SPX Up/Down Frequency Map - a statistical analysis.

In the world of statistics, there are two types of data. There is measurement data and frequency data. An example of measurement data is the SPX daily closing price. At the end of each trading day, the SP500 index's (symbol: SPX) last price is set at some particular value. We see that and record that measure of value as price data. In contrast to price data, we can also convert each close to frequency data. However, we don't mean converting the data into cycles or applying fast fourier transforms (FFT's) or applying spectral analysis. By frequency data, we mean classification frequencies. We could classify each trading day's close as either an up or down day. This is simply calculated by subtracting the yesterday's closing price from today's current closing price. We could then statistically analyze this series of up/down days (frequency data) to verify if the SPX is behaving randomly or not.

The statistical test used to analyze frequency data is the Chi Squared test. Let's for the sake of discussion defer explaining the gory details of the mathematics and elaborate on the concept of analzying frequency data (up/down days). The first assumption is that if the price action of the stock market as represented by the SPX were truly random, then there would be an equal number of up days and down days in any one period. So for example, if we use a 60 day period, the SPX would have 30 up days and 30 down days if it were reacting randomly. Now, if we were to sample another 60 day period, we would more than likely not get exactly 30 up and 30 down days. We might notice 28 up and 32 down or 36 up and 24 down. Notice that at all times the total always must equal 60 days (our sampling period) but that there would be some variation around 30/30 that would still be acceptable for classifying the period as random. At some point however, this variability exceeds the random assumption and the stock market is now no longer behaving randomly and is statistically behaving non-randomly. The question remaining is what is that number. Well, if the 60 day period is used, the number of up to down days that indicates a non-random behavior is 38 up to 22 down, or 22 up days and 38 down days. The chart below shows this but instead of showing you the actual number of up and days in a 60 day period, the chart only shows the difference between the number of up and down days and displays the net difference. So the ideal random condition of 30/30 would have a net difference of 0, and so the y-scale on the left side of the chart shows the ideal random condition of 30/30 as a value of 0 and the non-random behaviour as a net difference of +16 or -16. These states are highlighted with a blue horizontal line and coincidently notice that the +16 conditions occurred during the "Bull" market and the -16 condition has appreared during the "Bear" market.

Now, looking at the chart below you can see both the measured data and the frequency data simultaneously. The SPX daily close graph dipicts measured data, and the graph labeled "SPX Runs" depicts the frequency data or the net difference in the number of up/down days in a 60 day period. Also shown are two trend lines of the highs and lows of the frequency data. In addition, the red vertical lines are referenced to the cycle lows in the frequency data so you can evaluate how the stock market recently reacted to these conditions.

It's interesting to note that these cycles have been declining since 1995. In addition, it's interesting to note that during the "Bull" run of the late 1990s each time the frequency data pierced the non-random condition of +16 the stock market "hiccupped" or retraced before ultimately going higher. Secondly, it's interesting to note that when the stock market entered the "Bear" market in 2001, the frequency data pierced the -16 condition for the first time! Each time the stock market pierced the -16 condition, the market "hiccupped" or retraced (reversed trend slightly) and then went lower. This chart below shows the last 11 times that a non-random condition occurred. Seven +16 conditions and four -16 conditions. During the "Bull" run, each +16 condition was followed by a retracement and then higher prices. But also note that at the very top of the stock market prices went higher but the +16 condition didn't accompany this higher high indicating divergence - a failed cycle high. Then the market entered the "Bear" run and the -16 condition appeared. Each time the -16 condition occurred the market retraced rather dramatically and then made lower lows. Notice that with the last -16 condition something different has occurred - divergence. The last -16 condition which occurred in February 2003 did not simultaneously occur with lower lows. This is the first time in 11 cycles that the non-random condition has failed. So it will be interesting to discover the significance, or the lack thereof , of this particular circumstance.

Another useful finding that emerges from the frequency data is noting the regularity of the stock market to move from one extreme condition to the other. In other words, notice the cyclic nature of the up/down data. If we apply spectral analysis to this data, or test this data using a FFT, you would see that the stock market experiences a up/down low every 10-12 months. In addition, it's interesting to note that the low occurrs in the fall of each year. So if one were to spend the minimal amount of time and effort in timing the stock market, based upon this data, one could "buy" the stock market during the months of October and November. And if one were to divide the available investment money into six equal parts, one could invest use the following simple strategy.

A practical application - a simple trading strategy.

First invest only half of the available investment dollars into the stock market. So that if the market goes lower, you'll either limit your loss to only half of your investments and/or you'll have 50% of your investment money to purchase more at lower prices so that you can average your way out of the trade.

1. Buy1/6 in September

2. Buy 1/6 in October

3. Buy 1/6 in November.

4. Sell 1/6 in March.

5. Sell1/6 in April.

6. Sell 1/6 in May.

Remember you don't know when the top or bottom will occur and you're not a professional investor, you're just trying to find the most favorable time to buy and sell each year. Well, with this data,you can see that for what ever reason the stock market ebbs and flows. The lows are in the fall and the highs are in the spring. Sometimes the stock market makes higher highs and sometimes it doesn't. But one thing is clear, if you were to buy in the fall, you would be right more often than wrong. Secondly, if you were wrong, the stock market usually gave you a chance to break even. So considering the simplicity of the this approach to investing, and the fact that you are in control of your money and you are not dependent upon others, you can save alot of money because the cost of implementing such as strategy isn't much at all. You don't need a computer for this. You don't need to spend money on advisory letters, nor do you need to pay for advice. So don't need to make alot of trades, nor execute numerous buy or sell orders. All you need is to invest your money mid-month Sep. Oct. & Nov. and sell an equal amount mid-month Mar. Apr. & May. This isn't "sexy", complicated nor is it trying to "squeeze" every dollar out of a trade. This is designed for those that are pre-occupied with other matters and don't want, or care, to spend alot of time worrying about their investments. This simple idea is for those that have a life and want to keep it. It isn't for those who want to make a "killing", or get rich quick, but for those that want to try to cover the eroding effects of inflation and take a small chance on corporate America. This strategy would have given you more protection than simply buying and forgetting about your investments. But this simple approach unfortunately may not work for those of you with IRAs, pensions, and other retirement savings because you must have already chosen retirement plans that allow you to actively move money around mid-year. Unfortunately, the single act of making short term investment decisions may disqualify you because of your current retirement plans and this approach certainly presents problems for long-term investors. This approach doesn't even factor in the tax implications of buying and selling short-term investment versus long-term investments that are held for more than 12 months. But if you were to agree that captial preservation supercedes all else (and sometimes it doesn't) meaning that it is more important not to lose your money than to hold on to a losing investment then this simple seasonal approach to investing will create more wealth more safely than the alternative of buying and holding for tax reasons.

As proof that this simple approach would have created more wealth than simply buying and holding. Here is an illustration. As many of you know from looking at your investments, the stock market is at the same price levels that were seen in 1997-98. So if you bought the stock market (SPX) on 9/15/98 @ 1038 it would have lost 13.7% if you sold your investment on 3/15/03 @ 896. Now contrast this to the "Buy" Fall / "Sell" Spring approach from Sep. 1998 to May. 2003. If you invested $10,000 in Sep. 1998, Oct. 1998, and Nov. 1998 for a total of $30,000 and sold 1/3 in Mar. 1999, and 1/3 in Apr. 1999 and 1/3 in May 1999, you would have made $7,032 on $30,000. This isn't a net figure because this total profit doesn't substract the cost of making 6 transactions (3 buy, 3 sell) nor does it include any dividends which would affect the investment's total return nor does it deduct any amount for taxes due. But for the sake of this illustration, it shows you would have captured 23% in 6 months without thinking or worrying. Now if we apply the same rules to the subsequent years, the results are displayed in the table below. In summary, the "buy & hold" approach lost 13% while the seasonal approach made almost 23%. A difference of 36%, or more importantly, you didn't lose any money even if you factor in giving the federal income tax on capital gains.

Now let's factor in all costs, disbursements, and taxes. If you were to select a no load S&P 500 indexed mutual fund then there wouldn't be any transactions fees or costs. So in the example below the prices of the oldest SP500 indexed fund were used - the Vanguard's group, VFINX. In the simulation, all transactions took effect on the 15th of the month or the next business day. All disbursements were reinvested, which include dividends and all captial gain payouts. With regards to the Annual return, this represents buying $30,000 on the 15th and selling it the following year and day later so that these transactions qualify as long term investments under federal income tax rules. One year or less is defined as short term by the IRS. Also note that the captial gains tax rate has changed over the simulation and for those investors that hold their investments for 5 years the tax rate is even lower, which is currently at 8%. Also at this time, all dividends are subject to the same income tax rate as wages, but reinvested dividends captial gains are subject to capital gains tax rates. Total disdursements were $686, $472, $280, $406, and $501. The gain or loss for the year on these disbursements were $55, $7, -$51, and $50. Since these were such small amounts and the drop in long term captial gains rate was in effect for only two of the five years, the simulation applied the long term tax rate to the total amount despite this inaccuracy. Plus, the only year that the tax rate change had any impact is during the current year of the simulation which isn't final since we have to wait for Sep. 15, 2003. Even last year when the tax rate change began didn't affect the simulation because the strategy incurred a loss. So the drop in tax rate didn't affect the total return.

Notice how well the seasonal investment strategy worked compared to the buy and hold and flipping investments each year. This comparison shows quite convincingly that if you are an investor who wishes to invest in the stock market, the clear way to reduce your risk is to use the seasonal investment strategy. Even if your concerned about increased transaction costs and taxes, you're money will earn more and you'll make more money if you buy and sell during these six months. By taking your profits out of the market during the riskiest time of the year, you are better able to buy low and sell high more consistently and make more money.

Just look at the facts. If you tried to stay in the market to avoid paying taxes, you lost money over the past 5 years. And if you waited so that the investment could benefit from a lower long term tax rate your profits disappeared with every one elses who waited to for the same tax break. This thinking cost you $5,000 in gains over 5 years and after taxes you lost money instead of gaining money. So, bonds would have been a better choice rather than thinking you'll hang on to the investment until you qualify for a lower tax rate.

Lastly, what lesson can you walk away with from this simulation? You couldn't have made a million dollars unless you won the lottery, or got lucky and picked one stock in which prices went to the moon. The fact is that over the past 5 years if you could have bought at the January 1998 low of 912.83 and sold at the March 2000 high of 1553.11, $30,000 would be worth $51,043 without any disbursements, barring any transactions costs, and no taxes were paid. But if you invested in the Mutual fund the $30,000 would have grown to $50,519 including all reinvested disbursements. So the first lesson is that there is a hidden cost of  $524, which is called the management fee. But if you would have purchased stocks yourself the transactions costs would have been much greater, so buying the mutual fund was the only way to go. (Today, this transactions costs are lower and there are newer investment vehicles to consider. So you could buy all of the top 500 companies in the SP500 for a single transaction fee of only $10 or less and owning the SP500 directly versus owning an Sp500 Mutual fund is better. SPY is an exchange traded fund or EFT. It is a stock that you can purchase that represents owning the SP500.) Second, your original 348.311 shares grew in value to $49,122.30 with the remainder $1,397 due to reinvested disbursements. Out of the $1,397, $966 were the acutal disbursements. So if you were a guru you could have potentially realized a $20,000 gain on you $30,000 investment. Then you could have invested the $50,000 in a 10 year US bond @ 6.2%. So would be earning $3,100 for the past three years. This brings your total net worth up to $59,819. And if you parked your semi-annual interest payment into EE savings bonds your $9,300 would be worth $10,006. So the absolute best gain you could have amassed using stocks and bonds was $60,525. So the smartest investor had a chance to double their money.

What does that say about investing? If you can double your money - take it! Our seasonal strategy only produced $6,938 which is still quite good considering the losses most investors incurred. This means if you can make 10% per year, take it and run. That would have amounted to $3,000 per year or $15,000 over the last 5 years. So don't be greedy. A little bit each year is a lot easier on your emotional state rather than waiting for the "grand slam" or hoping for higher prices. Remember if you were a guru, you could have made only 20% on average per year not 50% or 100%. That's it. So if you settle for half of that you still ahead of most investors. As the evidence shows most investors lose money and at best earn 5% over the life of their investments. So the next time you're looking a 20% gain, maybe you'll take it pay the taxes and wait for another opportunity. In the end, it's better to take your profits and pay the taxes rather than waiting for a lower tax rate while you watch your profits slip away. And finally, remember that even the smartest investor only made 20% per year over the last 5 years.

So why is it that the stock market has this seasonal cycle? If one were to attach a reason for this, the stock market's response could be as simple as our basic perception of these seasons or it could also be as perverse as we generally don't have any money to invest. Most families are paying large tuition bills in the fall (college and private education). If we just say that the cycle of spending money begins in the fall with the tuition bills, it is quickly followed by the home improvement season and then it's followed by the holiday seaon. Then in the spring, its the financial season - taxes are due in April. In addition, we think in terms of a calendar year and many investors buy and sell their investments in December and in January. Lastly, in the spring companies report how well they did during these seasons and stock prices are bid higher when people have recovered from the spending season and have some money to invest.

Springtime couldn't be better timing for "Wall Street". They're in the business of selling stock and so their brokers are in full swing searching for eager investors. In addition, "Wall Street" firms convince companies to sell more stock to the public. This increases the supply of stock and now the brokers have more incentive to sell stock because their firms must get rid of the additional supply they just created. The odd coincidence that prices seem to rise when the supply of stock increases is contrary to the economic laws taught in high school and college. More supply is suppose to equate with a decrease in prices, but that isn't what's happening. What if the public doesn't know that the supply is increasing and the army of brokers trained to sell stock is effective in their goal? They are in effect artificially increasing demand while their brokerage firm is "pushing the stock" and when the brokerage firm has accomplished its goal of "unloading" the additional supply they created, the brokerage firm retreats its army of brokers from this stock and moves them on to another stock. The consequence of this is that the stock's demand dries up and prices drop. Of course, if the brokerage firm isn't successful at finding buyers for the stock the price will drop sooner than later, but this scenario is all too common and that's another reason why prices tend to rise in the spring. In summary, the springtime is when "Wall Street" times the offering of new stock to corporate good news just when investors get ahead of their bills, and gain a little extra spending money.

This overly simplitistic macro-economic view is by no means an economic certainty, but offers an elementary thesis for why the data displayed below occurs and why one should invest in the fall rather than in the spring. The fact that the Federal government fiscal year starts in October of each year also contributes to this cycle, but the beauty of this approach is that whatever the reason, known or unknown, proven or unproven, it doesn't matter since this has been the financial tidal flow for decades.

In 2003, this cycle was postponed due to the uncertainty of war and once the first shot was fired, the "Wall Street's" springtime cycle began in earnest. They increased the supply of stock in April and in May. It just started one month later. This means that the strategy outlined above should have been adjusted by one month. So if you had made that adjustment, the selling should have started in April not in March. Then you would have sold 1/6 in April, 1/6 in May, and 1/6 in June. So, in 2003 the original strategy cited above avoided losses but missed bigger gains. But remember that's what it is suppose to do. It's a simple investment plan that is designed to weather most storms. That's why the entry and exit are spit into three equal amounts. But think of this, had you recognized the one month delay in the springtime cycle of events and invested the other half of your investment dollars in March 2003, when the market made its low, and sold you investments in two installments, 1/2 in May and 1/2 in June 2003, then you would have changed the $418 gain into a $6,833.79 gain (not including dividends).

Remember you would have invested a total of $60,000 instead of $30,000 because you averaged down because you recognized the delay in the springtime cycle. Then you would have delayed the timing of the "sell" signal by one month and sold half in May and the other half in June instead of selling in thirds. Hindsight is great, but this illustrates to you that this strategy provides you the flexibility to alter the strategy if you see changes in the timing of the springtime events. The point is you can stick to the basic strategy or you can take advantage of opportunities when they arise. This strategy gives you that flexibility because you didn't invest all of your money. This not only gave you the ability to invest more at lower prices but it gave you the comfort zone to enable you to invest more when the opportunity appeared. You were positioned to take advantage of unfortunately economic conditions and make more money as a result of your planning.

Perhaps you can now better understand what the peaks and troughs of the blue line illustrate. But if we were to alter the seasonal trade by making trades in the fall when the net number of up/days is at or near a cycle low after reaching a non-random +16 condition then the trade in 2000-01 would have been avoided due to the fact that the net number of up/down days was near a cycle high and that high didn't reach the +16 non-random condition. In February 2003, another -16 condition occurred indicating that lower prices are in the stock market's future. But in addition to this condition occurring is the fact that this is the first time that a lower low wasn't simultaneously made. So in February 2003 a non-random condition appeared but it didn't coincide with the typical higher high nor with a lower low associated with the non-random condition +16 or -16. This is the first time is out of the last 11 non-random cycle highs or lows that this has happened indicating divergence.

Perhaps this is a signal of the bottom, but it is different than the state that appeared at the top. At the top, prices went higher while the market didn't confirm a non-random state. This means that the higher prices occurred randomly and there was no statitistical support for these higher prices. There was divergence in that stock prices went higher despite the fact the lack of a non-random condition appearing at the very top. In February 2003, the opposite has occurred. The market has demonstrated that it has gone down in a non-random fashion, but the market didn't confirm this down leg by making lower lows. In the previous 10 out of 10 non-random condtions higher highs and lower lows accompanied this condition. So this is something new and different which makes this occurrence special. Hopefully, some day soon the stock market will again reach the +16 condition with higher prices to confirm the stock market's new direction. Until then, capital preservation supercedes all else. Basically, don't lose money until the roads signs show an all clear ahead. Currently, the seasonal trade is on track to break even (Sep. 2002 @891, Mar. 2003 @896), but then get out and wait for next fall (2003). But if the trade doesn't break even (current buys @ Sep.891, Oct. 860, Nov. 909. Average Price 886.7), at the very least raise your stops to prevent losses. However, until proven otherwise, the current statistical evidence for the stock market's behaviour is non-random and it's pointing down.