what we do

Our focus is on the development of proprietary geodesic models that characterize the behavior of leveraged long/short ETFs in pairs trades using first principles of Hamilton-Lagrange-Euler mechanics. Because of tracking errors & daily compounding phenomena, equal weightings of leveraged ETFs in a pairs trade are virtually never 50-50. Daily data & graphics will show subscribers where neutral pair weightings have moved along the path of the pairs geodesic thereby providing multiple market direction & re-balance indicators.

blog archive

Thursday, April 30, 2009

SDS-SSO Model Update - April 30, 2009

Dear Blogger,


thank you! again for subscribing to the S&P 500 long/short ETF Model and welcome to new members who just joined and new list subscribers. today's analysis is available for download:

SDS-vs-SSO-20090430_subscriber.xls.zip - (or feel free to browse the directory.)

ignore the missing data error message that may pop-up when opening up the file. Excel for Windows looks for metadata that Excel for Mac doesn't generate.

if you ever misplace your login, send me a message using the email you originally provided when subscribing through paypal.

visit the blog for an archive of all subscriber updates and alerts. the archive is search-able and comments can be posted by everybody.
Today's Commentary

today the S&P 500 index finished just about even after almost making it to the stratosphere before pulling back from 888 around the time it became clear Chrysler put the final touches on their fed supported bankruptcy filing in New York. the S&P 500 index closed at 872.81. the major market indexes in general seem to be defying logic & gravity going into finishing yet another week of positive gains tomorrow since the MAR-6 low. (see below)

SnP-500_weekly_20090430.png


if you are aggressive, be very cautious here because market sentiment can change in a blink of an eye. on the other hand, if sentiment does appear to change for the worst and investors start running for the exits, think twice about selling all your long position. they often seem to all of a sudden change their their minds and reverse direction. if you can, hit up seekingalpha.com's home page from time-to-time tomorrow. their quotes are not as delayed as others if you don't have real-time access to level-1 market data.

if you are neutral or near neutral weightings for SDS & SSO, you should be in pretty good shape to ride out the volatility. i'll send an alert if i think the market is setting up for a rapid transition. again, make sure you refresh yourself with the most current neutral for SDS & SSO to keep a gauge on your next move if the market takes a sudden turn south (or north for that matter.) re-balance if you need to with enough time to spare before 2 PM EST tomorrow. i say 2 PM because lots of daily counter-trends to an otherwise uneventful trading day occur around this time + or - 30 minutes.

this weekend i'll have the first of many updates on portfolios tracking the neutral and aggressive scenarios.
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Wednesday, April 29, 2009

SDS-SSO Model Update - April 29, 2009

Dear Blogger,

  • thank you again for subscribing to the S&P 500 long/short ETF Model and welcome to new members and list subscribers.
  • SDS-vs-SSO-20090429_subscriber.xls.zip is available for paypal subscribers to download - ignore the missing data error message that may pop-up when opening up the file. Excel for Windows looks for metadata that Excel for Mac doesn't generate.
  • if you ever misplace your login, send me a message using the email you originally provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts. the archive is available to the public, is search-able and comments can be posted there as well.
Today's Commentary

polarity has switched back biased toward SSO. not surprising. look at the chart in the spreadsheet. the behavior of the market has been back and forth for the past 2-1/2 weeks. also, yesterday we had a re-balance signal which has also been back and forth with the market. i updated the backtest data for both neutral and ultra scenarios to accurately reflect these frequent vacillations.

take a look at the weights of your ETFs and evaluate whether you need to make any changes. the market has vascillated so much recently that it's deen difficult to make gains for reasons illustrated in yesterday's commentary. this "deflation" market recovery off of march's lows is defying gravity right about now. stay attentive and refrain from knee jerk reactions to the news in the mdeia. the market is very bull-headed at the moment and seems nothing is bad news anymore. this sentiment too will change.

i'm still looking into making final tweaks to go into the anlaysis of the model for the 2.0 release. i'm looking forward to completing this process by next monday.

cheers and
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Tuesday, April 28, 2009

SDS-SSO Model Update - April 28, 2009

Dear Blogger,

  • thank you again for subscribing to the S&P 500 long/short ETF Model and welcome to new members and list subscribers.
  • SDS-vs-SSO-20090428_subscriber.xls.zip analysis for paypal subscribers is available for download. ignore the missing data error message that may pop-up when opening up the file. Excel for Windows looks for metadata that Excel for Mac doesn't generate.
  • if you ever misplace your login, send me a message using the email you originally provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts. the archive is available to the public, is search-able and comments can be posted there as well.
Today's Commentary

1) looking at the charts in the spreadsheet and you'll see that there has been bias change from SSO to SDS. also, the PID re-balance indicator crossed the x-axis.

hence:

  • consider re-balancing your pair tomorrow if your neutral.
  • consider changing the polarity of your pair bias towards SDS if you are aggressive.

2) the markets gave up another lackluster of a performance in the broad indexes today. we're still just drifting in a no-man's land. as i mentioned in the previous EOD commentary, another PID model i'm looking at possibly superseding the current one has NOT crossed the x-axis. i'll keep you appraised of the changes here in the commentary for a while.

the polarity change signal however has not been altered and this signal should be looked at closely over the next few days. the chart shows this is about the 4th attempt in the last 3 weeks the polarity has tried to change. the first 3 attempts we unsuccessful. this is all characteristic of trading range performance.

the market likes to play head fakes and cry wolf. i am attempting to mitigate these psychological factors with a sound model. the current re-balance signals aren't making it easy to accomplish this. this is why i'm looking at another source of data but doing the same analysis to come up with a new PID tuning algo.

3) today i initiated 2 pairs trades in my brokerage account to track actual trades to compare against the models back-testing results. 1 pair is neutrally balanced according to model signals and the other is an aggressive scenario following re-balance and polarity change signals. i will include an overview and summary of the results each weekend.
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

SDS-SSO Model Alert #1 - April 28, 2009

Dear Blogger,

so far, the market's haven't been able to escape a trading range (no-man's land) that started April 9th in the S&P 500. see below a chart for SSO from APR-9 to today.



today, we're right smack in the middle of the range for SSO and i see no sign of it breaking out of the range today. from top to bottom, the amplitude for the range is about 12% for SSO and somewhere close to 6% (minus slippage & what not) for the S&P 500.

the SDS-SSO arbitrage model uses 12 trading day MA's in the analysis which is virtually the same period of time as this no-man's land. one good thing about moving averages is snap judgements are curtailed and numbers are easier to work with.

one not so good thing about moving averages is it's difficult to make sense of things on a daily basis when markets fluctuate at the same period or frquency as the model uses to average various pieces of data. but as long as the amplitude of prices variations stays relatively small as it is now, the model will do a decent job at averaging out performance.

this is not an alarm for liquidation or other drastic measures. just an observation for awareness.
best regards,
mike james


Managing Member
Equity Informatics,LLC.
phone:302-220-3864

Monday, April 27, 2009

SDS-SSO Model Update April 27, 2009

Dear Blogger,

  • thank you again for subscribing to the S&P 500 long/short ETF Model and welcome to new members and list subscribers.
  • SDS-vs-SSO-20090427_subscriber.xls.zip is today's analysis for paypal subscribers. please ignore the missing data error message that may pop-up when opening up the file. Excel for Windows looks for metadata that Excel for Mac doesn't generate.
  • if you ever misplace your login, send me a message using the email you originally provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts. the archive is available to the public, is search-able and comments can be posted there as well.
Today's Commentary

today's trading in the S&P 500 was rather lackluster. perhaps the pig flu had something to do with the performance. the model still indicates a bias to SSO so follow closely over the next few days if the model changes polarity.

in typical fashion, i'm always looking for improvements in the model. over the weekend i spent some time using different source data to calculate the P's, the I's and the D's in the control loop. i found some interesting things and will be watching how this variation compares with the current PID algo.

also i will be creating some new portfolios in one of my trading accounts to follow a neutral scenario and an aggressive scenario to a "T" and will publish the results on a weekly basis as a weekly wrap-up update. up to now, my model trading has been mixed in with other trades of other assets and has been difficult to isolate the pairs trade performance by itself w/o a whole lot work.

besides the pig flu, nothing else i see has fundamentally changed the market sentiment. i think government GDP numbers come out this week so they could be game changes. if so watch for an alert.
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Saturday, April 25, 2009

SDS-SSO Model Update - April 24, 2009

Dear Blogger,

thank you! again for subscribing to the S&P 500 long/short ETF Model and welcome to new members who just joined and new list subscribers. today's analysis is available for download:

SDS-vs-SSO-20090424_subscriber.xls.zip - (or feel free to browse the directory.)

ignore the missing data error message that may pop-up when opening up the file. Excel for Windows looks for metadata that Excel for Mac doesn't generate.

if you ever misplace your login, send me a message using the email you originally provided when subscribing through paypal.

visit the blog for an archive of all subscriber updates and alerts. the archive is search-able and comments can be posted by everybody.
Today's Commentary

House cleaning

the first thing i need to get out of the way is i nixed the '60s psychedelic theme in the beta 2.0 spreadsheet release. i thought the color coded column names matching the color of it's corresponding chart line would be a nice usability feature. the next day i opened the file and said NOT. so i came up with a more aesthetically pleasing and professional color theme matching the color of the new company logo i created. that too will probably get updated but it will probably stay roughly the same color. i hope you like it.

Overview of the market

ok, this week's stock market performance was interesting to say the least. as i have posted previously, we have been in a trading range from Apr-9 when the S&P 500 closed at 856.56 to friday's eod close at 866.23. the intraday high in-between this period was 875 on April-17 and the intraday low was 823 on this past tuesday Apr-21. this suggests to me that buyers got cautious after the index has run up so high and so fast from the 666 low on Mar-9. and the bears have gotten their shorts squeezed so they had to cover early on but weren't willing to begin selling later due to the high volume of buying. the index could have gone either way this week and euphoria won out over pessimism.

on last night's show, jim cramer said it's the mutual funds getting back into the game, not the hedge funds, causing the buying frenzy. this may or may not be true but even if it is, i have to ask "what's the thesis for all the giddiness into the 7th week of market recovery?" one possibility could be the market really thinks 6 - 9 months from now the economy will start showing signs it's working it's way out of the recession. another thesis could the market got so sold off that equity valuations were just too enticing to let go by, even up to friday's close. another thesis is regardless of the state of the economy, the fed and the treasury are on the mark with saving the over-leveraged banks and liquidity is unfreezing the credit iceberg.

there are other plausible theses, but i think it's sort of a combination of these 3 above. the markets did get too over-sold. a snap-back was over-due. earnings and guidance from some big banks, tech and industrial companies beat estimates and projected somewhat rosy guidance for the year. quantitative easing by the fed has given confidence and leadership around the globe. but all this good news may be a little over-rated after the 5th week of the run-up. are these signs of an emerging and imminent bull market? i don't know. i do know that regardless of the direction the stock market takes, we can still profit.

What the model is telling us

the model says, as i started off from above, we are in a sort of "no man's land" particularly for aggressive users of the S&P 500 Index Arb Model. no man's land in this instance is a region where PID vacillates close to zero. this movement is accompanied by several crossings through zero which is our indicator to re-balance the ETF pair to neutral weights or for aggressive users to change their weightings bias from one extreme to another. non of this type of vacillating movement generates profits for aggressive users. for delta neutral users, the motion is a bit of a nuisance but no big deal one way or another. see the green line on the chart below.

benchmark_performance_090403.png

the model generates profits when PID is on either side of the x-axis. the coefficients i have chosen for the model provides the above characterization. remember, the x-axis is like the fulcrum point of a see-saw. the longer PID stays above or below zero, the more time we have to accumulate gains. the same is true of the magnitude of PID. the greater the absolute value of PID, the rate of gains increases. so time and value are important to making gains using this model. if time is short and the magnitude of PID is small between transitions, the less potential to make gains. the behavior describes a see-saw or a swing that is oscillating ever so slighlty about equilibrium. not much potential for fun for anybody.

the mechanics of the model is based on classical mathematics used to derive equations of motion for a system of two point masses or two solid bodies in coupled oscillation with respect to one another. in this case i have used calculus of variations and my own variant of the hamiltonian equation to derive a long/short ETF dynamical relationship. finally, the key to completely describe the system is assuming a set of boundary conditions (such as sliding versus rolling motion for example) and a method of integration to solve the equation of motion. once an engineer has the equation of motion for a system, theoretically the engineer has enough information to control or stabilize the systems motion. thus, there is yet another level of control we can pursue which is a pre-set rate of return using our paired ETFs. this may come as a special update or in a new version release of the model.

bits and pieces of this discussion and other details will be background for a users guide i am writing for these ETF models. i understand the concepts behind the model may still be a black-box but stay tuned for future alerts and updates with more illustrations to fill in the blanks.

what action should be taken now?

aggressive users should maintain a significant over-weight to SSO and significant under-weight to SDS. i let you decide that percentage based on your tolerance for risk. be alert though because changes can quickly ocurr as we've seen recently.

users wanting to stay in the ETFs but remain neutral, make sure you re-weight your pair on monday using the neutral weights specified in the spreadsheet that were calculated for yesterday, friday APR-24.

comments and questions are encouraged.

best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Friday, April 24, 2009

SDS-SSO Subscriber Alert - April 24, 2009

Dear Blogger,

buyers are out in force today. based on the market action this week and the model data, i'm calling for a re-balance.

if you're neutral, re-distribute your weightings as best as possible accordingly:

SDS SSO
0.5390 0.4610

if you are aggressively positioned, re-polarize to be biased to SSO and no longer SDS.
best regards,
mike james


Managing Member
Equity Informatics, LLC
phone:302-220-3864

Thursday, April 23, 2009

SDS-SSO subscriber update - April 23, 2009

Dear Blogger,

  • thank you again for subscribing to the S&P 500 long/short ETF Model and welcome to all new members that just joined. the latest analysis is available for download. click here to browse the directory or click the link below to download just today's update.
  • today's filename is: SDS-vs-SSO-20090423-subscriber.xls - ignore the missing data error message that may pop-up when opening up the file and click OK. there are no macros in these spreadsheets but it would not hurt to virus scan the file before you open it.
  • if you ever misplace your login, i can send your info if you email me a message from the original email address you provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts. the archive is searchable and comments can be posted as well.

Today's Commentary

the bulls managed to drag the S&P 500 index up today by almost 1%. to me the market has become "irrationally exuberant" as alan greenspan put it in the late 1990's. but the model doesn't care much about psychology and we need to pay attention to what it's telling us.

the model still says we are in a relative "no-man's land" but probably not for long. i say relative to mean relative to where it's been in the last 6 - 8 weeks or so. the S&P 500 has closed up for the last 6 straight weeks which it hasn't done since since the beginning of 2007. so far this week we are down just over 2%. so tomorrow's trading will be interesting to say the least.

(S&P 500 weekly)



i also might add the S&P 500 has been range bound since Apr-09-2009. so stay put for now as we have been all week and watch what happens tomorrow to see if we can break out of this range one way or another.
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Wednesday, April 22, 2009

SDS-SSO subscriber update - April 22, 2009

Dear Blogger,

  • thank you again for subscribing to the S&P 500 long/short ETF Model and welcome to all new members that just joined. the latest analysis is available for download. click here to browse the directory or click the link below to download just today's update.
  • today's filename is: SDS-vs-SSO-20090422-subscriber.xls - ignore the missing data error message that may pop-up when opening up the file and click OK. there are no macros in these spreadsheets but it would not hurt to virus scan the file before you open it.
  • if you ever misplace your login, i can send your info if you email me a message from the original email address you provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts. the archive is searchable and comments can be posted as well.

Today's Commentary

as i indicated on my seekingalpha instablog, the bears managed to lower the market in the last hour of trading today. i think the selling caught buyers by surprise. the market sold off mid-day after a decent run-up from negative territory and then rallied higher by mid-afternoon when the selling started again. the s&p 500 went down in the afternoon as fast as it went up at the opening.

(chart of the S&P 500 intraday)



from my limited perspective, i don't see anymore catalyst for the rally to continue since the mar-09 lows. buyers seem to be desparate to drive up stock prices higher in the face of terrible economic news in the short & long term. the rally has been a nice relief but nothing goes straight up or straight down. i believe we are still in an overall declining market scenario.

the chart below shows, on a daily basis, the s&p is bouncing around it's bollinger band mid-point. this is as good as any signal to sell. volumes have been increasing since apr-9 or so. a couple more days of choppy markets will probably break the will of buyers spirits.

(S&P 500 on a daily basis for 6 months)

benchmark_performance_090403.png

from the model point of view, the PID value is still positive but only slightly so. the polarity chart in the analysis is showing signs of switching bias to faster relative daily growth of SDS compared to SSO. in the past several weeks, bias has approach the switching point and backed off 2 other times. we're at the same point and i expect by friday we'll see a new market direction change.

we're still in the proverbial "no-man's land" so i wouldn't be looking to change any positions in the pair until we know for sure where the market is going after the next couples of days. so basically stay put and wait for the market to change before adding any new money to the pair or re-balancing.
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Tuesday, April 21, 2009

SDS-SSO subscriber update - April 21, 2009

Dear Service Subscriber,

  • thank you again for subscribing to the S&P 500 long/short ETF Model and welcome to all new members that just joined. the latest analysis is available for download. click here to browse the directory or click the link below to download just today's update.
  • today's filename is: SDS-vs-SSO-20090421-subscriber.xls - ignore the missing data error message that may pop-up when opening up the file and click OK. there are no macros in these spreadsheets but it would not hurt to virus scan the file before you open it.
  • if you ever misplace your login, i can send your info if you email me a message from the original email address you provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts. the archive is searchable and comments can be posted as well.
Today's Commentary
this will be short because there's some thunderstorms on the east coast. internet connection got cut once already composing this message.

today's reversal of yesterday's pullback should be taken in stride. the market is frenzied right now and nobody has a reasonable chance of telling what the market is going to do from one hour to the next. expect this type of choppy trading for a few more days. ofcourse when the week is over, we'll have a better sense of general market direction.

the PID re-balance indicator is back in positive territory. don't get all excited about this. the indicator has limited foresight. the derivative term in the PID controller may give a fuzzy clue which way the market was headed when the market closed. unfortunately the dervative data is very discontinuous and any smoothing just makes the signal lag instead of lead.

i think it would be a fools errand to be aggressive at this point. stay cautious by staying neutral. given the choppyness around no-mans land, i would consider waiting til friday to re-balance unless there's a significant move in the market in either direction in the next two trading sessions.




best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

S&P 500 Index model alert - April 21, 2009

Dear Service Subscriber,

with the market waffling around like it is, we're in a kind of no-man's land again. especially for aggressive investors/traders, being light on the throttle at this point is probably a wise disposition to maintain. in the past i issued an alert with a chart i entitled statistical process control chart. there was a region of the re-balance indicator chart which plotted out + or - 1/2 of 1 STDEV of the re-balance indicator values superimposed along with the indicator signal. i will probably re-visit that analysis and submit a recommended aggressive trader's no-man land spec to watch for.

see http://squark62.blogspot.com/2009/04/sds-sso-subscriber-alert-april-12-2009.html
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Monday, April 20, 2009

SDS-SSO subscriber update - April 20, 2009

Dear Service Subscriber,

  • thank you again for subscribing to the S&P 500 long/short ETF Model and welcome to all new members that just joined. the latest analysis is available for download. today's filename is: SDS-vs-SSO-20090420-subscriber.xls
  • if you ever misplace your login, i can send your info if you email me a message from the original email address you provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts. the archive is searchable and comments can be posted as well.

Today's Commentary

the spreadsheet now contains only PID neutral and aggressive scenarios for the SDS-SSO model. i'm still filling in the gaps in terms of formatting the data and generating charts right from the data in the spreadsheet. i've inserted graphics objects exported from the master spreadsheet so you have the latest visuals in the meantime.

i'm calling this release beta 2.0 indicating all performance scenarios are compiled using PID controls as the primary indicator for re-balancing. the model has indicated a re-balance on APR-16 when PID crossed from positive to negative. the previous tuning chart showed PID right at zero on APR-17. after double checking the data source fields i realized i did not have the x-axis dates matched with the right row of PID data. sorry about that. we have been in bear territory since last thursday.

as usual the neutral weights are included in the spreadsheet so you can decide which way you want to balance your pair relative to neutral. once i get your spreadsheet situated, i plan to pick up where i left off on a list of tasks i want to complete indicated in a previous update earlier this month. one more task i want to include in the users guide task is a section on how i use my model at 2 different online brokers. Interactive Brokers is one which is typical of most. FolioFn is the other broker which offers a proprietary trading platform in addition to being able to trade using limit orders, stop loss etc. both brokers are very efficient at executing orders and i use them both to manage SEP-IRA accounts of mine using the very same models you subscribe to. but using the FolioFn proprietary trading platform offers unique synergies.

as usual, be cautious and let's see what happens to the market this week with timothy geitner on-deck tomorrow to shake the markets one way or another. this whole thing with the TARP and stipulating conversion of bank shares the governments own from preferred to common is another game changer mid-stream making the market uneasy with how to interpret what the government intends on doing. a slew of earnings are getting posted this week and some interesting M&A continues in the pharma & the tech universe.
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

Sunday, April 19, 2009

SDS-SSO subscriber update for April 17, 2009

Dear Service Subscriber,

  • thank you again for subscribing to my online equity information service. the latest S&P 500 Index Arb Model analysis is available for download.
  • if you ever misplace your login, email me a request from the original email address you provided when subscribing through paypal.
  • visit the blog for an archive of all subscriber updates and alerts.
Today's Commentary

this will be short since i've sent out multiple alerts between friday and today. watch for possible S&P 500 market direction changes from bull country to the bear den. the last alert i sent today showed how the PID control algorithm indicated the S&P 500 is right at equilibrium (the fulcrum point of the see-saw) and pointing downward steeply. so tread cautiously and wait for a confirmed re-balance indication in an update perhaps as soon as this week.
best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

SDS-SSO PID alert April 19, 2009 1532 EST

Dear Service Subscriber,

First welcome new members of the SDS-SSO pairs model distribution list. from time to time i send out information bulletins such as this one. today i am continuing to discuss the concept of optimizing my ETF pairs model using a PID control loop i recently wrote.

P stands for proportional, I stands for integral, D stands for derivative. without going into a lot of theory, engineers develop code to keep a system or process of some sort at equilibrium or at a particular set-point. a thermostat in a car or house in most instances uses a PID control loop to maintain a particular desired temperature in side the house or water line to keep an engine cool. a sensor measures the parameter of a process that is being set to a particular limit. when the process reaches that limit, the PID controller switches on and begins to govern the process to reduce the error to within specified allowable deviations.

once the controller is on, the error is feedback into the process input signal and the controller calculates how much to adjust the input signal to maintain control. in the case of a PID controller, the error is broken down into 3 components - a proportional error, and derivative error and an integral error. the proportional error is a measure of how much the process is out of balance directly proportional to the ideal or set-point value. the derivative error is a measure of how faster the process is moving out of control. the integral error is an additive quantity that always increases in value until the process is in control. then it is reset to zero.

when everything is stable or at equilibrium, the sum of the error components is zero (0) even though one or more individual components are non-zero. the tuning chart below illustrates the concept. think of 2 children playing on a see-saw going up and down, up and down. when one child is at their peak, this event represents one of the peaks or troughs of the PID value in the chart. when the other child on the ground starts to push up, the former child begins to descend until both children are at the same height off the ground. if the children have the same mass and are equi-distant from the fulcrum, that brief moment constitutes the equilibrium point for this system or process. that point is where the PID sum crosses the x-axis of the chart below. and the cycle repeats itself.

the driving force in the see-saw example is the change in momentum imparted on the system by one of the children pushing up off the ground at their lowest point. the driving force in the SDS-SSO model is the inverse relationship between the 2 ETFs as the market changes tick-by-tick. another facet to point out is that both ETFs don't have the same momentum at every point in time even though one would assume so based on the thesis of 2x up must equal 2x down.

this imbalance can be compensated for a couple of different ways. with respect to the see-saw example, the imbalance can be compensated for by adding a weight to the center of gravity of whichever child is the least massive. the other method of compensation would be to have the heavier child move in closer to the fulcrum point which would reduce the amount of leverage this child has over the other child. then the see-saw will tilt back to even.

in the case of our ETF scenarios, i measure the small differences in leverage and adjust the weights or the amount of money in one ETF or the other. and the PID controller enables me to compensate to maintain equilibrium in one case (the neutral scenario) and exploit these differences in the other case (the ultra aggressive scenario.)

as you can see, the PID value is right about at zero as of Friday the 17th. the system could stop on a dime and stay right here or bounce right back up back up. both of these possibilities have happened recently in the chart. i do my best to tune the model so false re-balancing signals don't happen but the market does what it wants to do.


benchmark_performance_090403.png

one more criteria needs to be considered to polish off the ultra aggressive scenario. the chart below shows the percent daily rate of change for each ETF. notice how the 2 signals cross each other and change polarity. to exploit the imbalance as i described above, the ETF with the highest weight has a polarity of > 0 or a bias to the upside. normally bias changes are co-incident with equilibrium changes (criss-crosses.) sometimes bias changes occurr after an equilibrium change and before the next event. this means a local extremum occured mid-cycle. this can be illustrated by using a elevator analogy. elevators our counter-balanced with weights and cables. suppose you enter the elevator at ground level and push the button for the floor at the top of the building.

before you get to your floor, someone on a floor 2 floors below the halfway point pushes the button to go down. prior to stopping to open the door to let the other passenger on board the elevator, the elevator and the counterweights are both moving toward each other. before the elevator and the counterweights pass each other at the same height, the two stop to let the other person board. but instead of going up first to let you off, the elevator skips this step and goes back down to let the other passenger off first. the level where the other passenger got on the elevator is like a local extremum. so in our example, the bias changed from going up to going back down before the elevator and the counterweight crossed each other at the mid point.

benchmark_performance_090403.png

again, i'll create a more concise illustration of these concepts by annotating these charts in time as events occur. look for an update email to go out this evening with the latest weightings and scenario performance updates.

best regards,
mike james

Managing Member
Equity Informatics, LLC
phone:302-220-3864

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