Back-Testing the Robert Lichello Automatic Investment Management (AIM) System for Timing the Stock Market
89Many have said the most important purpose for investing is to make money. In order to make money we face two key decisions, when to buy and when to sell. Simply put, we must buy when prices are low and sell when prices are higher than the buy price.
The difficulty is in the implementation, our emotions work against us, when markets are rising there’s a jubilation that makes it very easy to join in and buy when prices are high and moving higher. When markets are low, it can seem like there is no bottom, the market will never bounce back, which makes it easy to follow the herd and sell low. Ideally, what we need is a system that will reduce the emotion of investing by automatically telling you when to buy, sell, or do nothing. In the late 1970’s Robert Lichello published a book titled “How to Make $1,000,000 in the Stock Market – Automatically” which presents a stock market timing system that claims to do exactly that. In this article we will briefly explain this system then back-test it to see if there is any credence to these claims.
What is AIM?
Robert Lichello named his market timing system Automatic Investment Management or AIM. AIM is an algorithm that provides a logical system for managing your investments. It can be used with a stock or mutual fund portfolio. This system will instruct you when and how much to buy or sell.
To calculate AIM’s buy and sell quantities you need to know two things: how much money you have invested in the portfolio and the current value of your portfolio. To illustrate, let’s run through a couple examples.
Example of a buy order:
Portfolio Control (Amount of initial investment) = 1000 shares @ $10 per share = $10,000
One month later the stock price falls to $8, Portfolio Value = $8000
Add 10% to the current portfolio value = $8800.
Subtract 8800 from 10,000
Which equals = $1,200
Note, a positive value indicates a buy signal.
Because the value of your investment has decreased AIM has signaled you to buy 150 shares, the equivalent of $1200.
One of the interesting features of AIM is each time that you buy more shares your portfolio control increases by half the purchase value. In this case, the portfolio control would increase to $10,600. This is a built in risk regulator that will stop you from exhausting your cash reserves when the market is going down or building too much of a cash reserve when the market is going higher.
Example of a sell order:
Portfolio Control (Amount of initial investment) = 1000 shares @ $10 per share = $10,000
One month later the stock price rises to $13, Portfolio Value = $13,000
Subtract 10% from the current portfolio value = $11,700
Subtract $11,700 from $10,000
Which equals = -$1,700
Note, the negative value indicates a sell signal.
Because the value of your investment has increased AIM is telling you to sell 130 shares, the equivalent of $1700.
In both cases AIM has you making the correct decision, buying when your portfolio value goes lower and selling when it goes higher. If AIM is strictly followed it can be used to take much of the emotion out of investing.
Praveen Puri's Blog on Using an AIM-Based Trading System
AIM in the Real World
So, does AIM work in the real world? To answer this question we will use historic stock prices and run the AIM algorithm through its paces. We will use historical prices of one of the most active exchange traded funds (ETF), The S & P Depository Receipts, stock symbol SPY. SPY is an ETF that tracks the Standard & Poors index of 500 stocks.
From January 2000 to the end of 2011 the SPY price history has ranged from $68.11 to $156.48. During this period there has been two downturns in the stock market, one 5-year period of increasing prices and of course the current price increases since March of 2009. So we can test AIM through a couple buying phases, at least one selling phase, and get a read on the current market.
Now, let’s look at the results of the back-testing which is summarized on the time series graph shown below. All buy and sell transactions are noted with yellow text boxes that show the month/year, quantity bought or sold and closing price at the end of that month. Additionally, buy transactions are denoted with red markers, sell transactions denoted with green markers.
Results of the Back-Testing
The first thing we notice is that the initial purchase of 68 shares on 1/3/2000 is very near where the market peaked in August of 2000. Then as the market fell for the next two years AIM had us accumulating a total of 77 shares over five distinct buy signals in March and September 2001, and June, July and September of 2002. During this buying phase, we used up 67% of our cash reserves leaving us with $3290 in cash "insurance" should the market continue to decline. Additionally, our number of shares has increased by 113% from 68 shares to 145 shares, more than doubling our "potential" increase in equity value when the market trend turns up. Assuming FIFO accounting our average price per share has been reduced from $143.80 to $120.46.
After the market bottomed in 2002, we experience a 5-year period of rising prices. During this period, AIM would have us selling a total of 44 shares at four distinct selling opportunities in February 2004, November 2005, October 2006 and May 2007. At the end of this selling phase AIM has us building up cash reserves to $9,409 and we are holding 104 shares. Average price per share is further reduced to $108.36.
From the market peak in October 2007 there is nearly a straight-line tumble until February 2009. During that freefall, AIM has us accumulating a total of 106 shares over five distinct buy signals in September, October and November 2008, January and February 2009. At the end of this accumulation phase AIM has almost depleted cash reserves to $1,448 and we are now holding 221 shares at an average price per share of $96.48.
Finally, as the market started to pick up from March of 2009 through December 2011 AIM issues 5 sell signals for a total of 64 shares in August and November of 2009, March and December of 2010, and April 2011. At the end of this selling phase AIM has us building up our cash reserves to $10,148 and holding 156 shares at an average price per share of $86.25.
Stock Software
- Investment Software to Find Undervalued Stocks
Used by Many AIM Investors.
Conclusions
In spite of the initial purchase being close to a market top, the overall portfolio performance is not bad. As of 12/31/11 the hypothetical portfolio consists of 156 shares of stock and $10,584 in cash reserves for a total of $30,162 or a gain of 50.8%. Employing a buy and hold strategy would have resulted in a total of $23,040 or a gain of 15.2%.
AIM appears to do a good job of inventory management and control as exhibited by our cash reserves increasing by 7%, our share ownership increasing by $129% and the average price per share going down by $57.55 or a 40% reduction. However, one risk came out during the second accumulation phase, we very nearly ran out of cash to buy more shares as we had only 15% of our original cash remaining.
During the two market downturns AIM caught both bottoms with buy signals, on the up side AIM missed selling at the 10/2007 peak leaving about $158 of profit on the table.
Overall the AIM system appears to do a good job of identifying key buy/sell points. If you are disciplined enough to act only when AIM tells you to buy/sell much of the emotion of investing can be eliminated.
If you are interested in obtaining the source data for this analysis in spreadsheet form, send an email to dougburkeaz@aol.com with the words “AIM Back-Test” in the subject line.
Assumptions for Back-Testing AIM
It is always necessary to make some basic assumptions when doing an empirical analysis, here is the list for this analysis:
1. Initial amount to invest in the stock is $10,000
2. Cash reserve of $10,000 for future purchases
3. AIM decisions are based on the closing price of the stock on the last trading day of each month
4. Buy or sell price is the open price of the stock on the 1st trading day of each month
5. Minimum buy or sell lot size is 10 shares
6. Stock trading commission is $10.95 per trade
7. Rate of return on Cash reserve is 2% APR
8. Dividends distributed into cash account, not reinvested
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A very good first Hub - I'm glad I inspired you to write on here, and hope to see a lot more hubs. This is a difficult subject to write about and you've tackled it well. The other thing you might consider is to add some links to other books, perhaps explain some of the other methods that are not quite as good...
If I had any money left I would invest!
If you had started in 1993, would there have been any buys as SPY tripled from 1993-2000? Or would AIM have sold holdings and missed on the climb?
When I looked at AIM when the book came out, my conclusion was that it was great for sideways markets (or a sideways stock), but not for trending markets/stocks. There were a lot of people that lost a lot of money buying tech stocks on the way down in 2000 -- stocks that went belly up.
A simple 200-day SMA with 5% tolerance (to reduce whipsaws) on SPY would have given you better performance over the 2000-2009 period (and probably the 1993-2000 period). And I'm not that fond of TA.
I found the article well written and a very accurate summary of aim investing. I further found that using s&p a more sedate entity very good as it portrays average stocks performance
the book actually suggests 80% stock and 20% cash
hi
i just discovered this Aim user site. i am dying to share this observation to Aim investors. The observation to increase your profit margin, is not to buy when the stock
price is falling. Buy when the portfolio contorl stop rising.They are an inverse process. When the PC is rising, the stock price is falling.
In the example,the porfolio contorl stop rising on 9/3.
you would enter the market at this point buying the number of shares that created the portfolio control to rise.
you would have purchased $6,542 worth of stock at $90.00.
This is also safe. I think the profolio control of a stock going to powder, will not give a buy signal for you to invest. your risk is your initial investment.
I hope you and your readers keep this discussion going. I like the ideas both about Lichello's AIM program and the conversation about market trends. I like your suggestion of using SPY as a benchmark for testing. I'm currently backtesting a combo of Trend Following/AIM to see where the best results would be. I encourage others to also research their ideas using the SPY as a benchmark so that we can all compare our results.
I believe the original Lichello allocation was around 1977 and he set it at 50:50 stocks:cash. He started out very conservative after the bear market maulings of '69-'70 and '73-'74. Later editions cahanged it to 2/3 stock 1/3 cash reserves, and finally 80% stock 20% cash reserves. Testing with SPY from 1993-2010 should give some insight as to what would most likely be the best all-weather allocation ratio. I hope to check back with you all in the near future.
Great article! I've used AIM many years ago on one of my mutual funds. I don't remember what happened but I stopped AIMing after some time.
Currently I'm using TA for trading. I'm wondering if anyone has tried to combine TA with AIM. For example, if TA tells me to sell everything, I'll go 100% cash, and then reaccumulate stocks on the way down using AIM. Buy/Sell dollar amounts can also be adjusted with TA readings in mind. I know it's tricky to fine tune a simple and elegant system like AIM without messing it up. Just curious if anyone has already done some studies on this.
Works better with high Beta stocks than low Beta Indexes. It's all about volatility as in most investments.
Great write up on Mr. Lichello's AIM. Do you know the pros and cons of increasing the the frequency of the buys and sells? It seems that you'd make more with a weekly or maybe even daily buy/sell but, are you at risk of depleting your cash reserve? It wasn't mentioned in the book as to why monthly was chosen over weekly or daily.
Also since Mr. Lichello has past away and can no longer be consulted on AIM, Who's the most authoritative on AIM and AIM research. thanks you for taking the time
hi all, i have been using the aim model for the last week and pulled in about $1500.00, around 4%. earnings week helps with volatility. but i have been adjusting daily and only building up my cash, not depleting, so far. i started with about 65% stock and 35% cash. so far so good. i'll keep everyone posted.
Hi Doug,
I am not a very tech savvy guy, so if it’s ok, I’ll post my info on your page. I’ll just post my results for all to see, just so we can see how the aim model works, and hopefully continue to work.
Currently I am doing what probably any financial advisor would advise against. But that’s me. Basically, I am using my 401k and just reallocating funds, this way I am not paying taxes or commissions, to keep overall cost low. I will buy into my company stock and then when it’s up, shave off the profits to a stable fund, almost like a money market that we have. When it’s down, I’ll put money back in to the stock, pending the price. I have a price in mind that I feel is a good price.
Now, I have a little bit different method. I am trying to keep $20,000.00 in working capital, the rest of the money is in the stable fund. I just like the idea of 20k working, so I don’t use the exact formula as the aim model.
Starting total balance on 10/18 was $27,831.71
Balance as of 10/23 is $29,889.97
I know this is a short period of sampling but I just got the idea to work the aim model last week. I purchase Lichello’s book about 5 years ago but didn’t really have enough capital to work the model until recently, at least where I would be comfortable to work the model.
I deposit about $500.00 per month to my 401k and with price fluctuations, have not seem much growth until this last week. I figured I would try to build as much cash in my stable fund because it pays decent interest and I’m good with a fairly safe investment, especially if I am going to have $1 million in it.
This probably all sounds amateur, but I’m enjoying working the model so far. Until next time.
Ruben
Hi, Guys
I appriciate all the info. I was looking for back testing results for value cost investing. Which seams to be a better way to accumalate a position for AIM then dollar cost averaging. But my thinking was once the account got to big there was no way I would be able to keep up with the obligations needed in a down market like 1929-1932. So I googled constant value investing because the principals are somewhat simular value cost investing.
It would not surprise me if from 1929-1932 AIm would have made money based on the Dow because the market was so volitile. Of course the dow could not be traded & a huge number of stocks & investment trusts (another name for mutual funds) went bust.
@ crash lows I think it would be best to sell options when premiums are high for rebalancing account.
I agree that Spy is one of the better choices because lesss chance of going bust but a 90% or greater crash it is possible that it could.
In deflation almost everything goes down so diversification wont cut it for reducing the amount of cash needed for rebalancing.I think limits should be set for rebalancing account in a down market i.e., I limit the amount of risk in the market so I always have a positive cash flow after living expenses even if all my speculating money in the market went bust.
Instead of using a minium of 20 shares. The minium should be based on dollar value i.e., if the market was to trpple in value it would take a huge move for 20 shares to be sold
Hi all,
I wanted to provide a quick update, sorry I didnt get an update last week.
Well, its been 3 weeks of working my investment strategy of keeping 20k in working capital and pulling off profits and putting money in when I drop below 20k.
So far so good, I ended the week with a balance of $32,274.62! Almost a $5,000.00 increase in about 3 weeks.
I'll keep providing updates.
Ruben
I used 75% and 25% with my husband's portfolio using no-load mutual funds and I am up over 50% during one of the worst recession we have had. Also, I switched up the SAFE portion a bit differently as well. With my portfolio, I used 2/3 & 1/3; it did not fair as well due to the type of mutual funds I chose. The good news is that I did not lose much at the beginning because I was well diversified and I am up considering what this recession has done to the economy. One think I liked about this book was it takes the thinking out of it. Also, I have done some tweeking to the system enabling my returns to be higher. Anyways, I recommend this book.
Take care and enjoy..
I've been using AIM for close to 10 years and it totally works. I'm way up, to the point where I quit my job and just trade stocks for a living. I even created an iPhone app to take all of the work out of AIMing for me, (you can get the app at www.undertrader.com)
While it might not give you the best returns, it will give you consistent returns and it allows you to take the emotion out of trading. Just trust the system.
I have always wondered why the Lichello Brake is set at 10% rather than some other amount. I assume from it that it is a completely arbitrary number. If we apply a 20 @ brake the Cash Burn Rate would be much smaller and on the deeper price dips one would have more buys at lower prices. On the price rising side one would sell off at a much lower Equity Dump Rate and achieve more equity value increase as the price rise continues.
This means that setting the AIM parameters optimally is really a matter of price behaviour. To compensate for this I have developed an AIM derivative (Vortex AIM) in which the sizes of the AIM Trades are determined by Aggression Factors for buying and selling, which would ideally be functions of price behaviour ( as well as investor profile) but this can only to be achieved by analysing previous stock behaviour, optimise all the system parameters for the past behaviour and redo the optimisation at regular intervals so that new prices create the parameter values. For as long as the price behaviour remains reasonably similar. . .for example for a sideways trading range, the optimised parameters will remain approximately constant. This way at least the trade sizes will not be limited an arbitrary 10 % Lichello Brake but will be optimised for a particular equity via the optimisation work. Only if the equity breaks out to far off its characteristic slow behaviour is an "overlay management" move required to safeguard the investment(bail out).
If you do not have an optimisation subroutine in an investment program one needs to optimise manually and that is a time consuming process. I used to use an Vortex AIM Excel spread to do the optimization and the one can simply plug in the paramater values into the trading program.
Doug, I will try to find the price download and Report back to you. I will do two things with monthly prices and your guidelines:
1) Set the parameters based on my best guess as to what they ought to be(gut feeling and a bit of experience);
2) Optimize the run for a start Pint on a new investment as of 1/2011 and then run is as I see fit.
I find the trading commission of $ 10,95 per trade high but for this type of fund it is about the same as for trading cost is Holland. . .which stand now at € 10 per trade via the ABN AMRO Bank as broker. . I prefer trading mutual funds for the reason of low trading costs, frequent trading then does not "hurt" as much.
Regards.
Doug,
I do not understand where you get you SPY prices from. I downloaded monthly SPY prices from 3 January 2000 to the end of December 2010 and the values I get are quite different than you have placed on your Chart: $ 148,25 Starting Price and I get a closing price for that day of about 135, there must be something wrong. . .How many funds with the name SPY are there?
As an afterthought It is meaningless to compare on a Back Test because the systems operate in a different way.
See additional comments on the AIM Forum today.
Doug,
In response to my comments on the AIM Forum on comparing Back Testing your AIM Test with a Vortex AIM Test this is meaningless, as Vortex AIM does not have a Standard By The Book Default Form. In Vortex the trading aggression is set by a two free parameters set by the investor to match his investment profile(Conservative or Aggressive).
So have take a step have and did some optimising runs on the 11 year data and basically I get two results:
1. Using rather high Holding Zones which are not typically expected to be applicable(one uses this as one expects high volatility in large swings);
2. Using moderate holding zone which are more often expected to apply.
Other factors in the estimation are:
3. No dividends are used. . .(no idea what they are)
4. 2 % Base Interest per year is compounded each month as I use monthly prices. So the interest is added to the Cash Position;
5. I have done an optimisation run also with the low Holding Zones and the Cash/Equity Ratio at 50% at the start.
My annual yield is calculated with my ROTAI Method:
Return On Time Averaged Investors. . .it is the actual average investment over time;
6. I use a Cash Limiting Factor in the sense that if a Buy is larger that the Reserve I use "brake" on the buying to spend only a portion of it to make it stretch out to lower prices;
7. there were no prices beyond 12-12-2010 date so I used the 03-01-2011 prices as last trading action.
(My comma's are decimal points)
$ 20 000 Investment Total
Minimum Trade Value= $ 1000 for each run
Trading cost = $ 10,95/Trade
Prices from: http://finance.yahoo.com/q/hp?s=SPY&a=00&b=1&c=200
Result 1 High Holding Zones
Cash to start= 72%
Buy HZ= 40%. . . Sell HZ= 18%
Buy Aggression Factor Fb= 0,8 . . .Sell Aggression Factor Fs= 0,47. . . .as Fb and/or Fs rises Trading amount becomes larger
Cash Limiting Factor = None
PV(End 2010)= $ 33888
ROTAI = 16,6% per year
Trading cost = $ 88 (8 trades)
Interest earned = $ 2917
Run 2 Low Holding Zones
Cash to start= 50%
Buy HZ= 20%. . . Sell HZ= 7,5%
Buy Aggression Factor = 0,8 . . .Sell Aggression Factor = 0,6
Cash Limiting Factor = 0,5
PV= $ 25789
ROTAI = 2,3% per year
Trading cost = $ 164 for 15 trades
Interest earned = $ 2385
Run 3 as Run 2 but Cash to start also optimised
Cash to start= 72%
Buy HZ= 20%. . . Sell HZ= 7,5%
Buy Aggression Factor = 0,8 . . .Sell Aggression Factor = 0,6
Cash Limiting Factor = 0,6
PV= $ 28195
ROTAI = 5,8% per year
Trading cost = $ 164 (15 trades)
Interest earned = $ 2682
I have not tried a run with a lower Minimum Trade Value.
This factor could also be varied in the optimisation but it will be more time consuming. Possibly more intermediate trades would capture more profit. Optimisation is done manually in the Excel Spread.
It is obvious that with a high holding zone more cash can be invested at the bottom price but a 40 % holding zone would eliminate all trades if the stock starts cycling in a low volatility horizontal trading range.
In practice the investor should keep his finger on the buttons to adjust the operational parameters if that is needed. I will make a few more runs later with a lower trading minimum value. If more profits result then the higher trading cost is justified.
Doug,
The smallest trade size used was $ 1334 and resulted from the Holding Zone automatically, not from the Minimum Trade Amount function. The Minimum Trade Amount was error.
Very interesting I'm using a similar approach with leveraged ETFs (not inverse). Advantage with a 3x type is that you can use 1/3 of the investment to get the same effect. This means you can leave more money in cash to buy as the etf inevitably goes down. Just make sure its an etf that you feel is good for the long term. Also you should use etfs that aren't correlated. Thanks for you article.
I am reading this and after trying for a decade to find a TA that works (and finally just buying and holding in my self-directed IRA) I am re investigating Lichello's method. I read his book about 20 years ago but back then I didn't have all the access and opportunities to invest that we have now. I am encouraged to read this article and comments and surprised to see that people are actually using the AIM still!! What a testimonial to its effectiveness. After studying I find that it combines conservative investing (by halving possible upside returns) in return for greatly protecting losses by averaging down. Lichello must have been a genius to come up with this formula.
In reference to the remarks about why he uses 10% safe and one month time table. He mentions in his book that you are basically letting the system do the work for you rather than trying to figure out what stocks are going to do next and by waiting to check them once a month you are keeping yourself from making a hasty decision and diverting from a tried and true conservative strategy.
After seemingly coming up with some great strategies using TA (but finding later after paper trading that they all fail in the long run) I can understand that this man was speaking with wisdom and experience.
I am now going to re invest my efforts into studying this technique.
I think that with the advance of technology we have much more resources than he ever dreamed of back then for which to pick better stocks in which to utilize his strategy. Which screening methods has anybody used before that have shown the best stocks to use for this approach?
Thank you for this valuable information! I am back in the game of sensible investing.
Has anyone used the "Automatic Investor" software (cost = $297) available on the internet? It states that it is based on Lichello's book.
Thank you for your back-testing!
As I just come across value averaging.
Is AIM better than value averaging?













dabeaner 2 years ago
A nice introduction to AIM. Any viewers interested should be sure to get dburkeaz's spreadsheet and order Lichello's valuable but inexpensive book from Amazon.
For even more information, search the web for "Veale" and "Core Position Trading", in addition to "Lichello".