Trading Model Construction: Tracking the S&P 500

Step 3. Make Observations

When scrolling through my database I have noticed that the S&P 500 tends to run in streaks. That's to say a positive day is likely to be followed by another positive day until that streak ends. Similarly, down days tend to be followed by down days. Furthermore, since the S&P 500 is up over time, I have to conclude that two things:

1. There are more up days than down days and/or...

2. The magnitude of up days is greater than the magnitude of down days.

Step 4. Develop Calculations

This is my favorite step: torture the data.

The hypothesis (step one) and observations (step three) present many questions which we will need to look into. This can be an iterative process, whereby questions beget new observations, which then result in further questions.

Question 1: What is the distribution of up days and down days?

Result: For the period under review (1950 - 2007), there were a total of 14,592 trading days. Of those days, 7,817 (53.57%) were up days and 6,775 (46.43%) we down days

Question 2: What is the magnitude of up and down days?

Result: On average, when advancing, the S&P will be up 0.61%. On average, when declining the S&P will drop 0.63%.

Step 5. Define the Trading Rule

With the magnitude of up and down days roughly equal and the quantity of up days far exceeding that of down days, let's revise the hypothesis (step one) in order to define a trading rule.

Here it is: If the S&P advances for the first time in a row, hold it until the S&P declines.

Step 6. Back-Test & Step 7. Determine Whether the Model Makes Money

I went back to my database and created this table:

DAYS IN STREAK	OCCURRENCES	RATE OF CONTINUATION	AVERAGE RETURN NEXT TRADING DAY
1	3332	N/A	0.25%
2	1963	58.91%	0.20%
3	1122	57.16%	0.14%
4	611	54.46%	0.12%
5	345	56.46%	0.13%
6	196	56.81%	0.16%
7	110	56.12%	0.10%
8	62	56.36%	0.12%
9	34	54.84%	0.26%
10	20	58.82%	0.27%
11	13	65.00%	0.04%
12	7	53.85%	-0.22%
13	1	14.29%	0.12%
14	1	100.00%	-0.03%
15	0	0.00%	N/A
Source: LakeView Asset Management, LLC

By reading the results of the back-tested data, I can now determine if the model makes money.

This table is a back-testing of returns if you bought the S&P at the market close on a day in which it went up for the first time in a row and held it until the close of the day in which the index declined.

Here is how to read this table:

Days in streak. The amount of consecutive days that the S&P rose.

Rate of continuation. The frequency by which a winning streak was extended. For example, 54.84% of the time an eight-day winning streak extended to at least a ninth day.

Average return the next day. One-day streaks will return on average 0.25% on the following day (whether or not day two is up or down), two-day streaks will return -- on average -- 0.20% on the following day (whether or not day three is up or down) and so on.

As you can see from the data, if you catch a streak, you can pile up some nice gains. (If you are curious, the 14-day streak took place in April 1971. Had you traded this model then, the return for that streak would have been 3.54%).

Some observations from the table:

Up until a 12-day streak, the rate of continuation is greater than 53.57%. Thus, it appears more likely for the S&P to rise on subsequent days of a streak than on any random day.

If the average up day minus the average down day has yielded a -0.02% return, then waiting until a new winning streak begins will likely generate higher returns.

On average, we get at least one winning streak per year that lasts eight or more days. (The last streak of at least eight days was in 2004 and it lasted nine days).

Step 8. Determine Whether the Model Can Be Traded?

Clearly, as individual investors, it is not feasible to trade the entire S&P 500. Thus we have to look for a close substitute. The best proxy for the S&P would be one of its ETFs, such as the "Spyders" SPY or the Ultra S&P 500 SSO.

Homework Time

As you build your own trading model, your homework is to "paper-trade" the model above via the SPY or SSO.

Remember, before you put any real capital to work, test how well (or poorly) your trades would have performed.