A system for riskless long-term profits in real markets

I post it here, because there was interest about my previous article on a similar topic. I didn't plan to write this article soon, but I was motivated by the other topic. I just finished it, so there might be some minor mistakes.
The following article presents examples for "beating the market" with historical prices. I have given links to spreadsheets with data and calculations. A help would be appreciated in Example III - outperforming a stock index. I don't have the time and data to do the calculations now, but if there is intereset, I'm sure that they will be done sooner or later. I am confident that the system presented here will outperform stock indexes.

 

1) Introduction

The system described in the article “A system for riskless long-term profits in efficient markets” was simplified as much as possible in order to be as understandable as possible. The examples were theoretical and the price movements were simulated using Excel. Here I present examples from the real world.

2) Important notes

2.1) The system is most profitable when the price moves up and down but at the end returns to its starting point. In this case the number of up movements is equal to the number of down movements, the price is the same, and our profit is maximum. The sequence of up and down movements is irrelevant – this is a property of the Kelly bet.

2.2) A property of my trading system is that it requires a long time to be profitable when the price moves away from its starting point. If the number of movements is large enough, the system will make profit – because of the “law of large numbers” we can expect enough up movements in the long run.

2.3) In the first article the theorethical examples were made by simulating price movements to a certain point, for example 100% increase or 50% decrease. But actually we don’t need to constantly watch the prices and be ready to readjust the portfolio whenever a certain point is reached. We have positive expected values also when we readjust the portfolio periodically, for example once a month or once a day.

2.4) The profits are “riskless” only in the sense that they are not riskier than the other possible strategies – for example “buy and hold”.

3) Example I

I have used historical monthly closing prices for S&P 500 and Dow Jones Industrial Average, downloaded from http://finance.yahoo.com/. We assume that we have $2000 in January 1950 and we are wondering how to invest them – in S&P 500 or in DJIA. I compare two portfolios, which follow two different strategies:

Portfolio 1- the strategy is to buy and hold. We buy S&P 500 with $1000 and DJIA with the other $1000. We hold them until March 2010.

Portfolio 2 – the strategy is to readjust the portfolio each month. At the end of each month we buy S&P 500 with half of our dollars and DJIA with the other half.

This is what would have happened in the real world:

In February 1950 S&P 500 closed at 17,22, up from 17,05 the previous month, while DJIA closed at 203,44, up from 201,79 the previous month.

Portfolio 1 has 1000*(17,22/17,05)+1000*(203,44/201,79) = $2018,147492

Portfolio 2 has (1000/17,05)*17,22+(1000/201,79)*203,44 = $2018,147492

Then we readjust Portfolio 2 according to the strategy and now we buy S&P 500 with 2018,147492/2 = $1009,073746 and we buy DJIA with the same amount of dollars.

At the end of March 1950 S&P 500 stood at 17,29, while DJIA was 206,05.

Portfolio 1 has 1000*(17,29/17,05)+1000*(206,05/201,79) = $2035,187302

Portfolio 2 has (1009,073746/17,22)*17,29+(1009,073746/203,44)*206,05 = $2035,195163

This means that already in March 1950 our second portfolio was bigger than our first portfolio. By the end of March 2010 the hypothetical portfolio 1 would have had $122389,8952, while the hypothetical portfolio 2 would have had $123218,2646. The difference is significant.

Here is a link to a spreadsheet with the data and calculations:

http://docs.google.com/leaf?id=0B3b6-3_7QGPuZTkzYjc3ZGUtY2VmMC00NWNiLTgwNGYtNzU5NzUyN2MwNDM4&hl=en

4) Observations about Example I

4.1)First of all, obviously in the real world it is not possible to divide our money infinitely, therefore it’s not always possible to buy S&P 500 and DJIA with exactly half of the money. And of course I haven’t taken into consideration transaction costs. The purpose of the examples is to show the logic behind the system for riskless long-term profits.

4.2) I chose monthly readjusments of portfolio 2, but the period could be anything – day, week, year. The shorter the period, the better are the hypothetical results.

4.3) There are exchange traded funds which seek to replicate the daily returns of DJIA and S&P 500 in different proportions, for example twice (NYSE: DDM and NYSE: RSU). The hypothetical results of portfolio 2 could have been achieved by a fund which replicates the strategy.

4.4)Although in March 2010 portfolio 2 is larger than portfolio 1, this was not always the case. There were periods in which portfolio 1 was larger. This happened when the ratio between DJIA and S&P 500 moved significantly from its starting point. As I wrote in 2), the system requires a long time to be profitable when the price moves away from its starting point. In January 1950 DJIA/S&P 500 was 11,83519062. In May 1985, the month when portfolio 1 outperformed portfolio 2 the most, the ratio DJIA/S&P 5000 was the lowest – 6,939646531. The last month in which portfolio 1 was higher than portfolio 2 is April 2001. At the end of March 2010 DJIA/S&P 500 is 9,283693765, which is significantly away from the starting point, but still portfolio 2 was able to outperform portfolio 1. It’s performance will be the best when (if) DJIA/S&P 500 returns to its starting point.

 

5) Example II

I have used historical daily closing prices for gold and silver, downloaded from http://www.lbma.org.uk/index.php. We assume that we have $2000 on 1st of April 1968 and we are wondering how to invest them – in gold or in silver. I compare two portfolios, which follow two different strategies:

Portfolio 1- the strategy is to buy and hold. We buy gold with $1000 and silver with the other $1000. We hold them until 6th of April 2010.

Portfolio 2 – the strategy is to readjust the portfolio each month. At the end of each month we buy gold with half of our dollars and silver with the other half.

This is what would have happened in the real world:

On 2nd of April 1968 gold was 37,3, down from 37,7 the previous day, silver closed at 2,202, down from 2,259 the previous day.

Portfolio 1 has 1000*(37,3/37,7)+1000*(2,202/2,259) = $1964,157517

Portfolio 2 has (1000/37,7)*37,3+(1000/2,259)*2,202 = $1964,157517

Then we readjust Portfolio 2 according to the strategy and now we buy gold with 1964,157517/2 = $ 982,0787585 and we buy silver with the same amount of dollars.

On April 3rd 1968 gold stood at 37,6, while silver was 2,195.

Portfolio 1 has 1000*(37,6/37,7)+1000*(2,195/2,259) = $ 1969,01636

Portfolio 2 has (982,0787585 /37,3)*37,6+(982,0787585 /2,202)*2,195 = $1968,934316

By 6th of April 2010 the hypothetical portfolio 1 would have had $37979,13269, while the hypothetical portfolio 2 would have had $38031,515. Here is a link to a spreadsheet with the data and calculations:

http://spreadsheets.google.com/ccc?key=0Anb6-3_7QGPudG04TjRnOHBIVmRIME80U09MU3RRb3c&hl=en

6) Observations about Example II

6.1)The observations in 4.1) and 4.2) are relevant here aswell. There are exchange traded funds which seek to duplicate the daily returns of gold and silver in different proportions, for example twice (NYSE:UGL and NYSE:AGQ). The hypothetical results of portfolio 2 could have been achieved by a fund which replicates the strategy.

6.2) Although on 6th of April 2010 portfolio 2 is larger than portfolio 1, this was not always the case. The main reason for this is the fact that the gold/silver ratio moved very significantly since 1st of April 1968 – from 16,68880035 to 63,21149554 – it is almost 4 times higher than the starting point, but still portfolio 2 was able to outperform portfolio 1. It’s performance will be the best when (if) gold/silver returns to its starting point.

7) Example III

It is very similar to examples I and II, but it might be more impressive.

I claim that my system can outperform any index which follows stock prices. In order to do that, one just has to randomly select half of the stocks which are included in the index and periodically readjust his portfolio, so that in every period he invests half of his dollars in one half of the stocks, and the other half of his dollars – in the other half of the stocks. Of course one has to take into account how the index is calculated. I consider the Dow Jones Industrial Average to be the most convenient, because it is price-weighted and can be replicated by just buying the constituent stocks.

Unfortunately, I don’t have the time and data to do the calculations now. If somebody is interested to do it, I will be thankful. Here is a list with historical components of DJIA:

http://www.djindexes.com/mdsidx/downloads/DJIA_Hist_Comp.pdf

Also needed are daily, weekly or monthly historical prices for the constituent stocks. After this the calculations are the same as with examples I and II – portfolio 1 buys and holds all the stocks (which is how DJIA is calculated), while portfolio 2 is periodically readjusted.

I am confident that my system will outperform the DJIA and other indexes when tested with historical prices. And it will outperform them in the future.

8) Why there are periods in which my system underperforms the “buy and hold” portfolios?

The reason is the way it is created. Since we have positive expected values, we need to maximize them. The positive expected values exist because of the way prices move – an up movement in gold/silver (for example) of x is equal to a down movement in silver/gold of 1/x. The optimal portfolio is buying the asset (gold or silver) with half of the money – this was demonstrated in the first article with the Kelly formula. This way if the price goes up, we profit from only half of it, but when it goes down, we lose from only half of the movement. So if gold/silver rises 100%, our hypothetical silver portfolio rises 50%, but when gold/silver drops 50%, the silver portfolio drops only 25%.

This means that in periods when gold/silver is rising, our system will underperform a hypothetical portfolio which buys and holds gold. If the price is moving around some average, our system will be better. When (if) the price drops to its starting point, our profits will be maximum.

 

I have several issues with this:

1. "The profits are “riskless” only in the sense that they are not riskier than the other possible strategies – for example “buy and hold”"

Most people do not view "not riskier" as riskless. I am just saying if you tell someone you have a "riskless" strategy, they assume you mean it cannot lose money.

2. I cannot stand seeing commas where there should be periods! Sorry, but this is a mostly U.S. forum and the examples, etc. are shown in U.S. dollars and on U.S. exchanges - XYZ stock is not at 56,78 - it is 56.78. I realize the other way may be standard in Europe, but it is simply incorrect here. Sorry for feeling this way, but it's like if I go to England and insist on driving on the right side of the road.

3. Back In 1950, would someone have known about this? Also, please consider what commissions would have been back then to constantly change your portfolio(s).

4. There are potentially a zillion ways to backtest a strategy that would have been no worse then a main index (for example, some people claim Covered Call writing would have been better - other ways would be just to buy when a moving average hits and sell when it falls, etc). There is really no big discovery here at all IMO. How about just going long until Oct every year and then selling and going long again in Dec - you would have missed just about all the biggest crashes, etc. But so what.

JJacksET4

 

Looks a little volatile to me. Only $50 a quarter to try it!


System Description

The system is designed for long-term profits. Although the results might be volatile in some periods, there is no bankruptcy risk and the system will surely beat the S&P significantly. The profitability is proven by backtests.
The system is based on fundamental knowledge. Trading is done using very strict money management rules. The author of this system has also authored the first system for riskless and sure profits - http://sambian.wordpress.com/2010/02/07/29/
The profits in the system from the article are minimal, while the profits from the system presented here are huge, and they are also riskless.

"Riskless?"

http://www.collective2.com/cgi-perl/c2systems.mpl?systemid=43930402

 

There are at least two problems with your backtesting.

1. You don't take into account commissions and slippage. $800 difference between the two portfolios in the first example wouldn't even be enough to cover the commissions.
2. In reality you can't trade at the closing price, so the actual trade price would be different from the close. This may not sound like a huge thing, but it can add up to quite a bit over time. Essentially, your backtest is suffering from look-ahead bias. You assume you trade at the closing price yet you don't know what the closing price is until after the fact.

 

Sounds like a typical ET post. Some one goes through a lot of trouble to share something, in no way is trying to solicit money from it, and people call them stupid.

Don't take the words to harsh. This forum is full of the venom that frustrated traders carry with them.

 

Especially with options, the slippage is the biggest factor. It would be great if you didn't begin every trade negative, but with options, every trade starts off in the hole.

 

This is a huge topic and I haven't had luck to really discuss it with anybody who understands my point of view. But still I'll try to explain it:
If you want to preserve your wealth, you have no choice but to hold something. It could be dollars, euros, gold, silver, stocks etc. The prices of everything fluctuate, and if they follow random walks, you have no reason to prefer dollars to euros for example etc. But still you have to choose some good in which to keep your wealth. If you choose dollars, there's a probability that its value against the euro will fall, i.e. you "lose money". If you choose to keep your wealth in euros, there's a probability that its value against the dollar will fall, i.e. you "lose money". If you have no idea what will happen with the price, you are in trouble - you risk "losing money" whatever you do. Then you can use my system and get optimal results, i.e. "losing less money" from all possible price movements.

Ok, sorry for that.

I'm just showing that the idea works when tested with real prices. This is how it's done.

 

I registered at this site almost 6 months ago, my registration is expiring and I will not renew it, so you will not be able to try my volatile system . I can't trade properly there, my results with my real accounts for the same period were much better and less volatile. For your information - in the last year and a half I am up 88%, and I trade with all my savings. And yes, I trade without risk
And by the way, "volatility" is not "risk" to me