Posts Tagged ‘bell curve’

Australian government’s contingent liability to exceed AU$1 trillion

Sunday, March 29th, 2009

In October last year, the Australian government splashed its AAA rating to bank deposits (including the deposits of credit unions and building societies) and wholesale bank debt. Last week, there’s news that they’re splashing their AAA rating to state government’s debt.

This is akin to parents giving their children supplementary credit cards unsupervised. Indeed, a particular child named “Macquarie Bank” used the Australian government’s ‘supplementary credit card’ on a debt-gouging spree overseas.

Altogether, the Australian government is projected to have a contingent liability of more than AU$1 trillion, which is almost the entire GDP of Australia (compare that to the last budget surplus of around a puny $20 billion). The nature of contingent liability is that it is not really a liability- it is a liability that arises if certain events arises. This may not be a problem if debt defaults follow a nice Bell curve. But in the real world, is this a realistic assumption? As we said before in How the folks in the finance/economics industry became turkeys?Part 2: The Bell curve, that great intellectual fraud,

Bell curve simply means that things revert to the mean in the long run. Also, as you deviate further and further away from the mean, the probability of that deviation will drop faster and faster. Therefore, by the definition of the Bell curve, extreme deviation from the mean is extremely unlikely, so much so that it is close to impossible.

Very unfortunately, it is obvious even from just a casual observation of the world around you, the universe is often not ruled by the Bell curve. Extreme events occur frequently, which by definition of the Bell curve is close to impossibility.

Our feeling is that a huge unquantifiable percentage of all these debts will have a high degree of correlation with each other. Another way to look at this is that what makes a particular debt go bad is what makes the others to go bad as well. This means these debts will not follow a Bell curve. If you look at Australia’s money supply graph in Australian money supply growth in September 2008, you can appreciate the level of leverage in Australia’s financial system. What if Australia faces a huge macroeconomic margin call? Should that happen, there goes the Bell curve.

We shudder to think how the Australian government’s sovereign debt rating will fare when the day of testing comes. With so much contingent liability on their shoulders, we believe the Australian government is setting itself up to be run over by a Black Swan. For those who are new to Black Swans, we recommend Failure to understand Black Swan leads to fallacious thinking.

Fund managers bewildered by Bell curve breakdown

Tuesday, November 4th, 2008

Today, we will talk about the Bell curve again. As we quoted Nassim Nicholas Taleb in How the folks in the finance/economics industry became turkeys?Part 2: The Bell curve, that great intellectual fraud,

So the Gaussian [Bell curve] pervaded our business and scientific cultures, and terms such as sigma, variance, standard deviation, correlation, R square, and the eponymous Sharpe ratio, all directly linked to it, pervaded the lingo. If you read a mutual fund prospectus, or a description of a hedge fund?s exposure, odds are that it will supply you, among other information, with some quantitative summary claiming to measure ?risk.? That measure will be based on one of the above buzzwords derived from the bell curve and its kin. Today, for instance, pension funds? investment policy and choice of funds are vetted by ?consultants? who rely on portfolio theory. If there is a problem, they can claim that they relied on standard scientific method.

For the mainstream money-shuffling professionals in the finance industry, their training are rooted on the Bell curve. The Bell curve was formulated back in early 19th century by a mathematician named Carl Friedrich Gauss. It gave a ‘structure’ for systematically evaluating risk and estimating probability. It is the root of mainstream finance and economics and is used everywhere, from options valuation, risk management and measurement, forecasting, portfolio allocation and so on.

There is an underlying assumption with the Bell curve. As Peter Bernstein wrote in his book, Against the Gods- The Remarkable Story of Risk,

… two conditions are necessary for observations to be distributed normally, or symmetrically, around their average. First, there must be as large a number of observations as possible. Second, the observation must be independent, like rows of the dice…

People can make serious mistakes by sampling data that are not independent.

In today’s volatile financial market, price movements are not independent. As we mentioned in Fading glory of the financial services and ?wealth? management industry, October 2008 saw the most fear and panic in the financial markets. We see instances whereby highly leveraged funds have to sell because prices are falling, which in turn depresses prices further. Traders and investors, being confused about what is going on, reacted as prices moved, which in turn leads to more price movements. Funds have to liquidate their positions because investors are demanding redemptions due to falling prices, which in turn lead to more falling prices. Central bankers, governments and regulators observed the behaviour of the financial markets and reacted accordingly, while the markets observed and reacted according to authorities’ reaction. New information about the economy are confusing, contradictory and yields no insight, therefore forcing market participants to base their decision on other participant’s reaction. If price movements are not independent, this basic assumption of the Bell curve breaks down. If so, then all these financial theories that the finance and economics industry rely on breaks down as well.

Assuming that governments are going to fight vigorously the natural deflationary forces with inflation, we can expect more confusion and volatility ahead. Meanwhile, there will be more soul-searching, witch hunts and re-evaluations in the finance and economics industry.

How the folks in the finance industry got the idea of ?risk? wrong!

Wednesday, January 17th, 2007

In our previous article, How do you define risk?, we put forth our criticism on the way risk is measured by many in the financial service industry. Today, we will look at the underlying theory behind their measurement of risk. The recommended reading for today will be How the Finance Gurus Get Risk All Wrong.

As you may have noticed, ?risk? is often expressed as a nice and simple number in the world of finance. For example, in many stock research publications, the ?risk? of a stock may be defined in terms of a number called the beta. You may see risk jargons like standard deviation, the Sharpe ratio, variance, correlation, alpha, value at risk and so on. All these mathematical definitions of ?risk? give it a scientific feel, which seem to give us the impression that ?risk? can be measured and controlled. Unfortunately, in reality, these definitions and measurements of ?risk? are pseudo-science. The reason is because the underlying theory behind all of them is flawed in the first place.

What are the assumptions behind these conventional measures of ?risk?? They are all based on the assumption that price follows a statistic device known as the normal distribution. If a stock price follows a normal distribution, it means that at any given day, there is a 50% chance that it will go up and a 50% chance that it will go down by the same amount on average. In the long run, the vast majority of stocks? price will hover around its average, with a smaller percentage deviating from it. In other words, the behaviour of stocks? price will follow a bell curve like this (horizontal axis?stock price, vertical axis?probability of the price being at that level):

Bell curve

Is this a valid assumption?We doubt so. As you can see for yourself in the real market, prices often do not follow such behaviour?frequently, they move in trends and at times, exhibit extreme behaviour. As the article in the suggested reading (How the Finance Gurus Get Risk All Wrong) said,

The inapplicability of the bell curve has long been established, yet close to 100,000 MBA students a year in the U.S. alone are taught to use it to understand financial markets.

Thus, as contrarians, this is not the way we define risk.