J200 and Normal distribution - PART II

I’ve received several questions about previous post (J200 and Normal distribution) from my trading friends on Skype and on one of the forums where I am active (www.page88.co.za), so I have decided to respond here on blog.

If we assume that we have ideal trend following end-of-the-day (EOD) trading system (100% win rate), then that system is going to mirror market and will produce results that are not normally distributed, as our market is not normally distributed when it comes to difference of daily price changes at market close.

However, as our trading system is not perfect I’ve decided to test distribution of trades for that particular system and for additional eleven trend following trading systems that I trade and/or paper-trade (5min-15min-30min-EOD). For all of them it was more than clear that trade distribution is not normally distributed, with systems successfully relying on market extremes and successfully catching market events during which market reaches extremes several standard deviations from the mean. Of course, this kind of distribution catches some big fat-tail losers too, but as long as these systems continue to catch more positive fat-tail events, they are going to continue to perform. (Please note that these fat-tail events can result from daily returns and/or follow through or can be result of massive one-directional short-term burst in volatility.)

One of the items on my to-do list is to look at normally distributed trend following systems with 60%+ win rate, just in order to have few different machines when compared to these twelve systems I follow, as for all of them win rate is somewhere between 30 & 45%, with average win/average loss ratio being between 2 & 3.

When it comes to mean-reverting strategies and their distribution – I am not actively exploring anything in regards to mean-reversion and I am not willing to comment on this, as I haven’t done homework yet.

Finally, all of this gives me nice platform to come to the point that I wanted to make since I started with original post:

If one’s system has proven (with enough data sample; over many market conditions; with enough out of sample data, etc.) to be able to provide trade entries that over time yield positive results through fat-tails, then trader has to be extremely disciplined in letting profits run, as over time system will lead to positive results. All of this, of course, until system breaks down and that is something that I will be writing more on in the future.

Proper money & risk management are to be employed, as almost always trading great system(s) with too little capital will lead to ruin of one’s trading account.

Trade with trend!

PS.

Attached graph shows trade distribution for one of the variations of our 30min system for period: 19.12.2007 – 03.02.2010.

J200 and Normal distribution

This graph represents distribution of difference of daily prices at market close (in percentage terms).

Simply put, I’ve calculated how today’s close compares (in percentage terms) to previous day’s close. Data is for Top40 (J200) and it was calculated from 05.02.1996 – 05.02.2010 (total of 3440 trading days).

Attached table shows what the values for daily return (mean) & standard deviation of daily returns are and I’ve included values up to 6 standard deviations from the mean.

Finally, third table is just there to give us basic information on what various standard deviations beyond the mean are for normal distribution. (For more information on normal distribution, among other sources, I would recommend Wikipedia.)

It is obvious that our market is not normally distributed. This leads me to conclude the following:

If market is not normally distributed, than simple trend following system (derived from technical market observations) will produce results that are not normally distributed.

For more reading on daily distribution of US Markets, please read the following:

http://marketsci.wordpress.com/2008/10/27/fat-tails-normal-distributions-random-walks-and-all-that-jazz/

http://ibankcoin.com/woodshedderblog/2008/10/26/on-fractals-and-market-crashes-part-1/

Trade with trend!

Why volatility dropped - PART II?

These two tables represent net open positions for two corresponding periods in 2008/09 and 2009/2010, with first table showing us 6-month open interest for period August 2009 – January 2010, while second table is highlighting 6-month open interest for period August 2008 – January 2009.

Let’s start by comparing first rows of both tables (net open positions of Index futures for given periods):

As I wrote in my previous post (Why volatility dropped) we saw that number of traded ALSI contracts over those two periods stayed the more or less the same. What happened with open positions?

It is obvious that open positions increased during last 6 months when compared with same period in 2008/09 – From approximately 338.000 contracts on average for 6 months period in 2008/09 to around 508.000 on average for corresponding period in 2009/10.

What we may conclude from last two posts is that more people are leaving their positions overnight, while daily volume, more or less, remains constant. That by itself can drop volatility and that is what was happening over last few months.

Trade with trend!

Why volatility dropped?

Last night I was browsing on JSE web site and I’ve found very nice documents showing monthly statistics for futures and options traded in South Africa. (More information could be found here: http://www.jse.co.za/Documents-and-Statistics/Marketstatistics/Equity-Derivatives-Market-statistics.aspx)

Posted above are just two tables from documents published on mentioned web site.

First table represents number of contracts traded from August 2009 to January 2010, while the second table represents number of contracts traded from August 2008 to January 2009.

If we compare first rows (Index futures) for those two tables we can see that volume is very much the same. Average for period August 2009 - January 2010 is 1.141.932 contracts per month. Average for period August 2008 - January 2009 is 1.140.761 contracts per month. In my opinion, this small difference could not take away volatility from our market.

If we compare second rows (Single stock future) for those two tables we can see that there is drastic change. Average for period August 2009 - January 2010 is 6.683.356 contracts per month. Average for period August 2008 - January 2009 is 41.635.729 contracts per month. This represents decrease of about 83%.

What we can conclude from those two tables is that ALSI traders are still out there, but traders in single stock futures are gone from the market.

How this influence volatility?

Trading ALSI, we often forget that ALSI is futures contract based on Top40 (J200) index. Top40 index is calculated as average for Top40 South African companies and cash value of Top40 is based on cash values of each stock that makes part of Top40. If trades in single stock futures dropped 83% year-on-year that means that volatility in cash market for stocks dropped by, more or less, the same margin (Remember that SSF issuer must hedge what it is sold to you by buying 100 shares for each contract for that specific share.). So, we have situation in which shares volatility dropped, causing Top40 volatility to drop, which is at the end causing ALSI volatility to drop.

Last two rows of these tables represent total number of futures and options traded on JSE. It is obvious that number of contracts traded for instruments dropped by quite some margin, especially over September and December (close out months). Such a big drop could have, for sure, caused volatility drop, which makes our systems underperform levels of return from year 2008 and early 2009.

Trade with trend!

J200 15min chart

Hereto is presented Top40 (J200) 15min chart.

J200 was in the long down channel that broke around 22. January 2010. New steeper channel was formed and it was broken yesterday and backtested during morning session. Target for that channel is around 24700. At the same time, this target will test downtrend line which started early in January 2010. MACD showed positive divergences before this upsurge, pointing to us that bears are losing momentum.

Small falling wedge was formed as well and it was broken on Monday, with target being reached already.

Conclusion is that we can get another 300 points on this upside move.

Trade with trend!

J200 60min chart

Quick look at Top40 (J200) 60 minutes chart:

Top40 currently is very close to long term support around 24100-24200 (horizontal black line). This support going back all the way to August 2008 and in recent history was tested 5 times as resistance and then as support. 

Conclusion is that Top40 can bounce from here, especially if we take into consideration 2000 points drop from 11. January this year.

Trade with trend!

Top40 (J200) weekly chart

Last week produced biggest weekly drop since early September 2009 and that itself is a valid reason to evaluate charts.

To make it clear, system is still long on weekly chart. Entry was in July 2009 around 21000 and trade is in profit so far with approximately 3500 points accumulated in 6 months.

Market turned its downslide in March 2009 and never looked back. After some 10000 points rally market progressed all the way to 25936, right up to 61.8% retracement level - if drawn from top in June 2008 to low of March 2009. Previous major high (August 2008) is very close to turning point. There is rising wedge on first chart that broke last week, with target around 20000, if it plays out as it should. RSI and Stochastic did not show some massive negative divergences on the way up, but trend line on RSI is broken for now.

Second chart shows bigger picture. Top 40 weekly chart (from mid 2002) is shown. There is long trend line (thick green line) from 2003 that was tested 4 times so far. In recent times this trend line played support in December 2008 and March 2009, and that stopped Top40 from drooping further. What else seems obvious on that chart - 26000 is not only double resistance based on first chart as there is even 23.6% retracement level for the bull market which started in April 2003 and ended in Jun 2008. That makes 26000 triple resistance and Top40 could not breach it first time. Finally, there is clear support just below 23000 (black horizontal line) that was tested 6 or 7 times so far.

Conclusion is that Top40 dropped a bit last week, but nothing yet suggests we are going to see similar drop to one from mid 2008. Healthy correction is very welcomed at this point of time. Will follow weekly perspective and report if something changes.

Trade with trend!