## Posts Tagged ‘**Randomness**’

## The Problem of Correlation As Causation

The confusion of supplanting correlation for causation is one of the most common logical fallacies we make. This is the *fallacy of correlation*. The basic premise is that you will attribute a connection between two experiences as the root cause of one experience being the cause of the other.

While it’s one of the easiest logical fallacies to spot, we continually fall for the trap of the *fallacy* *of correlation*. It does require a minor exertion in mental analysis to catch ourselves spiraling down it’s pitfalls, but it’s shouldn’t be too much to ask a person to invest that energy into their own line of thinking. None-the-less, it’s a logical fallacy which pervades everyday thinking, and, regretfully, even scientific research.

As a general schematic, think of the *fallacy of correlation* to be as follows:

- Event
*A*occurs synchronously or chronologically to Event*B*‘s occurrence, therefore - Event
*A*is the cause of Event*B.*

The possibilities of the relationship between Event A and Event B are too numerous to conclude *A* caused* B*. Some of these include:

*A*is the cause of*B;**A*is the cause of*B*, and*B*is the cause of*A*(or both events sharing a circular causation);- an unknown Event
*C*is cause for either*A*or*B,*or both; - the incidence of
*A*and*B*share no relationship other then temporal occurrence.

It is rare for Case 1 to be true, yet far too often we prefer it from the other possible Cases. This is often the outcome when a layer of plausibility exists within our empirical history interconnects two events(*Hume’s* definition of causation). Plainly stated, if I have been witness to two events occurring in the past, I am likely to make a connection between these two events when the happen again in the future. They are believable.

## Why Your Blog Hits Aren’t Really Yours

With the explosion in the number of blogs littering the internet, every blogger takes extraneous efforts to increase their visitor count. The all important hit count is the singular indicator whether your blog is popular or not.

There are blogs dedicated soley to advising bloggers on who to get their blogs noticed, and attract a larger share of readership. Focusing on key words, interlinking blogrolls, content distribution, and comment links in other blogs are all part of the “how to get your blog hits” mantra.

You’ve followed all the steps to get you blog hits – selected a topic to focus on, included important key words in your tags and post titles, built a nice shared blogroll with other blogs, and politely commented on other blogs to get the word out about your blog. After all these steps your blog is averaging a couple hundred hit per day. All things considered, you’ve done fairly well for yourself. But your blog is middle-brow. One of among tens of thousands of other blogs that suffer from medicrioty in terms of hits.

## Cantor Fitzgerald Moving HSX Into The Real World

The trading firm Cantor Fitzgerald will be starting a real world version of the Hollywood Stock Exchange – an online virtual trading world where players buy and sell movie and celebrity stocks. Cantor will now offer movie studios to purchase bonds relative to a movie’s financial performance.

Cantor is actively recruiting veteran HSX traders to participate in advertising and selling these bonds to movie studios. Cantor Fitzgerald needs “experts” to sell their product. While there are undoubtedly individuals who have fared appreciably more successful then other traders on HSX, I’m hard pressed to say there are any “experts” in the fantasy trading game.

Let us assume the Cantor incarnation will operate similar to HSX. A movie stocks price is based on it’s expected total gross(for wide releases four weeks, twelve weeks for limited release). On it’s opening weekend, a movie will adjust according to it’s weekend gross along with an internal multiplier(typically 2.8).

## The Unpredictability of Sports

As with all systems that aren’t manufactured, for instance casinos, sports is a highly unpredictable arena. But littered with experts from former players to journalists eager to give you their arrogant self-predictions for future seasons.

Every season for every sport, these experts publish their predictions in newspapers, magazines, and television shows(the latter particularly prone to bombastic proclamations of arrogance). The experts put on record every year(and every week) their elevated knowledge in the sports domain. Take a quick look at just how much these so-called professionals really know, and you’ll find that sports is as unpredictable as most everything in life. That guy on ESPN whose studied football for twenty years is probably no better at predicting the final NFL standings then you or me.

Take a look at ESPN’s preseason power ranking for the NFL. The error rate is astounding. Of the 16 bottom ranked teams, 5 of them made the playoffs this season. Two of the supposed three worst teams ended up with records 11-5 records(Atlanta and Miami). The Titans were ranked 16th and ended up with the best record in the league. The Jaguars, Saints, and Seahawks were all ranked in the top ten, but not one ended with a winning record.

## Financial Risk Management: The Problem With Applying Statistical Models To A Random System

Having digested more then my fair share of reasons behind the market crash from television to radio to print to the blogosphere, I’ve been saturated by the common theme of corporate greed and corruption. I don’t buy it as anything other then a compulsory and secondary component to a free market economy. This is, of course, beyond obvious.

Add to the equation profitable longevity, and the greed/corruption arguement becomes less credible. If I gave you the option of taking $5000 right now or $1000 for the next ten years which option would you take? Profitable longevity is not a difficult concept to understand, yet it seems lost on the relentless pounding being doled out on anyone remotely associated with the market crash – market traders, business executives, and government officials.

While there are certainly businesses that run counter to profitable longevity, i.e. Enron, this is not an isolated incident of a single lending institution engaging in suicidal greed. The problem spans entire business sectors including lending institutions and trading firms. From a logical perspective, it’s difficult to assume that two entire business sectors concurrently decided to knowingly engage in practices fueled by excess at the cost of self-destruction.

The need to balance profit and longevity within the financial sector following the Great Depression, the concept of stock and bond risk management was born. By the 1950s, financial risk management evolved from a concept into a full fledged theory centered around mathematical diversification. A decade later risk management theory adopted stochastic calculus in order to better account for the inherent randomness involved in stock trading. Today the financial corporations are littered with what are known as quantitative analysts, otherwise known as quants.

The role of a quant is to develop sophisiticated mathematical and statistical models designed to simulate stochastic processes and it’s potential impact against illiquid products. Uneffected by supply-and-demand price fluctuations, illiquid asset management depends entirely on these quant models to determine value. Another tool employed by quants is the process of statistical arbitrage that relies on quantitative data mining in order to determine the expected value of an asset. These two quant instruments are the foundation for the risk management techniques finicial corporations employ today.

Stochastic calculus attempts to deal with multiple outcomes and given an array of possible initial values, marks the possible outcomes for multiple initial conditions. While it accounts for a wide possibility of paths, it determines which paths are more probable and which ones are more improbable based on the probability of the initial conditions being present(whose sheer numbers can be exponentially mindnumbing). Statistical arbitrage relies heavily on gathering statistics over time, in order to create a computational value based on the expected outcome where multiple outcomes exist.

These two systems are attempting to deal with and account for rogue events. It is in trying to deal with events which have never occurred previously that a fundamental flaw becomes apparent. These two systems, particularly statistical arbitrage, relies almost exclusively on the collection of event data. These statistical models derive their accuracy from the amount of data collected. Hence, the more finite a time data is mined, the less accurate the model becomes. In order for either of these models to be bulletproof, it would require an infinite amount of time to aggregate data.

Here we have two systems employed by the financial sector to determine the improbability of events and conditions which have never occurred. The problem exacerbates itself when you consider how the data that is amassed is disseminated.

In order to map these probable and improbable events, statistical analysis employs the use of the Gaussian curve. It’s a bell curved shaped graph illustrating the probability density of all potential values. The Gaussian curve bends downwards at it’s edges towards improbable events and upwards towards the probable. The width of the curve correlates to the weight of those probable events against those improbable ones. Basically, it charts the normal distribution for events, and giving an indication of which events are more probable then others.

The Gaussian curve is essentially a median value for all possible events. And that is where it fails. A model cannot really account for and give the proper value to a rogue event, the most improbable of occurrences, when it gives greater value to standard, the most probable of events. It fails in calculating the impact of heavy swings against the normal distribution value. A singular, yet improbable event, will hardly impact the height or width of the curve against the statistical weight of a multitude of those that are likely.

To better illustrate this take 100 middle class American households, and calculate the average income. Now put every name of every adult in the United States, and put them in a hat. Randomly draw one name from the hat. Now take that persons household income and recalculate our income average. 99% of the time you would have selected someone close to the median US household income of $40k. The average will not make an appreciable movement upwards or downwards. You could have selected the poorest household in America and the number would hardly have budged. Let’s say you draw from the hat again, but this time you pick out someone in the top 1% income bracket out of the hat with an improbability factor of 298,128,548 to 1. Recalculate the average again. A massive swing upwards in the average will occur. An event that has a 0.01% chance of occurring will appreciable change our end value, where as 99.99% of possible events will not.

One singular, blip on the Gaussian curve can drastically effect our end value. But the curve itself doesn’t properly adjust for that highly improbable, rogue event. Combine this massive swing due to random events with quant statistical models that are ineffectual in mapping these Gaussian blips, and you can begin to see where the problem might lie.

Let’s throw these inadequate models in bed with profit longevity, and it becomes a sticky situation. Financial corporations have a tricky balancing act to perform. Faced with reams of data pointing at the normal distribution of the Gaussian curve coupled with the blind spots for events which have never occurred in stochastic calculus and statistical arbitrage, conclusions have to be made as to which path to follow.

Taking the path of improbability would severely limit potential profits. Under performing profit margins threat longevity. Following the road towards the probable, gives some assurance in profits and promotes company longevity. The decision making process cannot even account for rogue events which the statistical models fail in forecasting.

The historical housing market rise and fall would, at it’s very least, qualify, as an most improbable event. A case could be made that it was a rogue event incapable of being calculated by the quants models. Instead of tossing around the idea that corporate greed was at the center of the economic crisis our country now faces, let’s consider that, at best, the financial sector was presented with misrepresented data by a fundamentally flawed model. And, at worst, their models simply were not able to account for never before seen event chain.

Either way, the quant risk management system might be to blame, and desperately needs to be reexamined to better account for those improbably catastrophic occurrences. No amount of money infusion will turn failing statistical financial models into pinpoint accurate prediction machines – if that’s even possible. Or maybe we should just learn to accept certain levels of risk that randomness carries with it rather then constantly acquiescing to the fat cat blame game.