## Tuesday, October 14, 2008

Here is a recent chart-of-the-day I found quite interesting:

It's interesting in the sense that, in 1929, the stock exchange actually fell much more abruptly over a short period, but, as shown on this graph, on the longer timescale of a year, it actually fell less than in the current crisis. So it seems to point out the existence of various kind of volatility, one short term, and the other long-term.

One may propose a few remarks to explain this difference:
- There is much more volume today, implying some kind of inertia in the market
- The traders, despite all their shortcomings, seem more aware than their ancestors of economic forces and less liable to panic moves, but more liable to early reactions anticipating the worse.
- The way the authorities have managed this crisis is much better than what was done in 1929, and it seems to have at least spread the fall on a longer time-period, which, in itself, is a very positive achievement.

On the contrary, it may also indicate that, while the digestion of bad news is more progressive , this one still has to run its course fully. And that may be a teaching of the relative powerlessness of existing institutions which are basically only reactive in absence of proper regulations.

On a more technical aspect, all this indicates that the two volatilities are intimately connected and that basically, what is taken from one goes into the other, the final distribution being a result of current psychologies and existing institutions.
Despite the uncontroversial nature of that remark, it is a bold statement if one takes the time to extend it to all kinds of assets, and in particular to currency pairs. To perform this extension is however nowhere near obvious. We all heard of the wild variations of currency value in the 29 crisis, but the monetary system was then very much different from what it is today. In particular, there was a gold standard, and the arbitrage system we have today was not in place. In absence of a careful analysis, it would be specious to conclude anything detailed.
However, without that analysis, and given the current, more "efficient" system of currency pairs, it may already be possible to conclude that very high volatily in the currency market is to be expected in the coming months.

### The weight of news

The following article from the Federal Reserve addresses the matter of the effects news announcements have on some assets price (taken in a general sense):
http://www.ny.frb.org/research/current_issues/ci14-6.html

It's a purely statistical approach and therefore lacks any model to really make sense of the data. In particular, the sample of data does not reflect the difference that may exist between a bull market reaction and a bear market reaction.
Some interesting comments however on the type of assets that are the more reactive, on the indices that elicit the most volatility, on the timing of the most significant reaction.

## Friday, September 5, 2008

### Who is selling the EUR?

Today saw some remarkable activity in the EUR rates.
This morning at about 10:15(CT), there was a sudden drop of about 50PIPS on the EUR/USD, then at 13:18, -30PIPS in less than a minute, and at 16:12, more than a 100PIPs drop in less than 5 minutes, clearly some big accounts are liquidating their EUR reserves.
All this may find an explanation in the remarks from Juncker about the EUR still being over-valued.

During the same time, the DJ dropped by 344 points, so the US stock market does not seem relevant with regards to the current movements of the USD, stronger forces seem to be at play here.

This certainly invalidates my earlier analysis that linked the future of the USD to the US economy, and especially to the unfolding of the current crisis. At least for now, the market appears to follow the consensus of the central banks in working towards a strengthening of the USD against the EUR, or rather towards the general weakening of the EUR.
As for today at about 5PM CT, the EUR has lost about 300 PIPs against the USD, and about 600 PIPS against the JPY. Interestingly the USD also dropped by about 250PIPs against the JPY. Japan seems to be at the heart of the matter in these movements.

The big question is up to which level this weakening will continue ? I, for now, expect to see it going towards the 1.3, or even 1.2 USD mark, if the current logic is respected. At this level, we shall see what the EU deciders say about the overvaluation of the EUR.

## Saturday, August 9, 2008

### EUR/USD medium term outlook

These last few weeks, I have been holding the belief that, for the next year or so, the EUR/USD will have a high volatility between 1.4 and 1.6.
This week, it dropped from 1.55+ to 1.5, that's an impressive drop, and we start hearing from a possible big trend reversal, possibly the outset of an upward trend for the USD, the materialization of the strong USD policy promised by Paulson and Bernanke beyond the customary rhetorical value such chantings have.

As of now, I have been considering the risk of being wrong on the upside higher than the one of being wrong on the downside. Should I then reconsider my approach ?
Anyway, here is the details of my thought so far, up for comment:

My first assumption is that EU economy is still overall structurally healthier than its US counterpart, even though some banks have suffered from the credit mess, the level of the write-downs (and the depth of their consequence in the overall economy)is still very far from what we saw in US.

Secondly, I assume that there is a general psychological bias for the USD, whereby the investors actions (in EUR/USD particularly) over-react to bad EU news, and under-react to bad US news. This bias is actually justified in view of the market dynamics, where the european markets mostly mimic the US market. What I mean by bias, is that it does not reflect pure fundamentals, but is mostly a psychological attitude in the mind of investors that have spent most of their lives with considering the USD as the reference currency, the safe haven away from the world uncertainty. This bias however is really challenged by the current crisis, and it tends to fade a bit, and may well vanish totally, which is why, until now, I considered my risk of being wrong on the upside higher.

Now, considering that Paulson and Bernanke really mean to walk the talk, can they really do it? Clearly, the Fed may be able to do a few things, especially with the support of the ECB and the BOJ, both having a strong interest in a strong USD to ease the pressure on their respective economy. We can then reasonably expect a collaboration between the three largest players on this market to push for a strong USD. But is it enough?

US economy is expected to deteriorate further. According to Krugman, some bad loans are going to mature up to 2011, real estate is expected to continue its drop, being only half-way through according to some estimations.
In addition, USA is going to have a new government in less than 6 months, one who will inherit some serious liabilities from the current one. A new government, elected on the current buzzword of "change", can hardly be expected to have a tight budgetting poliy in his first year, especially in view of a reform of healthcare, of necessary expenses on infrastructure, on energy policy,...etc.
Such a policy may seriously strain at a strong USD policy, which I rather see as incompatible with running an ever-increasing deficit (something about which the investors should see the EU, despite some very bad members, relatively immune from, given the conditions of the Growth and Stability Pact).

So, will the USD pull it off, and are we really seeing the first signs of a complete reversal, or is it just the last song of the swan before its slide into the 1.8 or so, just awaiting the next big write-down ?

JP

## Wednesday, July 16, 2008

### What to expect: Trend and Volatility

I assume here that the price evolution is modelised by a Fractional Brownian Motion (FBM) of index-$\alpha$ (0<$\alpha$<1): href="http://www.codecogs.com/">$X:[0,\infty)\rightarrow&space;\mathbb{R}$

where X(t) represents the price at time t, so that we have the following equality (E1) about the expectation of dependent price increments (demonstration in [FALC03]pp267-268):

$E[(X(t)-X(0))(X(t+h)-X(t))]=\frac{1}{2}[(t+h)^{2\alpha&space;}-t^{2\alpha&space;}-h^{2\alpha&space;}]$

Clearly the value $\alpha$=1/2 seems to play a very specific role in that equation, since it cancels out its right-side term.
$\alpha$=1/2 indeed consists in the classical Brownian Motion (Wiener Brownian Motion:WBM) where the increments over time of the variable X are independent.
This index $\alpha$ is directly linked to the Fractal Dimension Df by the relation:
$\alpha=2-D_{f}$

Therefore, when $\alpha$=1/2, which is happening when Df=1.5, we have a genuine Random Walk.
When such is not the case, however, we can say:

1) Df<1.5
This case is equivalent to $\alpha$>1/2, and we can then expect from the equality (E1) that X(t+h)-X(t) tend to be of the same sign as X(t)-X(0), therefore, if X(t) has an history of increasing, the next move X(t+h) will be more likely to be up, similarly if X(t) has an history of decreasing, the next move will tend to be down. In this case, we are in a trend.

2) Df>1.5
This case is equivalent to $\alpha$<1/2.> In this case, X(t+h)-X(t) tend to be of the opposite sign of X(t)-X(0), therefore, following the same logic as above, we are in a trend reversal period.

## Wednesday, July 9, 2008

### Intermezzo

Here is one of the other things (from the title), I may, every now and then, discuss.
I am currently reading "The rest is noise" by Alex Ross, he also has a Blog here: http://www.therestisnoise.com/
The book is a journey through the music of the 20th century. I am just starting it, but my first impression is that it's a pleasant read, well-written, that takes the reader through the mind, life and works of some great composers. The first chapter covers R. Strauss and Mahler, and their intriguing relationship, that no doubt plays a prominent role in their attitude to their art, and that Ross subtly uses to inform their respective compositions.

A little digression here.
It seems the musical 20th century started with a beautiful woman (Salome) kissing the lips of a beheaded John the Baptist (Jochanaan) in a frighfully orchestrated bliss (in the final scene of Salome, by R. Strauss, inspired by the play of Oscar Wilde). The tune was set for the 20th century to unfold: The old religious lores were to be taken out of their somniferous yoke of dogmatism, and lay bare the darkest secrets of the soul.

## Tuesday, July 8, 2008

### Comments on some existing fractal-related tools

A few indicators, that relate to fractals (or seem to do so) are already easily available on several platform.

The first, maybe the simplest is called "Fractals", and when you use it, it draws little arrows, some pointing up, others pointing down, like this:

This indicator, however, has nothing to do with fractals, it relates to Elliot Wave Theory, as explained here: http://trading-stocks.netfirms.com/fractals.htm

A derivation of this is called the "fractal channel" which links the little arrows, similarly, it has nothing to do with fractals.

More relevant then is the Fractal Adaptive Moving Average, which relates to Kaufman's AMA, but uses fractal theory to determine the current volatility of the market in order to adjust the speed of the MA. The idea of the AMA is to slow down the MA when the market is moving sideways, and to speed it up when there is a trend. To achieve this objective, John Ehlers developped the FRAMA, using the Fractal Dimension as a direct measurement of Volatility, he explains his method in a file (title: FRAMA) that can be downloaded from this address: http://www.mesasoftware.com/technicalpapers.htm

On the following graph, I plotted a simple 16-MA (blue), an exponential 16-MA (yellow) and the FRAMA in red (with a reference period of 16 as well). Below are the fractal dimension used by the FRAMA (and computed from the formula of the above paper), as well as a more sophisticated fractal dimension (to which I will come later):
Clearly, during the sideways market (until about 16:45), the FRAMA is somewhat smoothier than the two others, and when the trend goes on, it also reacts faster. Therefore, we can say that the FRAMA is a good AMA. However, it could be better, the computation of the fractal dimension is rough to say the least, it oscillates between extreme values (from 2 to below 1) that don't even make sense mathematically. The FDI plotted in the lowest window, displays a more reasonable fractal dimension (the period to calculate both is 16), for those interested in this tool, I would therefore advise to use the FDI and that might entail a modification in the factor -4.6 in the computation of the coefficient alpha (from the FRAMA paper) where Ehlers recommends:

$\alpha=\exp(-4.6(D-1))$

The fractal dimension Df in the FDI follows the following formula:

$D_{f}=1+\frac{Log[2\sum_{i=1}^{N}\sqrt{(\frac{close(i)-close(i-1)}{pricerange})^{2}+\frac{1}{N^{2}}}]}{Log(2N-2)}$

Where N is the number of periods(price valuations) considered. Df provides us with some idea of volatility, when Df gets close to 2, it means that we have very high volatility, the closer to 1 and we have low volatility or, in other terms, a well-defined trend. But that's very general qualitative comments, the passage to a computable quantity is trickier. Elhers assumes that price movements are following a lognormal distribution (which is not the case) and, on this basis, comes to compute the value of alpha as an exponential. I will, in the near future, share my reflections on how to get an identified numerical measure of entropy (volatility) from Df.

But for now, my point is merely to say that the fractal dimension is an indicator of volatility, it does not inform on the direction of the market. To get this direction, many analysts rely on MA or combination of them (such as Ichimoku, Bands,...), those indicators may be refined, using the fractal theory, but they then become hybrid indicators, mixing two diverging conceptions of what price movement is about.

As of now, and as far as I know, the only technical tool fractal theory is providing is a measure of volatility, but volatility in itself may be an interesting information to set up one's stop and position size. It may not be necessary to use volatility as a mere entry variable into another indicator.

## Thursday, June 26, 2008

### From Economics to Fractals

Here is an interesting site that makes the link between economics theory (the "Fundamentals") and the fractal behaviour of the market:
http://www.debunking-economics.com/
For a more precise link to Fractals, and a few other interesting things such as Behavioural Finance (slide 33 and above) or the PayBack Period (slide 70 and above):
http://www.debunking-economics.com/Lectures/Managerial/ManagerialEconomicslecture11FinanceAlternative.ppt
This site seems very rich, and I just discovered it, so there may be other documents of interest in there.

## Wednesday, June 25, 2008

### Why fractals?

A significant part of TA, if not all, is based on Averages, and as such, it relies heavily on the Gaussian (or Normal) Distribution which is the statistical translation of the Random Walk Theory.
Indeed for Averages (and that includes all kind of Moving Averages, Simple or Exponential) to really be as meaningful as TA considers them, prices variation must actually be described adequately by the Gaussian Distribution and its counterpart in random process, the Brownian Motion.

It is interesting to note that there is a contradiction inherent to the practise of TA. In his "Technical Analysis of the Financial Market", John Murphy wrote (with good reason):
The Random Walk Theory (...) claims that price changes are "serially independent" and that price history is not a reliable indicator of future price direction. In a nutshell, price movement is random and unpredictable(...) It also holds that the best market strategy to follow would be a simple "buy and hold" strategy as opposed to any attempt to "beat the market."

Something I completely agree with, but then, if a technical analyst is to reject this Random Walk view of price movement, shouldn't he reject as well the mathematical ramifications of this assumption rather than to use them as tools.
In a Gaussian model, the average (the mean) clearly is a good information to consider, it is the quantity that has the highest probability to be realised, and the closest to the average, the higher the probability is.

The large pool of experimental data we have from financial markets, however, tells us that they don't follow a Gaussian distribution, they diverge from it in various ways but a remarkable one is that they are fat-tailed , which means that the probability for the variable to be far away from the average is actually higher than in the Gaussian model (i.e. extreme variations are more frequent than what is predicted by the model). And that is important, because it tends to make our beloved Average less useful, in terms of prediction, while the differences are not such that Averages don't retain any usefulness. But more precise tools may likely be derived from a more fitting model of the real price movement.

Another problem with the Gaussian model is that it assumes continuity and evenness of change. Benoit Mandelbrot in "Fractals and Scaling in Finance" wrote:
In the classical (Gaussian) theory of errors, a large change would typically result from the rare chance simultaneity of many large contributing causes, each of them individually negligible. In economics, this inference is indefensible. Typically, the occurrence of a large effect means that one contributing cause, or at most a few turn out ex-post to be large.

This non-evenness, as well as the discontinuity of price movement (which is obvious given the structure of the process of price determination, the apparent continuity is just an artefact of price representation), contribute even further to undermine the validity of information given by Averages and even more so, by Moving Averages.

Mandelbrot again, remarks:
In particular, price continuity is an essential (but seldom mentioned) ingredient for all trading schemes that prescribed at what point one should buy on a rising market, and sell on a sinking price. Being discontinuous, actual market prices will often jump over any prescribed level, therefore, such schemes cannot be implemented.

Then, what are the alternatives to the Gaussian Distribution ?
Mandelbrot goes on discussing a few of them in his above-mentioned book. I won't do that here. The alternative I wish to discuss on this blog is the one most promising, in terms of modeling the behaviour of price movement, as far as I know.
It is the option involving the use of fractals. The models developed with fractals have so far shown a better fit than Gaussian models (as well as other alternatives), and I therefore hope that they can lead to the development of more efficient TA tools than the ones existing today.