Diagnosing Wall Street, Lehman Brothers and Merrill Lynch

[anildhope]

Diagnosing Wall Street
How Fractals Can Explain What's Wrong with Wall Street: The geometry that describes the shape of coastlines and the patterns of galaxies also elucidates how stock prices soar and plummet
By Benoit B. Mandelbrot

Editor's Note: This story was originally published in the February 1999 edition of Scientific American. We are posting it in light of recent news involving Lehman Brothers and Merrill Lynch.

Individual investors and professional stock and currency traders know better than ever that prices quoted in any financial market often change with heart-stopping swiftness. Fortunes are made and lost in sudden bursts of activity when the market seems to speed up and the volatility soars. Last September, for instance, the stock for Alcatel, a French telecommunications equipment manufacturer, dropped about 40 percent one day and fell another 6 percent over the next few days. In a reversal, the stock shot up 10 percent on the fourth day.

The classical financial models used for most of this century predict that such precipitous events should never happen. A cornerstone of finance is modern portfolio theory, which tries to maximize returns for a given level of risk. The mathematics underlying portfolio theory handles extreme situations with benign neglect: it regards large market shifts as too unlikely to matter or as impossible to take into account. It is true that portfolio theory may account for what occurs 95 percent of the time in the market. But the picture it presents does not reflect reality, if one agrees that major events are part of the remaining 5 percent. An inescapable analogy is that of a sailor at sea. If the weather is moderate 95 percent of the time, can the mariner afford to ignore the possibility of a typhoon?

The risk-reducing formulas behind portfolio theory rely on a number of demanding and ultimately unfounded premises. First, they suggest that price changes are statistically independent of one another: for example, that today's price has no influence on the changes between the current price and tomorrow's. As a result, predictions of future market movements become impossible. The second presumption is that all price changes are distributed in a pattern that conforms to the standard bell curve. The width of the bell shape (as measured by its sigma, or standard deviation) depicts how far price changes diverge from the mean; events at the extremes are considered extremely rare. Typhoons are, in effect, defined out of existence.

Do financial data neatly conform to such assumptions? Of course, they never do. Charts of stock or currency changes over time do reveal a constant background of small up and down price movements—but not as uniform as one would expect if price changes fit the bell curve. These patterns, however, constitute only one aspect of the graph. A substantial number of sudden large changes—spikes on the chart that shoot up and down as with the Alcatel stock—stand out from the background of more moderate perturbations. Moreover, the magnitude of price movements (both large and small) may remain roughly constant for a year, and then suddenly the variability may increase for an extended period. Big price jumps become more common as the turbulence of the market grows—clusters of them appear on the chart.

According to portfolio theory, the probability of these large fluctuations would be a few millionths of a millionth of a millionth of a millionth. (The fluctuations are greater than 10 standard deviations.) But in fact, one observes spikes on a regular basis—as often as every month—and their probability amounts to a few hundredths. Granted, the bell curve is often described as normal—or, more precisely, as the normal distribution. But should financial markets then be described as abnormal? Of course not—they are what they are, and it is portfolio theory that is flawed.

Modern portfolio theory poses a danger to those who believe in it too strongly and is a powerful challenge for the theoretician. Though sometimes acknowledging faults in the present body of thinking, its adherents suggest that no other premises can be handled through mathematical modeling. This contention leads to the question of whether a rigorous quantitative description of at least some features of major financial upheavals can be developed. The bearish answer is that large market swings are anomalies, individual "acts of God" that present no conceivable regularity. Revisionists correct the questionable premises of modern portfolio theory through small fixes that lack any guiding principle and do not improve matters sufficiently. My own work—carried out over many years— takes a very different and decidedly bullish position.

I claim that variations in financial prices can be accounted for by a model derived from my work in fractal geometry. Fractals—or their later elaboration, called multifractals—do not purport to predict the future with certainty. But they do create a more realistic picture of market risks. Given the recent troubles confronting the large investment pools called hedge funds, it would be foolhardy not to investigate models providing more accurate estimates of risk.

Multifractals and the Market
An extensive mathematical basis already exists for fractals and multifractals. Fractal patterns appear not just in the price changes of securities but in the distribution of galaxies throughout the cosmos, in the shape of coastlines and in the decorative designs generated by innumerable computer programs.

A fractal is a geometric shape that can be separated into parts, each of which is a reduced-scale version of the whole. In finance, this concept is not a rootless abstraction but a theoretical reformulation of a down-to-earth bit of market folklore— namely, that movements of a stock or currency all look alike when a market chart is enlarged or reduced so that it fits the same time and price scale. An observer then cannot tell which of the data concern prices that change from week to week, day to day or hour to hour. This quality defines the charts as fractal curves and makes available many powerful tools of mathematical and computer analysis.

A more specific technical term for the resemblance between the parts and the whole is self-affinity. This property is related to the better-known concept of fractals called selfsimilarity, in which every feature of a picture is reduced or blown up by the same ratio—a process familiar to anyone who has ever ordered a photographic enlargement. Financial market charts, however, are far from being self-similar. In a detail of a graphic in which the features are higher than they are wide—as are the individual up-and-down price ticks of a stock—the transformation from the whole to a part must reduce the horizontal axis more than the vertical one. For a price chart, this transformation must shrink the timescale (the horizontal axis) more than the price scale (the vertical axis). The geometric relation of the whole to its parts is said to be one of self-affinity.

The existence of unchanging properties is not given much weight by most statisticians. But they are beloved of physicists and mathematicians like myself, who call them invariances and are happiest with models that present an attractive invariance property. A good idea of what I mean is provided by drawing a simple chart that inserts price changes from time 0 to a later time 1 in successive steps. The intervals themselves are chosen arbitrarily; they may represent a second, an hour, a day or a year.

The process begins with a price, represented by a straight trend line (illustration 1). Next, a broken line called a generator is used to create the pattern that corresponds to the up and- down oscillations of a price quoted in financial markets. The generator consists of three pieces that are inserted (interpolated) along the straight trend line. (A generator with fewer than three pieces would not simulate a price that can move up and down.) After delineating the initial generator, its three pieces are interpolated by three shorter ones. Repeating these steps reproduces the shape of the generator, or price curve, but at compressed scales. Both the horizontal axis (timescale) and the vertical axis (price scale) are squeezed to fit the horizontal and vertical boundaries of each piece of the generator.

Interpolations Forever
Only the first stages are shown in the illustration, although the same process continues. In theory, it has no end, but in practice, it makes no sense to interpolate down to time intervals shorter than those between trading transactions, which may occur in less than a minute. Clearly, each piece ends up with a shape roughly like the whole. That is, scale invariance is present simply because it was built in. The novelty (and surprise) is that these self-affine fractal curves exhibit a wealth of structure—a foundation of both fractal geometry and the theory of chaos.

A few selected generators yield so-called unifractal curves that exhibit the relatively tranquil picture of the market encompassed by modern portfolio theory. But tranquillity prevails only under extraordinarily special conditions that are satisfied only by these special generators. The assumptions behind this oversimplified model are one of the central mistakes of modern portfolio theory. It is much like a theory of sea waves that forbids their swells to exceed six feet.

The beauty of fractal geometry is that it makes possible a model general enough to reproduce the patterns that characterize portfolio theory's placid markets as well as the tumultuous trading conditions of recent months. The just described method of creating a fractal price model can be altered to show how the activity of markets speeds up and slows down—the essence of volatility. This variability is the reason that the prefix "multi-" was added to the word "fractal."

To create a multifractal from a unifractal, the key step is to lengthen or shorten the horizontal time axis so that the pieces of the generator are either stretched or squeezed. At the same time, the vertical price axis may remain untouched. In illustration 2, the first piece of the unifractal generator is progressively shortened, which also provides room to lengthen the second piece. After making these adjustments, the generators become multifractal (M1 to M4). Market activity speeds up in the interval of time represented by the first piece of the generator and slows in the interval that corresponds to the second piece (illustration 3).

Such an alteration to the generator can produce a full simulation of price fluctuations over a given period, using the process of interpolation described earlier. Each time the first piece of the generator is further shortened—and the process of successive interpolation is undertaken—it produces a chart that increasingly resembles the characteristics of volatile markets (illustration 4).

The unifractal (U) chart shown here (before any shortening) corresponds to the becalmed markets postulated in the portfolio theorists' model. Proceeding down the stack (M1 to M4), each chart diverges further from that model, exhibiting the sharp, spiky price jumps and the persistently large movements that resemble recent trading. To make these models of volatile markets achieve the necessary realism, the three pieces of each generator were scrambled—a process not shown in the illustrations. It works as follows: imagine a die on which each side bears the image of one of the six permutations of the pieces of the generator. Before each interpolation, the die is thrown, and then the permutation that comes up is selected.

What should a corporate treasurer, currency trader or other market strategist conclude from all this? The discrepancies between the pictures painted by modern portfolio theory and the actual movement of prices are obvious. Prices do not vary continuously, and they oscillate wildly at all timescales. Volatility—far from a static entity to be ignored or easily compensated for—is at the very heart of what goes on in financial markets. In the past, money managers embraced the continuity and constrained price movements of modern portfolio theory because of the absence of strong alternatives. But a money manager need no longer accept the current financial models at face value.

Instead multifractals can be put to work to "stress-test" a portfolio. In this technique the rules underlying multifractals attempt to create the same patterns of variability as do the unknown rules that govern actual markets. Multifractals describe accurately the relation between the shape of the generator and the patterns of up-and-down swings of prices to be found on charts of real market data.

On a practical level, this finding suggests that a fractal generator can be developed based on historical market data. The actual model used does not simply inspect what the market did yesterday or last week. It is in fact a more realistic depiction of market fluctuations, called fractional Brownian motion in multifractal trading time. The charts created from the generators produced by this model can simulate alternative scenarios based on previous market activity.

These techniques do not come closer to forecasting a price drop or rise on a specific day on the basis of past records. But they provide estimates of the probability of what the market might do and allow one to prepare for inevitable sea changes. The new modeling techniques are designed to cast a light of order into the seemingly impenetrable thicket of the financial markets. They also recognize the mariner's warning that, as recent events demonstrate, deserves to be heeded: On even the calmest sea, a gale may be just over the horizon.

http://www.sciam.com/article.cfm?id=multifractals-explain-wall-street

 SCIENTIFIC AMERICAN   16 Sept 2008
Mathematicians predicted stock market volatility years ago

Crash, crash. Doom, doom. Panic on the Street. Wall Street yesterday suffered its worst decline since the Sept. 11 terrorist attacks – and the free fall suggests it may be time to consider burying the family stash of Krugerrands under the rose garden or tool shed.

The list of Chicken Little events was long:  investment house Lehman's bankruptcy, the capital crunch for mega-insurer AIG, the sale of Merrill Lynch to Bank of America. But Stormy Monday (a weather system that appears to be carrying over to be lingering) probably came as no surprise to a cadre of mathematicians who specialize in surveying the dynamics of markets.

One of those long-time market watchers is fractal pioneer Benoit Mandelbrot. In 1999, Scientific American published an article by Mandelbrot that showed how fractal geometry can model market volatility, while revealing the intrinsic deficiencies of a cornerstone of finance called modern portfolio theory (for which there has been awarded more than one Nobel Prize in Economics).

Mandelbrot, 83, contends that portfolio theory, which tries to maximize return for a given level of risk, treats extreme events (like, say, yesterday's market shockers) with "benign neglect: it regards large market shifts as too unlikely to matter or as impossible to take into account." The faulty assumption of modern portfolio theorists, in Mandelbrot's view, is that price changes do not drift far from the mean when observing daily ups and downs—so extreme events are exceedingly rare. "Typhoons, in effect, are defined out of existence," he wrote.

In place of modern portfolio theory's reliance on the canonical Bell Curve, Mandelbrot drags in (surprise!) the fractal. A fractal is a geometric shape that can be divvied up into parts, each of which is a Mini-Me facsimile of the whole. If you look closely enough, you can see fractals everywhere. Besides monotonous screen savers, fractal patterns describe the distribution of galaxies and the shape of coastlines. Mandelbrot devised so-called multi-fractal generators that can use historical market data to simulate alternative scenarios of where stocks or other securities might be headed.

The experience of editing Mandelbrot a decade ago was both fun and exasperating. Trying to translate the complexities of multifractals into a finished text demanded a lot of neural gear grinding to say the least.

Dealing with this renowned creator of the Mandelbrot set was another challenge.

The conversation always seemed to drift back to his other favorite subject: how the rest of the world  did not appreciate the  value of his work. At one point, I asked  whether he believed he should receive a Nobel (highly unlikely for a mathematician).  One does not discuss such things, he said, as if it might jinx his chances.

We received a stack of letters and e-mails after the article was published, including a bundle from adherents of  the so-called Elliott Wave Theory alleging that Mandelbrot had lifted his ideas (on the multifractal nature of markets) from the work of Ralph Nelson Elliott in the 1930s. An insulted Mandelbrot dismissed the charges with withering disdain: "The idea is ancient, but his use and mine stand in absolute contrast," he responded in the magazine's letters column.

Perhaps the most telling criticism of Mandelbrot's work comes from the markets themselves. In the decade or so since his article was published, the use of multifractal market analysis is still largely an academic endeavor. But Mandelbrot should not be judged too harshly. Multifractals may not be in routine use on the trading floors. But Mandelbrot's work on market extremes has served to broadcast to the Street a notion that has been known forever on the street: Yes, Virginia, sh*t really does happen.

http://www.sciam.com/blog/60-second-science/post.cfm?id=mathematicians-predicted-stock-mark-2008-09-16

[anildhope]

23 Sept 2008
The Lesson Ignored

A Lesson that the markets ignored

By Richard Cohen <cohenr@washpost.com>

Of all the self-proclaimed experts I wanted to hear from about the financial crisis, the one I looked forward to the most was Nick Leeson, late of Britain's Barings Bank. In 1995, he bet hugely on Nikkei futures (whatever they are) and lost something like $1.4 billion. Leeson was 28 years old and often drunk, Barings was 233 years old and in fiduciary senility. Leeson went to prison, Barings went bust and Wall Street, without so much as a pause, went on its merry way.

Sadly, Leeson did not have much to say about the current financial crisis. Writing last week in the Guardian, he instead expressed bitterness that the former owners of Barings went on with their lives while he spent 4 1/2 years in prison. What he did not say, to the regret of us all, is how once again the kids were allowed to play with huge amounts of money without any adult supervision.

"I was astonished that nobody stopped me," he wrote in his book "Rogue Trader." "People in London should have known." Indeed.

The theme in the current financial crisis is not, as John McCain would have it, greed, since that, like lust, will be with us forever. Instead, it is transparency. Leeson, you may recall, was dealing from Singapore in exotic derivatives that his bosses in London little understood. All they knew was that Leeson was putting huge profits on the books, not that those books had anything to do with reality.

Somewhat the same thing happened on Wall Street. The complicated, exotic and downright erotic financial instruments cooked up at the investment houses were, in fact, little understood not only by the buyers but also by the sellers. You can see that from what they said and from what they did: Lehman Brothers, Bear Stearns, AIG and others all held on to financial instruments that were worth less than they once thought. This was truly a case of the blind leading the blind.

"The problem is that nobody knows what any institution owns and what the terms of the securities they own are and what they're worth," New York Mayor Michael Bloomberg said Sunday on "Meet the Press." He's saying what others on the Street having been saying for some time: Nobody knows what these things - securitized mortgages, etc. - are worth. And, just to darken the mystery (and maybe your mood), no one knows the value of the underlying real estate, either.

I started with Leeson for a reason. He is the personification of a generational gap in the finance industry. He was young and computer-savvy, and his bosses in London were neither. That was true on Wall Street, too. The very top guys really had little idea of what was going on below. Everything was going right. They were making lots of money, which they deserved - in their wonderful circular reasoning - because they were making it. This, I tell you, is the true magic of the vaunted market: It justifies both stupidity and greed.

Now the government is proposing another pig in a poke. The huge federal bailout is necessary, but Democrats are right to insist on detail and oversight. For too long, the financial markets have operated without much of either. Now the Bush administration is asking Congress for a blank check, what New Jersey Gov. Jon Corzine calls the "moral equivalent" of the congressional resolution that wound up authorizing the Iraq war. Corzine, a former Goldman Sachs chairman (not to mention U.S. senator), is a voice worth heeding nowadays. When I talked to him, he had just gotten hold of the two-page administration program. Two pages! This is another exotic financial instrument.

The wise words of William Goldman, the screenwriter, should echo in Congress's ears. He not only coined the phrase "follow the money" for "All the President's Men," but he expressed the sum total of knowledge about the making of movies with: "Nobody knows anything." The same has been true about opaque financial instruments. It's up to Congress to fix that.

The lesson of Leeson has yet to be learned. Financial markets have moved well beyond the trading of things that could be seen or measured or weighed. On Wall Street, older men employed the lingo of younger men to pretend they knew what was happening - but they didn't. Now, Congress is being asked to do something similar. That won't do. Bear down. Ask questions. Don't be afraid to regulate. Act as if you're the government, for crying out loud. Because if you don't do this right, you soon won't be.

http://www.washingtonpost.com/wp-dyn/content/article/2008/09/22/AR2008092201922.html

[sookthai]

Daily Mail    24 Oct 2008
Once-in-a-century Credit Tsunami
Financial crisis is 'once in a century credit tsunami', Greenspan says as he talks of his shock at state of economy
By David Gardner

'Once in a century credit tsunami': Alan Greenspan describing the financial crisis to Congress in Washington today

Former U.S. Federal Reserve chairman Alan Greenspan has admitted that he was blindsided by the 'once-in-a-century credit tsunami' that has wreaked havoc on the world's economies.

The man once hailed as one of the most accomplished central bankers in America's history confessed he was in 'a state of shocked disbelief'.

Mr Greenspan, who headed the Federal Reserve for more than 18 years, said the financial crisis 'turned out to be much broader than anything I could have imagined'.

And he warned the economic meltdown will drive millions of people out of work.

'Given the financial damage to date, I cannot see how we can avoid a significant rise in layoffs and unemployment,' Mr Greenspan told congressional lawmakers.

'Fearful American households are attempting to adjust, as best they can, to a rapid contraction in credit availability, threats to retirement funds and increased job insecurity.'

The humbled former Fed chief, who has written best-selling books on the economy, has been blasted by critics who claim he left interest rates too low for too long, spurring an unsustainable housing boom, and failed to crackdown on sub prime mortgages being doled out to home-buyers who didn't satisfy conventional borrowing requirements.

It was the collapse of these mortgages and rising defaults a year ago that triggered the current crisis.

Fighting to restore his battered reputation, Mr Greenspan blamed the sub prime collapse on over-eager investors who did not take into account the threats that would be posed once home prices stopped surging upward.

'It was the failure to properly price such risky assets that precipitated the crisis,' he added. 

Eye-popping: A disbelieving trader doing his numbers as shares on Wall Street tumbled last night before closing down almost six per cent

Mr Greenspan was hauled in front of the House of Representatives Oversight Committee along with former U.S. Treasury Secretary John Snow and Securities and Exchange Commission chairman Christopher Cox as Congress sought to discover how much regulatory failings contributed to the crisis.

'The list of mistakes is long and the cost to taxpayers is staggering,' said committee chairman Henry Waxman.

'Our regulators became enablers rather than enforcers. Their trust in the wisdom of the markets was infinite. The mantra became that government regulation is wrong. The market is infallible.

'For too long, the prevailing attitude in Washington has been that the market always knows best.

'The Federal Reserve had the authority to stop the irresponsible lending practices, but its long-time chairman, Alan Greenspan, rejected pleas that he intervene,' he added.

Mr Waxman, a Democrat, asked point-blank whether Mr Greenspan agreed he was wrong in failing to intervene in the markets when he was in charge of the U.S. central bank.

Mr Greenspan has long argued that regulatory intrusion slows the economy.

'My question is simple: Were you wrong?' asked Mr Waxman.

Mr Greenspan said he was 'partially wrong' in the case of credit default swaps, complex trading tools meant to act as insurance for bond buyers against default.

'I made a mistake in presuming that the self-interest of organisations, specifically banks and others, was such that they were best capable of protecting their own shareholders and the equity,' he admitted.

It was the closest he got to accepting some blame for the financial calamity that has reverberated around the world.

Mr Greenspan said stabilisation of home prices is vital to revive the paralysed economy, but he said that was not likely to occur for 'many months in the future.'

When the housing market finally recovers, then 'the market freeze should begin to measurably thaw and frightened investors will take tentative steps towards re-engagement with risk,' he added.

Until that happens, he said the government is correct to move forward aggressively with efforts to support the financial sector.

He called the £400billion package approved by Congress a fortnight ago 'adequate to serve the need' and claimed its impact was already being felt in the markets.

http://www.dailymail.co.uk/news/worldnews/article-1079485/Financial-crisis-century-credit-tsunami-Greenspan-says-talks-shock-state-economy.html

---

Los Angeles Times   23 Oct 2008
A bridge too far!

Dear Chairman Greenspan: Remember that cheap money?

 

Former Federal Reserve Chairman Alan Greenspan went before a House committee today to provide some insight on the "sources" of the current financial crisis.

One of those sources, you might suspect, would be Greenspan's decision to keep interest rates at ridiculously cheap levels from 2002 through 2004.

Yet he mentioned nothing about monetary policy in his five-page prepared remarks. Instead, the maestro focused on the failures of the free-market system.

 Here, Greenspan explained how investors fooled themselves:

"Subprime mortgages pooled and sold as securities became subject to explosive demand from investors around the world. These mortgage backed securities being 'subprime' were originally offered at what appeared to be exceptionally high risk-adjusted market interest rates. But with U.S. home prices still rising, delinquency and foreclosure rates were deceptively modest. Losses were minimal. To the most sophisticated investors in the world, they were wrongly viewed as a 'steal.' "

He also recalled how he mused about investors' lack of concern about the level of risk they were taking in the boom days:

"In 2005, I raised concerns that the protracted period of underpricing of risk, if history was any guide, would have dire consequences."

Yet as Rep. Henry A. Waxman (D-Calif.) noted at the hearing, the Greenspan Fed "had the authority to stop the irresponsible lending practices that fueled the subprime mortgage market," but chose to let them ride.

Greenspan also expressed surprise that the Wall Street rocket scientists who designed derivative securities had failed to account for worst-case scenarios in forecasting how their lab monsters would perform:

"In recent decades, a vast risk management and pricing system has evolved, combining the best insights of mathematicians and finance experts supported by major advances in computer and communications technology. A Nobel Prize was awarded for the discovery of the pricing model that underpins much of the advance in derivatives markets. This modern risk management paradigm held sway for decades. The whole intellectual edifice, however, collapsed in the summer of last year because the data inputted into the risk management models generally covered only the past two decades, a period of euphoria. Had instead the models been fitted more appropriately to historic periods of stress, capital requirements would have been much higher and the financial world would be in far better shape today, in my judgment."

So why wasn't he raising those questions about derivatives in 2005, instead of defending them as beneficial for the financial system (and arguing against their regulation)?

More important - and, again, missing entirely from Greenspan's explanation of the roots of the crisis -- why did the Fed maintain such a wildly easy-money policy from 2002 to 2004, when the central bank's benchmark short-term interest rate was no higher than 2.25% the entire period (and was below 1.75% for most of that time)?

Without cheap money, the credit-market bubble could never have reached the epic size that it did.

Greenspan must know this. Admitting it, however, apparently still is a bridge too far for him.

http://latimesblogs.latimes.com/money_co/2008/10/former-federal.html

[sookthai]

 28 Oct 2008

Credit crisis:

World in turmoil

 

A look at the regions of the world most affected by the financial crisis, and what governments are doing to try to alleviate the financial turmoil.

AMERICAS

ARGENTINA:

Background: Rich in resources with a well-educated workforce and one of South America's largest economies, but it has also fallen prey to a boom and bust cycle.

Key data: Gross National Income per capita: $6,050 (World Bank, 2007)

Latest: The government has nationalised the country's 10 private pension funds, putting it in control of almost $30bn (£18bn) of investments. Shares slumped in response to the move, which the government said was aimed at protecting the funds from global market turmoil.

BRAZIL:

Background: Natural resources, particularly iron ore, are highly prized by major manufacturing nations. Has become self-sufficient in oil, ending decades of dependence on foreign producers. Has had to be bailed out in times of economic crisis, but reforms in the 1990s, including privatisations, brought some financial stability. There is a wide gap between rich and poor.

Key data: Gross National Income per capita: $5,910 (World Bank, 2007)

Latest: On 22 October, Brazil announced a plan to allow government-controlled Banco do Brasil and Caixa Economica Federal to purchase shares in private financial institutions. It hopes that the measure will shore up the market, but shares fall 10% and trading is suspended for the fifth time in recent weeks. On 23 October, the government abandons its tax on foreign investments and announces plans to sell up to $50bn in dollar swap futures contracts to try to stop its currency falling.

CANADA:

Background: One of the world's richest nations - thanks partly to immigration. The North American Free Trade Agreement, involving Canada, the US and Mexico, has brought a trade boom. Has been asserting sovereignty in the Arctic with the possible bounty from previously-untapped reserves of oil and gas at stake.

Key data: Gross National Income per capita: $39,420 (World Bank, 2007)

Latest: The Bank of Canada cut its key interest rate by a quarter point, to 2.25%, on 21 October.

This is the second cut this month - the bank cut the rate by half a percentage point on 8 October in a co-ordinated effort with other central banks.

On 10 October, Finance Minister Jim Flaherty attempted to ease the credit crunch by announcing CAN$25bn ($21bn) of asset-swaps between the country's major banks and the government-owned Canada Mortgage and Housing Corporation (CMHC). The Bank of Canada said three days later it would provide exceptional liquidity to the financial system "as long as conditions warrant".

MEXICO:

Background: Major oil producer and exporter. Nearly one-third of government revenue comes from the industry. Much bought by the US. Prosperity remains a dream for most Mexicans. Rural areas are often neglected and huge shanty towns ring the cities. Many poor Mexicans try to cross the 3,000-km border with the US in search of a job.

Key data: Gross National Income per capita: $8,340 (World Bank, 2007)

Latest: On 21 October, the Mexican government said it would offer $3.92bn in loan guarantees to help local firms refinance debt maturing in 2008. This is in addition to President Felipe Calderon's proposal to spend $4.4bn on infrastructure and energy projects to boost the economy.

Earlier in October, the central bank sold a combined $8.9bn in foreign currency reserves in a week to prop up the falling peso, which recovered somewhat on 13 October after falling to an all-time low against the US dollar.

US:

Background: The world's foremost economic and military power. Despite relative prosperity in recent years, the gap between rich and poor is a major challenge. More than 30 million Americans live below the official poverty line, with a disproportionate percentage of these being African-Americans and Hispanics.

Key data: Gross National Income per capita: $46,040 (World Bank, 2007)

Latest: The Treasury has said it wants to implement its $700bn financial bail-out plan quickly. It also announced plans to inject $250bn into many of the nation's banks, including JP Morgan Chase, Goldman Sachs and the Bank of New York Mellon Corp.

 

 

ASIA-PACIFIC

AUSTRALIA:

Background: In the past 20 years has made its near neighbours a priority in foreign policy and its economy is geared towards Asia. Migration continues to shape Australia.

Key data: Gross National Income per capita: $35,960 (World Bank, 2007)

Latest: Australia's central bank intervened to support its currency on 24 October and then again on 27 October.

It had last intervened more than a year ago and before that had not done so since 2001.

On 7 October, Australia's central bank cut its key interest rate from 7% to 6% - a much larger-than-expected reduction. The government later announced it would guarantee all bank deposits with financial institutions over the next three years.

CHINA:

Background: After stagnating for more than two decades under the rigid authoritarianism of early communist rule China now has the world's fastest-growing economy and is undergoing what has been described as a second industrial revolution. Relations with trading partners have been strained over China's huge trade surplus and the piracy of goods

Key data: Gross National Income per capita: $2,360 (World Bank, 2007)

Latest: China has also joined the interest rate offensive, cutting rates by 0.27 percentage points. It will join Japan, South Korea and other Asian countries in an $80bn reserve-pool scheme from mid-2009 to boost liquidity in the region.

HONG KONG:

Background: The former British colony became a special administrative region of China in 1997. Governed under the principle of "one country, two systems", under which China has agreed to give the region a high degree of autonomy and to preserve its economic and social systems for 50 years from the date of the handover.

Key data: Gross National Income per capita: $31,610 (World Bank, 2007)

Latest: The central banks joined the growing number of countries to cut their interest rates. Has promised to guarantee all bank deposits until 2010.

JAPAN:

Background: The world's second-biggest economy, achieving an economic miracle in the second half of the 20th century that was the envy of the rest of the world.

Key data: Gross National Income per capita: $37,670 (World Bank, 2006)

Latest: Japan's Economy Minister Kaoru Yosano said on 21 October the government was ready to support major banks with public funds, so that small and medium-sized companies would not struggle to access credit.

The authorities have also relaxed regulations on companies buying up their own shares.

A 1.8 trillion yen ($18bn) stimulus plan was approved by the lower house of parliament and the Bank of Japan has put 4.5 trillion yen ($45.5bn) into the banking system.

Prime Minister Taro Aso said more action was needed to boost the country's flagging economy.

MALAYSIA:

Background: Malaysia is one of the world's largest producers of computer disk drives, palm oil, rubber and timber.

Exports are a key part of the economy, but the government has been trying to increase domestic demand.

Data: Gross national income per capita: $6,540 (World Bank, 2007)

Latest: The government has offered to guarantee all local and foreign currency deposits up until the end of 2010.

NEW ZEALAND:

Background: Agriculture is the economic mainstay, but manufacturing and tourism are important and there is a fledgling film industry. New Zealand has diversified its export markets and has developed strong trade links with Australia, the US, Japan, and China.

Key data: Gross national income per capita: $28,780 (World Bank, 2007)

Latest: The government is planning to guarantee retail deposits, initially for two years.

SINGAPORE:

Background: Singapore is south-east Asia's hi-tech, wealthy city state. A former colonial outpost of Britain, Singapore has become one of the world's most prosperous regions - with a thriving port, and skyscrapers.

It is often referred to as one of Asia's economic "tigers". Singapore's economy has been driven by electronics manufacturing as well as financial services.

Data: Gross national income per capita: $32,470 (World Bank, 2007)

Latest: The government has offered to guarantee all local and foreign currency deposits up until the end of 2010.

SOUTH KOREA:

Background: South Korea is one of Asia's wealthiest countries. It enjoys major export success in a number of manufacturing industries, but especially shipbuilding, car-making, and electronics.

Key data: Gross national income per capita: $28,780 (World Bank, 2007)

Latest: On 27 October, South Korea's central bank cut its key interest rate from 5% to 4.25% at a rare, unscheduled meeting.

Previously, South Korea's government had pledged to guarantee foreign-currency borrowing by the country's banks to help stabilise financial markets.

The finance ministry, the central bank and the financial services commission said about $100bn of borrowed funds would be covered by the deal. The government will also provide $30bn of liquidity to banks, and there will be more aid to small businesses.

 

 

EUROPE

AUSTRIA:

Background: One of the eurozone's strongest economies which has grown faster than average for the last four years. It exports products such as vehicles and luxury commodities to other European nations and increasingly to newer EU member states such as Hungary.

Data: Gross national income per capita: $42,700 (World Bank, 2007)

Latest: Chancellor Alfred Gusenbauer said on 13 October that his government would provide up to 85bn euros ($114bn) in interbank loan guarantees and up to 15bn euros ($20bn) in equity to support the country's banking sector. The government had already announced a guarantee for all personal bank savings, applicable from 1 October.

BELARUS:

Background: The country became independent in 1991 after the collapse of the Soviet Union. Much of its growth in recent years has stemmed from its access to relatively cheap Russian gas and oil, which it has been able to sell on the international market at a higher price.

Data: Gross national income per capita: $4,220 (World Bank, 2007)

Latest: Belarus has been in talks with the International Monetary Fund to obtain funding in the wake of the recent financial turmoil.

BELGIUM:

Background: With few natural resources, Belgium is reliant on imported raw materials and so is vulnerable to rising commodity prices. Roughly three-quarters of its trade is with other EU countries; Germany, Netherlands and France are its biggest trading partners.

Data: Gross national income per capita: $40,710 (World Bank, 2007)

Latest: The government agreed to guarantee bank deposits of up to 100,000 euros ($136,000) - an increase of 80,000 euros.

The country's largest banking group, Fortis, needed the intervention of the Belgian and Dutch governments and the sale of some of its assets to French giant BNP Paribas, to stay alive after getting into difficulty over the purchase of Dutch bank ABN Amro.

DENMARK:

Background: Danes enjoy one of the highest standards of living in the world thanks to successful exports and extensive government welfare measures. It opted out of the European Economic and Monetary Union but its currency, the krona, is pegged to the euro.

Data: Gross national income per capita: $54,910 (World Bank, 2007)

Latest: The Danish parliament approved a government-backed crisis plan, which includes an unlimited guarantee on savings deposits. The central bank has raised its key interest rate by 0.5 percentage points to 5.5%.

ESTONIA:

Background: Estonia regained its independence after the collapse of the USSR in 1991 and since then has established one of the strongest economies in Central Europe. Its electronics and communications sectors are particularly strong. It joined the EU in 2004 and its currency is pegged to the euro.

Data: Gross national income per capita: $13,200 (World Bank, 2007)

Latest: The government more than doubled its bank deposit guarantee to 50,000 euros ($68,000), in line with other European Union member states.

FRANCE:

Background: Nicolas Sarkozy was elected President in 2007 promising sweeping economic and social reforms to tackle sluggish economic growth and high unemployment. He aims to cut taxes, make employment rules more flexible and rein in powerful trades unions. According to French finance minister Christine Lagarde, the country looks to be heading for recession.

Data: Gross national income per capita: $38,500 (World Bank, 2007)

Latest: The chairman of French savings bank Caisse d'Epargne has quit over the loss of 600m euros (£466m) in a "trading incident" amid global market chaos.

Charles Milhaud said he accepted full responsibility for the lost cash and is expected to leave without a pay-off.

GERMANY:

Background: Once celebrated as Europe's economic powerhouse, recent falling export orders and rising costs have pushed Germany to the brink of recession. The cost of incorporating the German Democratic Republic is also still being felt.

Data: Gross national income per capita: $38,860 (World Bank, 2007)

Latest: On 17 October the German parliament overwhelmingly approved a 500 billion euro ($675bn) financial rescue package. The plan includes a fund to provide up to 400bn euros in interbank loan guarantees and 80bn euros ($109bn) to acquire stakes in troubled banks.

The government stepped in on 6 October to avoid the collapse of Germany's second-biggest commercial property lender, Hypo Real Estate. In an attempt to prevent a subsequent run on banks, the government announced it would guarantee all personal bank deposits in the country.

GREECE:

Background: Greece saw rapid economic change after World War II, thanks largely to the success of tourism and shipping. The country is one of the poorest in the eurozone and the public sector accounts for 40% of GDP.

Data: Gross national income per capita: $29,630 (World Bank, 2007)

Latest: The Greek government said on 3 October it would fully guarantee all bank deposits of citizens, but an official added that this was a "political commitment" and the banking system was not at risk.

HUNGARY:

Background: Hungary's transition from a planned to a free market economy was smoother than for many of its former Soviet neighbours. By 1998 it was attracting nearly half of all foreign investment in the region, much of it from Germany. It has struggled with a low employment rate and a large budget deficit.

Data: Gross national income per capita: US $11,570 (World Bank, 2007)

Latest: On the evening of 26 October, news of a "substantial financial package" from the International Monetary Fund (IMF) contributed to reassuring investors somewhat, and slightly boosting the forint against the dollar.

Hungary's central bank raised interest rates by three percentage points on 22 October to counter a sharp fall in the value of its currency, the forint. The emergency move took bank rates to 11.5%. The currency has suffered as investors have pulled out of forint assets amid worries about its banking system.

ICELAND:

Background: After gaining independence in 1944, Iceland become one of the wealthiest nations in the world. Its prosperity initially rested on the fishing industry, but amid the gradual contraction of this sector, the financial sector expanded dramatically overseas. Before the global credit crunch took hold, Icelandic banks had foreign assets worth about 10 times the country's GDP, with debts to match.

Data: Gross national income per capita: $54,100 (World Bank, 2007)

Latest: Iceland's central bank increased its key interest rate from 12% to 18% on 28 October, saying it was part of its agreement with the International Monetary Fund (IMF) to borrow $2.1bn.

On the same day, Iceland's prime minister said the country needed to borrow about $4bn on top of the IMF loan and had approached the European Central Bank and the Federal Reserve as well as its nordic neighbours for help.

On 24 October it became the first Western nation to go to the IMF for support since 1976. Negotiations with Russia for a big loan to support the country's banking system had earlier collapsed.

Iceland got in financial difficulties after it took over its three biggest banks: Landsbanki, Kaupthing and Glitnir.

IRELAND:

Background: Since joining the European Community in 1973, rapid growth has transformed Ireland from a largely agricultural society into a modern, hi-tech economy. Its rapid growth, fuelled by foreign investment and a construction boom, saw it dubbed the Celtic Tiger. This year however, it became one of the first eurozone countries to slide into recession.

Data: Gross national income per capita: $48,140 (World Bank, 2007)

Latest: Ireland was the first government to come to the rescue of its citizens' savings, promising on 30 September to guarantee all deposits, bonds and debts in its six main banks for two years.

The move initially prompted consternation among some European partners, but other countries have since followed suit.

ITALY:

Background: One of the largest European economies, Italy's major industries - including motor vehicles and fashion - enjoy international success. Its rate of economic growth, however, has lagged behind the European average with high rates of unemployment, particularly in the south.

Data: Gross national income per capita: $33,540 (World Bank, 2007)

Latest: Finance Minister Giulio Tremonti said on 13 October that the government would spend "as much as necessary" to support his country's financial institutions. The governor of the Bank of Italy, Mario Draghi, meanwhile announced it would temporarily swap up to 40bn euros ($54bn) of bonds for Italian bank debt.

On 8 October, Prime Minister Silvio Berlusconi said the government was prepared to buy stakes in failing banks while waiving voting rights in an effort to guarantee stability. It would also step in to back deposits up to the current insured level of 103,000 euros ($141,000) if necessary, he said.

NETHERLANDS:

Background: The Netherlands is one of the world's biggest exporters of food products thanks to its highly mechanised agricultural sector. After two decades of strong growth and low unemployment, the economy ran into more troubled waters as global trade slowed in the early years of the new millennium.

Data: Gross national income per capita: $45,820 (World Bank, 2007)

Latest: The Dutch government provided a 3bn euro ($3.8bn; £2.4bn) cash injection to the insurer Aegon on 28 October.

Previously it had given ING a 10bn euro ($13.4bn; £7.7bn) cash injection.

The government is also offering a 200bn euro package of loan guarantees to Dutch banks.

NORWAY:

Background: Norway enjoys one of the highest standards of living in the world, in large part due to the discovery in the late 1960s of offshore oil and gas deposits. It is among the world's largest exporters of fuels and fuel products. Some of the considerable surplus revenue is in a fund, which has been valued at $250bn, which is invested abroad.

Data: Gross national income per capita: $76,450 (World Bank, 2007)

Latest: The central bank, also outside the eurozone, said it would issue up to 350bn kroner ($55bn) in bonds to banks to help improve liquidity in the market.

POLAND:

Background: In 1989, the year communist rule ended, Poland was struggling with massive foreign debt and on the verge of economic collapse. After a difficult period of economic liberalisation, it enjoyed fast economic growth - expanding by 6.5% in 2007. Membership of the EU in 2004 saw funds flow in to the country and workers flow out to other member states.

Data: Gross national income per capita: $9,840 (World Bank, 2007)

Latest: The government has been meeting to assess the eurozone financial rescue agreement, while the central bank has been preparing a package to help build confidence in the Polish banking sector.

PORTUGAL:

Background: Portugal is continuing the process of liberalising its sluggish economy. Jose Socrates' Socialist Party, elected in 2005 after promising to revive the country's fortunes, has sharply cut spending by reducing pensions, raising the retirement age and withdrawing civil service benefits in an attempt to reduce one of Europe's biggest budget deficits .

Data: Gross national income per capita: $18,950 (World Bank, 2007)

Latest: The government said it would guarantee bank deposits and offer a financing line worth 20bn euros ($27.5bn) to guarantee the liquidity of its banks.

RUSSIA:

Background: Russia is a country of massive natural resources. High commodity prices and an expanding banking sector have helped it develop into a fast-growing economy and to accumulate large foreign reserves. It has expanded by an average of 7% a year since the financial crisis of 1998.

Data: Gross national income per capita: $7,560 (World Bank, 2007)

Latest: The upper house of parliament, the Federation Council, passed a law on 13 October giving the state-run Bank for Development and Foreign Economic Activities (Vnesheconombank) 1.3 trillion roubles ($50bn) to pay off or service Russian banks' foreign loans. It came after President Dmitry Medvedev announced 950bn roubles ($36.4bn) of long-term help for banks at an emergency Kremlin meeting on 7 October.

SPAIN:

Background: Spain grew quickly in the decades following the death of dictator General Franco in 1975 as its economy was transformed. After the Europe-wide recession in the 1990s, Spain enjoyed relatively strong growth thanks to further liberalisation and by a construction boom which is cooling rapidly . The government has managed to bring down Spain's stubbornly high unemployment rate in recent years.

Data: Gross national income per capita: $29,450 (World Bank, 2007)

Latest: Spanish Prime Minister Jose Luis Rodriguez Zapatero announced on 13 October that his government would set aside a maximum of 100bn euros ($134bn) to guarantee interbank loans for the remainder of 2008. But Mr Zapatero said the government would not, for now, take steps to recapitalise Spanish banks, because "we do not have solvency problems".

On 10 October, the government announced the creation of a 30bn euro ($40bn) fund to buy assets from Spanish financial institutions to help stabilise them and unfreeze credit. Three days earlier, it had increased bank deposit guarantees to 100,000 euros ($136,000) from the current 20,000 euros.

SWEDEN:

Background: Sweden survived its own credit crunch in the 1990s when house prices slumped and unemployment and bankruptcies rose rapidly. The government injected capital into failing banks and guaranteed depositors and creditors of stricken banks. Most of the money was regained as the economy recovered.

Data: Gross national income per capita: $46,060 (World Bank, 2007)

Latest: The Swedish central bank cut interest rates by half a percentage point to 3.75% on 23 October, its second reduction in just over two weeks, and said it planned further cuts within six months.

Sweden has guaranteed new medium-term liabilities of banks up to a level of 1.5 trillion crowns (£117.2bn; $205bn). It is also putting 15bn crowns into a fund that will be used in case a bank needs emergency capital.

SWITZERLAND:

Background: Its financial sector has helped it become one of the world's wealthiest countries. It manages a third of the world's offshore funds and has been ranked the second most competitive economy by the World Economic Forum.

Data: Gross national income per capita: $59,880 (World Bank, 2007)

Latest: Switzerland takes steps to strengthen its largest bank, UBS, by giving it 6bn Swiss francs ($5.3bn; £3.1bn) in exchange for a 9.3% stake. The bank will also be able to transfer up to $60bn of toxic assets to a fund supported by the Swiss central bank. Credit Suisse was also offered government assistance but was instead able to raise 10bn Swiss francs from global investors to shore up its position.

UK:

Background: Europe's second biggest economy after Germany is dominated by its service sector. London is the largest financial centre in the world. After a period of strong growth spurred by a consumer boom fuelled by credit and a soaring housing market, it is on the brink of a recession after Office for National Statistics' figures showed economic output fell by 0.5% in the third quarter.

Data: Gross national income per capita: $42,740 (World Bank, 2007)

Latest: Following negotiations, the government announced on 13 October that it would inject £37bn ($64bn) of taxpayers' money into three major banks. Royal Bank of Scotland (RBS) is to receive £20bn, a further £17bn will be injected into HBOS and Lloyds TSB "upon successful merger", while Barclays said it would seek an alternative source for £6.5bn ($11bn).

UKRAINE

Background: Following the 2004 Orange Revolution, which established a pro-Western leadership, Ukraine was considered to be a bright star in the Eastern European area. But several years of in-fighting have meant the government has now reached an impasse on various issues. Steel is Ukraine's main export and the country's economy recently enjoyed a boom fuelled by high steel prices. However, the ongoing credit crisis has hit the country hard.

Data: Gross national income per capita: $6,810 (World Bank, 2007)

Latest: A loan from the IMF was announced on 26 October. But the $16.5bn (£10.6bn) loan is dependent on the bitterly divided parliament giving the green light to several anti-crisis laws, including the establishment of a fund to bail out the country's banks.

 

MIDDLE EAST

ARAB STATES:

Latest: Kuwait's central bank said on 26 October that the government would introduce legislation to guarantee deposit is in banks - after losses were reported at Gulf Bank. Traders have been protesting, demanding more protection for Kuwait's banking system.

Saudi Arabia said it would be making funds available to help-low income citizens who were struggling amid the financial downturn.

On 21 October it said it was pumping $3bn (£1.8bn) into its banking system to improve liquidity, reports suggested.

Share prices have dropped precipitously this year, amid fears of weakness in Dubai's property boom and exposure to global markets. However, economists expect growth to continue at a moderate rate as the region's oil wealth cushions the worst of the financial turmoil.

In an effort to boost confidence in the financial system, the Saudi Arabian Monetary Agency (SAMA) cut its benchmark interest rate on 12 October for the first time in almost two years. The government of the United Arab Emirates, meanwhile, promised to protect national banks and guarantee deposits, and Qatar launched a $5.3bn plan to buy bank shares.

 

 

SOUTH ASIA

INDIA:

Background: Economic reforms initiated from 1991 have helped transform India into the world's second-fastest growing economy, with manufacturing and information technology central to the boom.

India has benefitted from significant foreign investment and outsourcing by international companies. Economic growth of 7.9% in August was the slowest for three years, but is still strong by international standards. Substantial poverty remains, however, and per capita income is low.

Data: Gross national income per capita: $950 (World Bank, 2007)

Latest: India unexpectedly cut its repo rate by 100 basis points to 8%, in a bid to boost liquidity and stabilise India's finances.

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