"The deviousness of Black Swans ...".

Although we are in a new trading year, and the recent statistics such as GDP look good, I am far from sure that we are in a stable and upwardly mobile market. In addition I wonder if the past wisdom of "Das Uber President" is still intact, or more lately if it has deserted him in our time of economic need?

As recently as January 20th through to 22nd we had three consecutive days of around one to one and a half standard deviation moves in the DOW. This started me thinking about the probability of such a move. For example if one standard deviation is 68% then the probability of price moving outside this range is 32%. Not to bad, but what is the probability of three days in a row?

Market prices of the DOW as at 28th January 2010.

Under the Central Limit Theorem, price moves should be normally distributed, and as an adjunct to this, the law of large numbers would see the appearance of a greater than one standard deviation is just 32% chance in a year. However as Taleb points out in his various books, we are all being fooled by what constitutes randomness within the normal distribution and the inability of market price to converge to the mean.

Referring to the price movement in the chart above, lets look at calculating the probability of a single standard deviation move and then the combined probability for the three days, 20th, 21st and 22nd of January.

Probability of event.

First lets look at the theory. and set out the proof for a one standard deviation move. 

Proof of methodology.

We know that a 1 standard deviation = 0.68 or 68%, therefore a move greater than 1 standard deviation = 0.32 or 32%. To convert this to find out how many days we take the reciprocal and divide it by the number of trading days in the year, 220, as follows:.

.32/220 = 0.00145 x reciprocal = 687.5 x .32 /220 = 1 year.

Probability of a Black Swan.

Now the daily price moves during January were actually around 1.5 to 2 standard deviations, so lets settle on a 1.5 move for convenience and use the above method to calculate the January Black Swan. 

A 1.5 standard deviation move is calculated as follows: 1-((0.68 + 0.95)/2) = 0.185 or 18.5% chance of happening.

Next we calculate the probability of moving beyond a one Standard deviation move in one day as :

Probability of 1.5 standard deviation in a day 0.185/220= 0.0008409.

Next we need to get a little fancy and multiply the probability of a move for the first, second and third days together to calculate the combined probability of occurrence.

Thus the probability of 3 x 1.5 standard deviation in a row is 0.185/220 x 0.185/219 x 0.185/218. Notice how the number of trading days drops from 220 down by one day for each calculation to account for the remaining trading days in the year. 

Next we take the reciprocal to convert the probability of happening to the range in days that this event might occur.

So we Multiply out the 1.5 standard deviation moves to get combined probability of 3 back to back moves as above and then we divide by the number of trading days remaining , to get trading years :.

In our case the probability of getting three days in a row of greater than a 1.5 standard deviation move is equal to once every 1,394,945 years. 

Release the Swans to do their worst.

But wait, there is more than one swan. If you refer to the chart above you can see from the highlighted sections that over November and January we had a number of instances and that this three day event was not an isolated case. Lets now add the November plunge in as well to see how our probabilities work out.

The earlier moves in previous months can be included by multiplying out the event probability of 18.5% by the remaining number of days in the trading year.

Thus the probability of 5 greater than 1.5 standard deviation moves in a month is now :
0.185/220 x 0.185/219 x 0.185/218 X 0.185/217 x 0.185/216 x 0.185/215. Again notice how we drop the trading days from 220 down to 215 as each trading event happens.

When we convert this very small probability number to years, we get the probability of once every 222,020,900,000,000 years which is longer than the life of the known universe. And remember, this calculation is only taking into account the last two Swans in November and January. What about July, August, September and October ?.  I thought about looking at these, but my eyesight is too dim and my calculator too old to handle the pace.

So forget your endothermic or exothermic reactions, Hell just keeps freezing over and it is only January - It would appear that game theory is no longer a game!.

Trading in reasonable times - Alice are you sure ?.
 

Cheers

"... NAB, a whole lot of bull ...".

NAB 15th January 2010

When we last looked at NAB on 30th December 2009, we projected a retracement of price to a target of  $27.85 and in fact we achieved a price of $27.75 on the 5th January. Not bad. In fact we also thought that the retracement back up to this level would be short lved and that NAB would come back down to around $26.72 which in fact it has also done. Each of these moves can be seen in the chart above and the predictions can be verified in the earlier blogs for NAB.

Looking at the chart above the price action seems to have stalled and is channelling between the previous upper target of $27.81 and the lower target of $26.72.

My strategy for this situation is to be patient and see whether the wave three continues by price breaking to the down side or if price breaks the $27.81 level to the upside to also continue in a wave 3.

The weekly and monthly charts would seem to give the weighting to an upside breakout and with this in mind the upper price targets would be $30.09 as a first conservative target with a more aggressive target as $32.14.

The first target lines up with the 1.6 Fibonacci level whilst the second target lines up with both the MOB target taken from the previous wave 4 high as well as the 1.618 Fibonacci level.

Time will tell, but here's hoping NAB will be serving up a whole lot of bull.

Cheers

"The DOW at 400 as an extreme sport ...".

For almost as long as I can remember, Robert Prechter at Elliot Wave International, (EWI),  has been saying that the market is in for another crash and one that will be significantly more devastating than the last one in 2008. 

In a recent post, 18th January 2010, EWI published their forecast ,that the DOW will hit 400 by 2015. Yes that is right 400.  

The EWI chart looks to be a monthly projection and my reading of the chart seems a little different to EWI. However when I had a look at my own chart I could not get the same pattern. My analysis saw the DOW getting down to around 5500. Here are some of the thoughts that occur to me when I went over the chart:.

1. The Wave 4 that is in progress now has violated the upper Wave 4 channels and as Prechter points out in his book, if this happens then it is unlikely you will get a full wave 5 retracement.
2. The Profit Taking Index in GET is only 28, which less than the targeted 35. This would also indicate that there is a reasonable probability that there will not be a correct Wave 5 retracement along the lines in the EWI post.
3. Using the Ellipse study, it would indicate that the Wave 4 is still not over as the two ellipse have not converged. If this is the case we could see the current upward trend move higher for awhile yet. The implication is that any retracement from this higher end point would be also higher than the lows currently being projected
4. If we assume that the points above are correct, Prechter points out in his book that the retracement would be to the previous wave 3 low of 6440 rather than his projected 400.
5. Using the Ellipse tool on the previous Wave 4, this would seem to indicate that the end of a projected Wave 5 down would be somewhere between the current high of 10609 and the low of the previous wave 3 at 6440. 
6. If we assume that the above analysis is wrong and the current wave 4 dynamics hold true to the rules in prechter's book, then the targeted wave 3 low is around 5357 by November 2010 and not 400.
7. Again, if we assume that the current analysis is still wrong and we take a wider view and project a low from the previous wave 4 low back in October 2002, the projection only gets us around 5752 by November 2010 and nowhere near the 400 posted in the blog.
   

The interesting thing about this analysis is that many of the tests back each other up and give targets that seem to be close. Then again I could be wrong, but for all our sakes I hope not.

One other observation on the EWI chart is that they place the greatest reliance on the shape of the chart and inform us that price is approximate and the timescale for the chart is not reliable.

Cheers

"...I SPY ...".

SPY 15th January 2010.

Since August 2009, the SPY has been demonstrating some very interesting patterns. In summary here are some observations from the above chart :.

1. The SPY has stayed well within a two standard deviation regression channel, which has a correlation co-efficient of 98.2%.
2. Similarly, the SPY has ridden the Bollinger bands in almost a classic pattern of comming off the lower band and making a rapid rise to the upper band and riding this until the price hits the upper regression channel.
3. Note that at this point, the price, upper Bollinger and the upper regression line all coincide. Then within days, the SPY gaps quite dramatically down to the mid line in the regression channel.
4. Once the SPY has reached the mid line of the regression channel, it is a make or break situation. Either the price rises again to retest the upper regression line and Bollinger band, or the price breaks through the mid regression line and gaps quite suddenly to the lower regression line and lower Bollinger Band.
5. In all the time since August 2009, the SPY has only once broken through the mid regression line support to reach the lower Bollinger and lower regression line. Mostly the mid regression line holds firm as a support line and the SPY begins to rise within a day or two back up to retest the upper regression line.
6. Finally, in an obtuse sort of way, the 50 day moving avarege also acts as a loose support level for the SPY as well.

The SPY pattern in the chart above is almost an oscillation. One impressive feature of the charting package, Advanced GET,  is the uncanny accuracy of the ellipse study. Notice how each of the supports also coincide with the ellipse projections.

Interestingly, every ellipse for the upper resistance points misses the target. The upper ellipse studies are not plotted on the chart. In this instance, the ellipse is very accurate in projecting the support and turning points, but totally inaccurate in projecting the upper turning points and resistance levels.

So how can we use this information. Well depending on implied volatility, (which is another problem all together), we could do a slightly out of the money, Calendar or Butterfly around the 1155 level, and allow the SPY to creep up into our trade zone. This strategy assumes that the oscillating pattern of the SPY continues, attempts to optimise the theta decay. In addition, we are also assuming that the mid line of the regression channel will continue to have a reasonable probability of acting as a firm support to keep the price above the 1100 lower level of a trade.


Cheers

".... are we there yet ?"

 

Over the last few months it seems that even the unemployment numbers are having less of an impact on the market.

If you look at the chart, this is the worst situation that the US has experienced since the war, and employment still looks like it is on a downward slope. In addition the closest point to the level of unemployment now was way back in 1948. Everything in between 1948 and now was a mere trifle compared to what we are experiencing now.

However, it is a pity that the figures for the Great Depression are not included, as I think they would show around a 7% unemployment rate, and with the post war numbers, you have to factor in that many of the men did not come back from the war. So full employment would have been somewhat easier to achieve as there were less people to fill massive demand for war reparation and the restocking of goods and services in very depleted economies.

So, "... are we there yet ?". Is the market becoming complacent and running the risk of looking the other way when the freight train comes out of that tunnel that they have been seeing the light at the end ?.

There is a great line in the Lamb Lies Down On Broadway by Genesis:.

.... and I feel like a fly hovering, waiting for a windshield on a freeway ...".

Undeniably, the chart above clearly shows how devastating the global financial crisis has been in it's impact on employment. So are we now waiting for a large "smack" as we hit Wall Streets windshield, or does the chart above tell us we are near the turning point ?.

Cheers

"National Australia Bank - the new year rise ?"

Back on November 16th we looked at National Australia Bank, and asked, "where is NAB heading ...?". The price at the time was around $30.50, and our analysis showed that a Wave 4 had been completed and confirmed, and that the price was beginning to retrace down and had broken out of the regression channel. In fact we noted in the posting for November 16th that :.

 "... it would seem that the stronger weekly chart indicates that NAB is trending lower but only for the moment and that we should expect a near term low around $27.85 and then for the stock to resume it's upward trend early in the new year ...". 
 

As we can see from the above chart, NAB did in fact get to our target of $27.85 and then dropped substantially lower, when NAB announced a counter offer to AMP, to take over AXA Life Insurance, back on December 17th 2009. As a result of this announcement, NAB dropped over $3.

One short term opportunity for all the Bulls out there might be to look for a short term rise in NAB to fill the gap back up to the earlier target of $27.85.

But wait there's more ....

Note that we seem to have just completed a Wave 5 low and that any retracement back up to the earlier target may be short lived as the market pulls back to complete a wave 2 low which would be back down around $26.50. The good news is that if this pattern holds, then we would see the early beginnings of a new Wave 3 high, with a potential target back up around $31.50 by mid January 2009.

So where is NAB heading next ?.

Cheers.