04	1076.32
			4/13/04	<	>	=+	5
4/27/04	1146.84	1123.90							5/12/04	1076.32
			4/28/04	<	<	>	1
6/8/04	1142.18	1119.34						X	6/14/04	1122.16
6/24/04	1146.34	1123.41							7/26/04	1078.78
			7/1/04	<	>	>	5
8/27/04	1109.68	1087.49						X	8/31/04	1094.72
9/21/04	1131.54	1108.91
			9/23/04	<	<	=+	2
			9/24/04	<	>	<	3

9/17/04 - What are the odds that the subsequent week will follow the previous week's trend? The trend is defined as the following:

1. Buy if Friday's close is greater than the previous Friday's and Sell if it's lower.

2. Buy if Friday's close is greater than the week's midpoint, or else Sell it if it is below the midpoint.

3a. Buy if Friday's close is greater than the previous Friday's close and the volume increased.

3b. However, if Friday's close is greater than the previous Friday's close and the volume decreased then Sell it.

4a. Sell if Friday's close is lower than the previous Friday's close and the volume increased.

4b. However, if Friday's close is lower than the previous Friday's close and the volume decreased then Buy it.

5. Combine the Buys and Sells of rule 3 and 4.

6a. Buy if current week made a Higher High (HH) and Sell if no higher high was made.

6b. Sell if current week made a Lower Low (LL) and Buy if no lower low was made.

7. Combine the Buys and Sells from rule 8.

8a. Buy if current week made a HH and volume increased from previous week. Sell if HH was made but volume decreased.

8b. Sell if current week made a LL and volume increased from previous week. Buy if LL was made but volume decreased.

9. Combine the Buys and Sells from rule 10.

10. Buy every Friday  (an experimental control for statistical prevalence of "runs" or streaks)

11. Sell every Friday  (an experimental control for statistical prevalence of "runs" or streaks)

 

In addition, if a Buy was indicated, then the trend was up and the number of times the market rallied 1% higher from Friday's close was tabulated. while for down weeks, 1% lower was used. Basically, if you could make 1% the following week then that week was counted as following the trend. Here are the results.

Before the results are presented, here is a description of the data sample. The most recent 15 years of weekly data was used in this sample: 9/01/89 - 9/17/04 which represents a total of 786 weeks of SP500 index data. As a reference, the SP500 futures started at 353.7 and rose to 1128.5, gaining 774.8 points, or 220%. So if you followed the rules of this study, the best any strategy could produce was 786%, but anything greater than 220% would be better then buying and holding. Second, the weekly volume figure was not a pure set. The volume figures used originated from the NYSE daily volume from Sept. 1989 to Nov. 2001 and SP500 daily volume was used thereafter. Third, this study used the average daily volume for the week rather than the total weekly volume. The reason for using the average daily volume for the week was because comparing volume between full 5 day weeks to holiday weeks consisting of only 4 days would be misleading and erroneous. And if one took more time, you could even produce holidays weeks with only 3.5 days. But since this is just a preliminary study, half days are considered full days in this sample.

Next, the results are presented in a table that allow you to easily compare the results from one strategy to the other. Each strategy's rules generated both Buy and Sell signals which were tallied individually and then as a group. The total wins and losses columns combine the data from both the Buy and Sell signals while the net column represents the difference between the total number of wins to losses. The "% winners" column equals the total wins divided by the combined total of wins and losses and the Chi Squared values represent the degree of non-randomness, and determine if these results occurred by chance or not. All values less than 6.64, indicate that the results are no different than chance, or flipping a coin. All values highlighted in green indicate that they are not random. In addition, when comparing Chi, those strategies with the larger Chi values increase your odds of success. 

Rule 3 is of particular importance as it tested a popular and widely accepted strategy on Wall Street. It's always fascinating to discover how the most revered axioms on Wall Street don't pan out and it's equally remarkable to demonstrate that buying higher prices on increasing volume proves to yield the most unreliable results from week to week (rule 3). As a matter of fact, if you were to follow any one strategy, buying every Friday was simpler and better than all the other strategies except for one - buying when prices were lower and volume decreased.

Buying higher prices with increasing volume from week to week didn't improve your odds of success and was equivalent to flipping a coin. Concomitantly, selling higher prices when volume decreased from week to week didn't work well either. Third, selling lower prices with increasing volume didn't work either. But buying lower prices with decreasing volume from week to week produced the best Chi statistics and the best overall "% winners" of 67%, which is equivalent to 2 wins for every loss. The problem though is that the number of occurrences was low - 185 out of 786 weeks which works out to be only 1 trade out of every 4 weeks. Even the net wins of 63 indicates that you would be far behind the market if you adopted this strategy. So despite rule 4's great "Buy" side statistics (not total), it's still a loser in the broader context of comparing the potential gain of 63% to the market's 220% over the same period. Also worth mentioning is how badly all of the rules performed. For more details click here .

Hopefully these facts open your eyes to see that when you compare wins to losses, you need to determine not only if a particular strategy passes the "randomness" test as computed by Chi squared, but that it performs better than if you did nothing other than buy and hold. For example, if a trading system produces 2 winning trades for every losing one that sounds like a good system, but will it outperform simply consistently buying, selling, or holding?

In summary, although a few had results that were better than flipping a coin, none of these trend following strategies were any good and they were actually hazardous to your wealth.

Results: Weekly Trend Following									Chi Squared
Rule	Buy - Win	Buy - Loss	Sell - Win	Sell - Loss	Total Wins	Total Losses	Net	% Winners	Buy	Sell	Total
1	228	211	189	158	417	369	48	53%	0.6	2.8	2.9
2	247	209	185	145	432	354	78	55%	3.2	4.8	7.7
3	120	107	109	103	229	210	19	52.2%	0.7	0.2	0.8
4	124	61	94	68	218	129	89	62.8%	21.4	4.2	22.8
5	244	168	204	171	447	339	108	56.9%	14	2.7	14.8
6a	244	216	168	158	412	374	38	52.4%	1.7	0.3	1.8
6b	242	206	183	155	425	361	64	54.1%	2.9	2.3	5.2
7	486	422	351	313	837	735	102	53.2%	4.5	2.2	6.6
8a	116	114	119	111	235	225	10	51.1%	0.0	0.3	0.2
8b	89	52	109	88	198	140	58	58.6%	9.7	2.2	9.9
9	205	166	228	199	433	365	68	54.3%	4.1	2	5.8
10	456	330			456	330	126	58%	20.2		20.2
11			409	377	409	477	32	52%		1.3	1.3
Note: Chi squared values greater than 6.64 (1%  1 degrees of freedom) indicate non-random events and are highlighted in green. Chi squared represents the experimental control for this study which is identifying the odds of the results being due to something other than chance. Other experimental controls included are rules 10 and 11 which identify statistical streaks or "runs". Notice that if you followed the rule of buying higher weekly closes with increasing volume (rule3), you would have generated 120 wins and 107 losses which is according the computed Chi Squared value (0.7) no better than flipping a coin. This low chi squared value indicates that the results are due to a random process and that this rule should not be used if you wanted to earn 1% during the subsequent week. ©2004, The Small Investor's Software Co.

9/16/04 - How many hours apart are the daily high and low? As an extension to the question below, here's an interesting factoid for day traders. Out of the past 934 trading days, only 21 days had both the high and low within the same hour. Computing Chi Squared equates to 110. So this isn't a random behaviour ( For those of you mathematically inclined here are the values needed: observed: 21, expected: 133 which is 1/7 of 934 because each trading day contains 7 hourly periods. Non-observed: 913 versus expected 801 which is derived from 934-133). Once again, as with the weekly high/low separation, Wall Street avoids having the high and low occur in the same period.

9/12/04 - How many days apart are the weekly high and low? The question of frequency of occurrence is an interesting one. Did you ever wonder how often the High and Low occurred on the same day; or were separated by 1, 2, 3, or 4 days? Well, in the most recent 194 weeks (nearly four years), here's the data:

Weekly Highs and Lows: Separation Days Apart
Days Apart	0	1	2	3	4
Occurrences	1	30	68	59	36
Chi Squared	1436.2	3.0	19.3	10.0	0.3
Note: Chi squared values greater than 13.3 (1%  4 degrees of freedom) indicate non-random events. Values greater than 9.5 (5%  4 degrees of freedom) indicate likely non-random behaviours. ©2004, The Small Investor's Software Co.

Now let's explain this data. If you went to the Las Vegas and rolled the dice, what are the expected odds for rolling a 2? The answer is 1 out of every 36 rolls. Now using one die, what are the odds of rolling a 1? The answer is 1 out of 6. So using dice is easy. Now compute the odds by chance of having the Weekly high/low occurring on the same day. In this case, there are 5 possible outcomes divided by 194 weeks, or 38.8. So if we assume that the odds of separating the weekly high and weekly low by 0, 1, 2, 3, 4 days are equally likely (by chance or random), then which of these observed outcomes isn't likely to be by chance, or is non-random?

The answer to this question requires the use of a statistical distribution called "chi squared", which we have introduced to readers of this site before. Using Chi squared allows you to determine if some event is either likely due to chance or not. So in our data above, the there are three events that are likely not due to chance. If you look carefully, when the weekly high and low are separated by one day this occurs 30 out of the 194 weeks when the expected rate of occurrence is 38.8. The difference between these two values isn't that large and as such indicates through the computation of Chi squared that this is more than likely due to chance. But if you look at how many times the weekly high and low occurred on the same day in the past 194 weeks, you can see that this is a rare event. What's interesting here is that while anything is possible, it is interesting to note how unfrequently this occurs when it is expected to occur 38.8 times. So the computation for Chi squared in this case indicates that this isn't due to chance.

The perversity of these data is when you casually glance at the data. You'd be inclined to infer that 1 event out of 194 is due to a random freak of nature, or hence by chance; like getting hit by lightning. But that comparison is wrong. It's wrong because Chi squared examines two cases, the positive and the negative aspect of this event. Chi squared computes the deviation of the observed from the expected (1-38.8) and the non-occurrence from the expected (193-155.2). In this case, while there was only 1 occurrence of the weekly high and low occurring on the same day, there were also 193 weeks when this didn't occur. So the question remains why does this occur so infrequently when by chance (like rolling the dice), the expectation is much higher?

So thus far, the number of times that the weekly high and low occurred on the same day isn't by chance but the number of times that the separation was 1 day apart is likely due to a random process. In addition, notice that number of occurrences from 4 days apart are nearly the same a 1 day apart. This means that when the high or low occurred on Monday; the opposite extreme occurred on Friday, and it is more than likely due to a random process - it's by chance. However notice that when the separation is 2 or 3 days, the number of occurrences nearly doubles from the number of occurrences from 1 day apart. In these instances, Chi squared tells us that these are likely due to a non-random process. It's not by accident, or chance, that this occurs. When the weekly highs and lows are separated by 2 or 3 days, this is the most likely event and Chi squared confirms that this isn't due to chance.

So now put on your "skeptics hat" and ask, why are the weekly highs and lows more likely to be separated by 2 to 3 days and never (almost never) occurs on the same day? These data prove conclusively that the price action is contrived. Now ask yourself how can you use this information to time your trades or to improve your trading results? If you want to learn how Wall Street works and how to use it's behaviours to your advantage? Contact us.

9/10/04 - Something odd happened on 8/24/04. Up volume exceeded down volume and yet the market posted a lower close. Is this divergence tradable? This unusal event caused us to review the past 4 years and investigate the prevalence of this anomaly. So the question is, if today's up volume is greater than today's down volume, what are the odds of buying the close will make money? Well, if the closing price is considered an important factor, then this group of days can be divided into two groups. Group 1 would be those days in which the closing price is greater than the previous close and group 2 would be those days in which the closing price is below the previous close. A recent sample of end of data from 1/3/00 - 9/9/04 was used, which consists of 1177 trading days. Out of those 1177 days 592 days had up volume greater than down volume on the NYSE (note that the odds of this are exactly 50%, which is the same as flipping a coin. So 50% were up days and 50% were down days.). Out of the 592 days, 550 had closing prices greater than the previous session and 42 did not. So the first observation is is that it is rare for a trading day with greater up volume to close lower, but it does happen approximately 7% (42/592) of the time.

The next question is can this rare event be useful in making a one day trade. The quick answer is maybe. The reason for this is it depends upon how you implement your trading strategy. The data behind this scenario is this. If the following trading day's high and low are compared to the close from one of those 42 days, and the subsequent day's high to close range and the close to low range are compared. If the range above the close was greater than the range below the close then it was considered a favorable "buy". There were 24 days in which the market made a greater push higher than lower and had you bought you could have made money on those 24 days and lost money on the 18 days when next day's range pushed lower. So you could have made a profit buying the close 57% (24/42) of the time. The problem is that you couldn't be guaranteed a set amount. So making money from this depends upon how and where you placed your stops, and if you had "doubled down". As for the other 550 days (group 1), it was interesting to note that despite the fact that all 550 days were higher closes with greater up volume than down volume, the following day's range only produced favorable "buy" outcomes 47% of the time (no trading edge here). Again, the same problem exists with group 2, there was no set amount of profit that could be used, but it is interesting that those 42 days in group 2 actually have a trading edge in buying over those 550 days in group 1 - 57% versus 47%.

This runs opposite to common sense where one would be inclined to assume that if up volume exceeded down volume and the market closed lower, the next day would produce a down day, or more precisely, a larger range below the close than above it, because this represents divergence! So the lesson here is don't assume, and if you review those days in group 2, perhaps you could devise a strategy to take advantage of this "edge" so that you can profit reliably from these rare occurrences.

8/28/04 - Question: What is the price that the DJIA needs to be to yield the same return as 10 yr bond holders recieved during the last 10 years? Answer 8015. (capital appreciation only. This assumes that there were no dividends.) Conversely, those investors that bought the DJIA 10 years ago earned 9.6% versus bond holders 7.24%. Plus, equity investors also received an additional $1564 in dividends during that 10 year period. So equity investors earned a total of 11.5% versus bond investors 7.24%.

Now project this into the future. 10 year bond holders are currently receiving 4.25% and if we assume the same performance for the next 10 years then equities should yield approximately 8.25% including dividends. The important fact here is that if you find yourself earning more than this 8.25% then you might want to consider taking your profits to the bank. Earning 15% to 20% in one year is the equivalent of hitting a home run in baseball. So consider banking any large profits.

8/4/03: The SP500 is testing the 200 and 50 day Simple Moving Averages (SMA). The 50 day SMA is 1117.6 and the 200 day SMA is 1107.6  Today the resistance at the 200 SMA was too great.

What's particularly interesting is that the 50 day SMA also happens to be the same price as it was on 5/3/04. This date is relevant because 5/3/04 marks the remaining 6 months in President Bush's term. In summary, every Presidential cycle since 1950 saw prices rise above the 6 month remaining price with 3 months remaining (that's today). That's 12 cycles in a row! But of course, this cycle is different because this Presidential cycle has the worst stock market record in history! Investors are still down 24% from 11/7/00 - the worst on record. Will the SP500 flirt with prices above 1117 for a few days as history has shown us?  For more charts and details click here.

8/2/04 - 9:45AM rule examined. Many on Wall Street wait with anticipation for 9:45AM to arrive. For those traders, the game plan for the day gels at this time. It's the moment when day traders decide to go long or short for the day. So here are the statistics for those who have wondered how this works.

First, out of the previous 545 trading days only 286 days followed the rule to the close. That's only 52.5% of the time which is no better than following the following the previous day's direction which yields around 51%.  Second, if traders waited 10 more minutes, the odds of success improve slightly to 296 days. So if 9:55 AM were used, then out of the 545 days 268 days were higher than the opening price and 277 were lower than the opening price. Out of the 268 days that were higher at 9:55AM only 152 days closed higher than the 9:55AM price. That's 56.7% success. On mornings that were down at 9:55AM, 144 days ended lower, or 52.0%. So if you were to follow this rule, how would you mitigate your losses 46%-48% of the time? This strategy seems to have one win for every loss. So how would you manage your trades to be successful (ie profitable)?  So you might wonder how do traders do it. For more click here.

7/28/04 - Gaps Revisited. Here is a summary of gaps created in the SP500 futures pit. Since Dec. 2000, there have been 896 days. Out of those number of days, 201 days had gaps of greater than 1.9 points. Out of those up gaps, 58% were closed the same day. 219 days had down gaps greater than 1.9 points. Out of those down gaps, 56% were closed the same day. Lastly, that means 238 gaps out of 420 were closed the same day which represents 57%.

Another interesting observation was that the proportion of gaps closed varied with gap size. For some reason, up gaps 6 to 7 points in size get filled more often than gaps 5-6 points while down gaps get filled more often when they're 7-8 points versus 5-7 points. This is just something to tuck in the back of your mind the next time you see a morning gap of 5, 6, 7, or 8 points.

Gap Sizes in points
	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Gaps Up Closed	84%	64%	53%	41%	70%	54%	22%	17%	60%	0%	None	50%	0%	0%
Gaps Down Closed	82%	71%	59%	41%	44%	75%	35%	29%	29%	4%	0%	0%	100%	None

7/27/04 - Historically there's good evidence for a bounce.

1. Prices fluctutate more during the Summer.

2. Prices tend to rebound after the 5% stop loss level is hit.

3. The Presidential Cycle has a 100% track record for prices being above their 6 month remaining level (1117.49) at the 3 month remaining point (8/3/04).

7/27/04 - 5% Stops hit last 3 trading days. Many pundits advise traders to limit losses to only 2% per trade. However, many investors pull the plug when prices fall 5% off the recent highs. During the last three trading days, the 5% stop level was hit @ 1088.7 So did you ever wonder what are the odds of the market going higher one month later? The answer is that you have a 58% chance of prices going higher which is 8% better than chance. BTW, in case you're wondering about the amount of risk involved, prices on average went 20 to 40 points below the 5% stop level before turning higher.

This figure was computed using the following steps. First, the 5% stop level was computed for each day since 1992. Then it was determined if the day's prices closed below the stop level. Any day that closed below the 5% stop level was then included in the set of possible candidates, which constituted the total number of days. Then it was determined which of those days closed higher one month later. Then finally the proportion of days that closed higher one month later was calculated.

7/26/04 - Presidential cycle price fluctuations. It's now less than 6 months before we elect a new President. So it only seems fitting to review how prices fluctuate during the remaining 6 months of the Presidential term. The day in which 6 months remain in the term was 5/3/04 which had a closing price of 1117.49. This is the reference price for all prices until this term ends. Interestingly, during the last 13 Presidential cycles, all of these cycles had prices above their reference day with 3 months left in the term. This means that prices should be above 1117.5 around 8/3/04 to 8/6/04. For a current view of these charts, select the Charts Link. It's hard to believe that this has had a 100% track record, which constitutes 13 cycles in a row. Nothing ever has a 100% track record, or will it?

7/12/04 - What are the odds of the SOX index or SPX making a higher high (HH) when the close is above the 4 day simple moving average(SMA)? Below is a table of data to answer that question. Within this table there are several smaller tables. Essentially, the number of higher highs (HH) and lower lows (LL) were counted for the following periods: 30, 60, 100, 125, 200, and 252 days. Just for clarification, 60 days represet a quarter and 125 days represents a half-a-year while the 252 represents a full year. 100 and 200 are included because of their popularity. Those days in which the close was greater than the 4 day SMA were totalled and displayed on the row labelled "#days". Those days in which the close was greater than the 4 day SMA and the following day produced a HH are displayed under the ">SMA" column. Those days in which a HH was observed the following day when the close was below the SMA are displayed under the column "<SMA".

As you can see the odds of the SOX index making a HHs when it closes above the 4 day SMA in the most 30 day period is 0.615 or 61.5% and for the other periods is rises slightly to 0.666, 0.661, 0.679, and 0.654. This represents the number of days HHs were made to the total number of days above the SMA. So the odds are near 65% rather than 50% if it were due to a flip of a coin, or random. In contrast, if the close was below the 4 day SMA, the odds of a LL were less. They were 0.41, 0.55, 0.55, 0.59, and 0.57 for the periods cited. These ratios are closer to 50% so it appears that you are more likely to see HHs above the 4 day SMA than you are to see LLs belows the 4 day SMA.

The last column shows you another ratio. This ratio expresses the comparison of number of HHs above the 4 day SMA to the number of HHs below the 4 day SMA. In all periods, this ratio is greater than one, indicating that it is more likely to see a HH when the close is above the SMA. This seems rather obvious given that you would expect more HHs above the SMA, but this quantifies the charts rising trend. Notice that for the past year the ratio was 2.39 as likely to see HHs above the SMA than below it, but in the last 30 (1.33) and 60 (1.45) days this ratio is cut in half. This clearly states that the proportion of HHs above and below the SMA is nearly the same, which tells us that the trend isn't so clear.

One last point to make is while these observations real and current, it's easy to draw these conclusions. But these facts must be subjected to a statistical test to verify that they aren't just variations of randomness. This is an important distinction because using empirical data can be misleading if they aren't put into the context of other outcomes. Another important fact is that this table represents frequency data (counting the number of events) rather than measurement data (using actual prices), so for this we must use the statistical "Chi squared" test. As an example, although there were 8 days out of 13 total days that made HHs when the closing price was above the SMA, this could simply be a "run" and this result could be due to chance. It would be the same as flipping a coin and getting heads 8 out of 13 tosses. You would expect heads to appear every other flip but sometimes it doesn't turn out that way and you get a "run" of heads or tails.

Below each period are the Chi Squared results. As shown, the data for the number of HHs above the 4 day SMA indicate that for the 30, 60, 100, and 125 day periods, the observations are no different from flipping a coin. However, for the past 200 and 252 days, the number of HHs above the 4 day SMA is more likely than not to be unevenly split  and not due to chance, or in other words - not random. Ultimately the question remains, how would you use this information to make profitable trades in the SOX index? 

BTW, there's a table of results for the SPX below the SOX. It appears as though making LLs isn't by chance in the SP500 for all periods. In the most recent 30 days ending 7/9/04, 12 days closed below the 4 day SMA and 10 of those 12 days made LLs. This isn't by chance. So how are the odds different from the SOX and how would use the SPX's data to trade? For more information regarding utilizing frequency data, contact us.

SOX index Odds of making HHs or LLs using 4 day SMA
30	>SMA	<SMA	Ratio of days above SMA to total # of days above SMA	Ratio of days below SMA to total # of days below SMA	HHs Ratio of days above to below LLs Ratio of days below to above
HHs	8	6	0.615385	0.461538	1.3333333
LLs	5	7	0.294118	0.411765	1.4
#days	13	17
			HH >SMA Chi = 0.69	LL < SMA Chi = 0.53	Both fail randomness test
60	>SMA	<SMA
HHs	16	11	0.615385	0.423077	1.4545455
LLs	10	19	0.294118	0.558824	1.9
#days	26	34
			HH >SMA Chi = 1.38	LL < SMA Chi = 0.47	Both fail randomness test
100	>SMA	<SMA
HHs	32	17	0.666667	0.354167	1.8823529
LLs	19	29	0.365385	0.557692	1.5263158
#days	48	52
			HH >SMA Chi = 2.67	LL < SMA Chi = 0.69	Both fail randomness test
125	>SMA	<SMA
HHs	39	21	0.661017	0.355932	1.8571429
LLs	23	38	0.348485	0.575758	1.6521739
#days	59	66
			HH >SMA Chi = 3.06	LL < SMA Chi = 1.51	Both fail randomness test
200	>SMA	<SMA
HHs	72	31	0.679245	0.292453	2.3225806
LLs	38	56	0.404255	0.595745	1.4736842
#days	106	94
			HH >SMA Chi = 6.81	LL < SMA Chi = 3.45	HH passes test.  LL doesn't
252	>SMA	<SMA
HHs	91	38	0.654676	0.273381	2.3947368
LLs	51	65	0.451327	0.575221	1.2745098
#days	139	113
			HH >SMA Chi = 13.3	LL < SMA Chi = 2.56	HH passes test.  LL doesn't

SPX index Odds of making HHs or LLs using 4 day SMA
30	>SMA	<SMA	Ratio of days above SMA to total # of days above SMA	Ratio of days below SMA to total # of days below SMA	HHs Ratio of days above to below LLs Ratio of days below to above
Highs	10	7	0.555556	0.388889	1.428571
Lows	7	10	0.583333	0.833333	1.428571
#days	18	12
			HH > SMA Chi= 0.22	LL < SMA Chi=5.33	LL passes test. HH doesn't
60	>SMA	<SMA
Highs	18	13	0.580645	0.419355	1.384615
Lows	12	21	0.413793	0.724138	1.75
#days	31	29
			HH > SMA Chi=0.80	LL < SMA Chi=5.82	LL passes test. HH doesn't
100	>SMA	<SMA
Highs	33	19	0.611111	0.351852	1.736842
Lows	20	34	0.434783	0.73913	1.7
#days	54	46
			HH > SMA Chi=2.66	LL < SMA Chi=10.52	LL passes test. HH doesn't
125	>SMA	<SMA
Highs	42	24	0.6	0.342857	1.75