Pre – modern England, all the way from 1250 to at least 1860, was a society without persistent social classes. It was a world of complete social mobility, with no permanent over-class and under-class.  It was, despite all appearances, a world of complete equal opportunity. George Orwell could not be more incorrect when he observed: England is the most class-ridden country under the sun. It is a land of snobbery and privilege (George Orwell, 1941).

It’s hard to imagine anything else that better convey the true nature of central banking and the present cheap fiat money paradigm, than what we are currently witnessing. Given the recent turn out of events, with one government bailout after the other, today’s joint action could hardly come as a surprise to anyone. To assume any other response would be as naïve, as giving tons of money to a pathological gambler, believing he’ll not spend a dime!  

If we look at where we stand at the moment, and the Bullish percent indicator – that show the percentage of stocks on the NYSE that indicate some sort of buy signal – we see that the current 10 % is extremely low (by historical standards). Historically, a percentage below 30 has indicated an oversold market, with a strong likleyhood for a rebounce.

From the current depressed levels a slight increase in demand will act strongly for a positive correction. From a technical point of view the trigger for such an event usually happens when we see a reversal from a colum of O’s to a new column of X’s.

In the early 20th century the French mathematician Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) came up with an original idea of how one could portray asset prices in mathematical formulas. Like flipping a coin, his idea was that the evolution of asset prices could be conceived of as purely random events, with a 50-50 chance of ticking up or ticking down as the time passes.

Today, the same fundamental building block constitutes the foundation of modern financial theory, although in a slightly different flavour, now called Brownian motion. The idea is simple. Imagine a drunk, walking from a point A to some unknown point B in the future. With every step he takes his memory goes blank. He doesn’t know where he’s going or remember where he came from. If you trace his path as he walks, and add the criterion that the size of his steps is given by the Gaussian distribution, you’ll end up with something similar to a Brownian motion.

Today, the efficient market hypothesis, CAPM, the Black Schole’s option formula and pretty much every other tool in the financial engineering toolbox, all relies on this particular foundation.

Orthogonal to this view is the polish born mathematician, Benoit Mandelbrot. The (Mis)behaviour of markets is the chronicle of his long lasting pursuit of understanding the financial markets. Instead of Brownian motion and Gaussian distribution, Mandelbrot base his views on fractal geometry, a mathematical branch he himself originated. Fractal comes from the Latin word “fractus” meaning broken. The idea is that a shape is broken down into smaller shapes, each echoing the large. Fractals can be found in many places in nature, like the British coast line, branches on a tree, or parts of a rock.  The analogy to asset prices is the similarity between different frequencies of stock market data. We know that daily observations look very similar to lower frequency data, such as monthly observations. Hence the self similarity property of the parts to the whole.

 
Picture of the Mandelbrot Set.

By observing actual asset price dynamics Mandelbrot sought to create a realistic model of real life price movements. Instead of a Gaussian distribution, his research shows that asset returns exhibit so called “fat tails”. Furthermore he argues convincingly that asset prices experience both “long term dependence”, and “volatility clusters”, all assumed to be nonexistent by the now orthodox house of modern finance.

The fat tail distribution can perhaps best be explained by a gedanken experiment taken from the book The Black Swan written by Nicholas Nassim Taleb, an intellectual descendent of Benoit Mandelbrot. Imagine a population of 1000 people. When it comes to their length and weight its hard to imagine one additional person that could affect the average, other than by an incremental amount. We just don’t se people 20 meters tall or 5000 kilograms heavy. The occurrence of extreme events – that is far from the average – becomes increasingly rare the further from the mean we move. To borrow Mandelbrot’s phrasing, the physical attributes of height and weight don’t scale.

Now instead, imagine that the average of personal income is computed – instead of height or weight – over the same population. What happens to the average income if, lets say Bill Gates is added to the group of people. Clearly, he will not only affect the total income, but also to a large extent the average of the population.

While the Gaussian distribution appropriately describes the former, evidently income is of a completely different nature. Mandelbrot chose to call this characteristic by the name, wild randomness, in contrast to mild randomness. Inspired by Vilfredo Pareto, by using so called power laws, Mandelbrot manage to find the equivalent of the Pareto 80-20 rule for asset prices. According to Vilfred Pareto and the principle of factor sparsity, for many event 80 percent of the effects come from 20 percent of the causes. For example, Pareto showed the empirical tendency that eighty percent of Italians income went to twenty percent of the population.

By looking at historical data for cotton prices, Mandelbrot in an early essay showed that the price of cotton also displayed a pattern, much similar to the one Pareto found for income, and could be characterised by wild randomness. Instead of diminishing as observations went further away from the average, he argues that asset returns scale. According to the Gaussian distribution an event like the stock market crash 1987 could only occur once every billion billion years! Governed by the mathematics of power laws, the scaling property can be described as follows:

In market terms, a power law distribution implies that the likely hood of a daily or weekly drop exceeding 20 % can be predicted from the frequency of drops exceeding 10 %, and that the same ratio applies to a 10 % vs a 5 % drop. Thus the fat tails, and hence, the chance for the 1987 crash was certainly not one in a billion billion. [1]

Another of his contribution is the occurrence of long term dependence and volatility clusters in asset prices. According to the orthodox school, none of these phenomenons are neither supposed to happen (none the less be a major determinant of future events). For example, studies by Eugene Fama, Mandelbrot’s student, estimated the importance of long term dependence. He found that about 10 percent of returns during an eight year period could be attributed to the previous eight year period.

Mandelbrot’s theory of volatility cluster is one of his later achievements. He calls it multifractal time. The idea is as follows: Some days the market are “slow” while other days the market moves “fast” When the time is “fast” lots of large deviations occur in a short period of time, hence volatility clusters. Mandelbrot’s theory combines a fractal process with “clock time” in order to produce a process with what he “calls trading” time. In his words,

Price is a function of trading time, in turn trading time is a function of clock time.[2]

To sum up, why bother with such things as fat tails, long term dependence fractal time etc… The recent financial market crises currently in full swing should act as a fresh reminder. The (Mis)behaviour of market is a book about market risk, not Gaussian risk, but real risk. The type of risk that tells you the potential loss of your portfolio; not Betas, Alphas, CVAR, Sigmas etc… but real life probabilities, that is, at least if you want to believe Benoit Mandelbrot.

The (Mis)behaviour of markets is an important book. The current financial turmoil has exposed some of the troubles and internal weaknesess in present day models. The onset of the sub prime crises in the fall of 2007, is a schoolbook example of how events can turn bad, fast. Modern financial theory has shown unable to accomplish what it claims. While the modern financial house of cards is crumbling, practitioners are looking towards new alternatives. Time will tell if the pendulum once again swings in the direction of fractal geometry and Benoit Mandelbrot.

Sources:

[1] How The Financial Gurus Get Risk All Wrong: Benoit Mandelbrot and Nicholas Nassim Taleb, Fortune 2005

[2] The (Mis)behaviour of Markets: Benoit Mandelbrot, Basic Books 2004

Now, the million dollar question seems to be: when will price inflation slow? Looking around, we see a mixed bag of forecasts ranging from tomorrow and never. In reality inflation is really persistent. By this I mean, that once you experience a rising inflationary pressure it’s hard to make it go away, it stick to you like flypaper.

Looking back several years, I have plotted the yearly change in headline CPI in the graph below.

To get a rough measure of persistency we can look at the so called Auto correlation function, where correlation is computed for inflation with regards to its subsequent “lags”.

The result is perhaps more perplexing than one first think. In the graph below we see that inflation today is still affected by the inflation rate 140 month or almost 12 years ago!

No wonder Paul Volcker had to raise interest rates to 20 % in the 70s in order to break the back of inflation.

Based on this historical fact, I don’t intend to give a precise date when I think inflation will come to a halt. But instead, I here like to point out the strong tendency for inflation to “hang around”, for those who think otherwise.

Now, looking down at the global economic chessboard, during the last couple of decades the U.S. has been wearing the crown. However, this time around Paul Kasriel at Northern Trust, believes that he might be checkmate. He writes:

Our base case economic scenario is that the U.S. economy entered a recession in early 2008, will remain in a mild recession throughout 2008 and will begin to experience an anemic recovery in the first half of 2009. The base case includes a sharp deceleration in inflation in the not-too-distant future as energy prices stabilize and then retreat due to a slowdown in the growth of global demand for energy. The Federal Reserve will maintain the federal funds rate at 2% through the first half of 2009. In the second half of 2009, when economic growth picks up enough to stop the upward trend in the unemployment rate, the Fed will start raising the funds rate.  

Our risk case scenario is that the U.S. dollar begins to fall precipitously coinciding with a rise in Treasury bond yields. U.S. inflation does not moderate because of the depreciation in the dollar. As a result, the Federal Reserve is forced to raise the funds rate even in the face of a rising U.S. unemployment rate. This would be “checkmate” for the U.S. economy, turning a relatively mild recession into a severe one. Why might the dollar dive? Because the U.S. Treasury is forced to issue more debt in order to recapitalize either Fannie/Freddie/ the Federal Home Loan Bank System/FDIC, and the rest of the world balks at being the buyer of last resort for U.S. government debt. As this is being written on Friday, July 11, a hint of this is happening. Rumors are swirling that the U.S. Treasury will have to recapitalize Fannie Mae and Freddie Mac. Rather than resulting in the usual flight-to-quality bid for U.S. Treasury securities, yields on Treasury coupon securities are rising and the dollar is falling. Another factor that could precipitate a further sharp decline in the dollar might be the severing of the pegs that foreign monetary authorities have maintained between their currencies and the U.S. dollar. The byproduct of these pegs has been upward pressure on the inflation rates in these foreign economies. If these monetary authorities can no longer tolerate this imported inflation and sever their currency pegs to the dollar, the dollar would likely go into a tailspin. 

 

When it comes to the business of forecasting prices, future markets surve as a platform where traders agree to buy or sell merchandise at some future date. Reasonably such interaction should result in better predictions, than say pollsters. As Hayek pointed out, market prices have a dual role, except for allocating resources to their most productive use, they also contain information of their value. When people have a vested financial interest at stake, the above mentioned problems with polls could easily be avoided with futures.

This brings me to IEM or the Iowa Electronic Markets. Like future markets such as CME (Chicago Mercantile Exchange), IEM provides a futures market for political election. By looking at future prices for the current presidential election, we get a better picture of the probable outcome. By watching the price paid for a democratic versus a republican victory-future, we get the percentage probabilities for both parties geting the majority of votes, as can be seen in the picture belove:

We can see that the Democrats have been in favor, pretty much all the time since June 14th 2006, when the history started. But looking at the graph we see that the republicans gained support early on this year. 
At the moment, the likelihood for a Democratic victory are 62.8 percent probability versus 32.5 for a republican victory. 

The election is held 4th of November later this year. Who will win is by no way certain. Lots of things can still happen. Don’t just listen to the pollsters, and do remember to check the IEM futures market in the upcoming months!

Im currently on vacation in Paris, with limited internet connection I thought it be appropriate to comment on the recent market development.

The Dow Jones Industrial Average is by many seen as the back bone of the U.S economy. Looking at the “leading” blue-chip stocks today, they all seem quite tired. With the Dow down 9.4 % so far this month, we have to go back as long as to the Great Depression for a larger intra-month drop in June.

I have on many occasions mentioned the Bullish percent indicator, an indicator (contrarian) that gauges the current level of risk in the market, and has a great track record. On the 19th of May I wrote in “A Stock Market Correction” that we were in for a correction. The same date the Dow Jones index peaked at 13136.69 and the bear market rally was clearly over. Since then the index has plunged13,63 % to 11346,51 today.

Soon after the peak, the Bullish percent indicator switched to a column of “O’s, indicating that demand, once more had weakened and supply was taking over. At the moment we see the NYSE Bullish percent stands at 38 %, meaning that only 38 % of the stocks in the index is experiencing some positive momentum.

This development was also captured by the VIX index that some market analysts like to keep an eye on. The VIX index measures investors risk appetite by deriving 30 days expectations on market volatility from option prices. Since the middle of May we have seen a steady increase in the index, moving almost inversely to the broader market indices.

According to the often cited maxim, we are in a official bear market when stocks have fallen by 20 %. Even if we technically are not there yet, its only one tick away. Since the absolute bull market peak in October 9th last year when the Dow hit 14164.53 stocks are down 19.9 % of today.

However, official or not, there should be no doubt that both the U.S economy and the stock market both has been in a clear bear market for some time now.

The reverse of the law of large numbers, as its name suggests, describes the reverse effect of the law of large numbers, which crops up everywhere in the fields of mathematics, physics, engineering and the social sciences. Put simply, the law of large numbers, or LLN, says that the larger the sample, the closer the average will approach to the expected average. Rolls of a die, for example, fluctuate wildly around the expected average of 3.5 in a small sample, but converge on the average as the sample size increases…

…In his work Mr Kelly addresses what happens to the balance of expectations when so-called rational independent entities start copying each other. Since copying reduces the independence of individual entities, Mr Kelly designed an experiment to see what happens to the balance of expectations when the LLN goes into reverse and individual behaviour starts to merge into group behaviour.

The experiment focuses on a number of individual entities who are faced with a choice between two equally likely options – the market will go up or the market will go down. Given that the future is unknown, in an unbiased market, the likelihood of the next move should be a 50-50 bet.

“We first examined what was the most probable outcome of expectations when a large sample was all acting/choosing independently,” says Mr Kelly.

“Then, we gradually reduced the number of individual entities by allowing first one individual to copy another, then two individuals to copy a third (or one to copy another and a second to copy a different other) and so on. This progressed step by step to the ultimate extreme of everyone copying everyone else, so the market as a whole is acting as one.”

They found that as individuals move toward herd behaviour, the probability distribution changes from the normal bell curve, with expectations clustered around the 50/50 level, through a tipping point, where there is an equal likelihood of a balanced or unbalanced market of expectations, to a position where a market is almost certain to be unbalanced in its expectations. At this extreme, the whole market has the same view, so the balance of expectations is polarised one way or the other.

Austrian economists have already provided lots of counterexamples and, economic reasons why the efficient market hypothesis is deeply flawed (read more).

The work of Mr Kelly adds an additional dimension to this criticism. The idea of the reverse law of large numbers, provides insight how real market agents act and interact, contrary to the efficient market theory. By themselves, recent market bubbles should be evidence enough, that phenomenon such as herding- and crowd behaviour is present in determining asset prices.