Sunday, August 10, 2008

Regional Integration Increases correlation of regional stock prices

The Free Online Dictionary (by Farlex) defines a stock market as 'The market in which shares are issued and traded either through exchanges or over-the-counter markets. Also known as the equity market, it is one of the most vital areas of a market economy as it provides companies with access to capital and investors with a slice of ownership in the company and the potential of gains based on the company's future performance.'

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Stock markets, when viewed in abstraction, are essentially non-deterministic dynamical systems (stochastic systems). When these stochastic systems operate, current market prices are iterated from complex mathematical formulas that incorporate, among other things; preceding market prices and events.

Each stock market is a distinct stochastic system, that has its own 'unique formula' for pricing stocks. This 'unique formula' evolves constantly in response to:
  • Political events in the country, and, in the wider global environment.
  • Social trends in the country, and, in the wider global community.
  • Technological trends in the country, and, in the broader 'global village'.
  • Economic trends precipitating at a national and global level.
As regional political integration (and economic) progresses, nations within the respective integrated bloc increasingly resemble each other; politically, economically, technologically and socially (i.e countries within an integrated bloc converge towards a common order). Otherwise stated: regional integration 'homogenizes' countries with different traits. This has the effect of standardizing the underlying factors (or the 'unique formula for setting stock prices') that influence share prices within the region.

...What are the effects of this 'standardization'?

As regional integration increases, stock markets (within the respective integrated region) begin to behave in more or less, the same way: they increasingly become positively correlated.

(I suspect that) If you picked any two random shares, on any two random exchanges (within an integrated regional bloc) and studied them over a period of time; you'd find that the correlation of their prices increasingly approaches 1 (the number one).

Mathematically this can be expressed as:

Which reads As time approaches positive infinity, the correlation between two randomly picked share-prices (each from a different stock exchange within an integrated regional bloc) approaches one i.e they increasingly approach perfect positive correlation.

Note: the general assumption of the mathematical expression above, is that regional integration increases with time.

Where:

t represents time.
The 'lazy eight' represents positive infinity.
x1 Represents the price of the first randomly picked share at a specific point in time.
μ1 Represents the arithmetic mean of of x1 during a defined time period.
x2 Represents the price of the second randomly picked share at a specific point in time.
μ2 Represents the arithmetic mean of of x2 during a defined time period.
σ1 Represents the standard deviation of x1 during a defined time period.
σ2 Represents the standard deviation of x2 during a defined time period.

...And?

As stock markets (within an integrated region) approach perfect positive correlation, the (risk management) benefits of intra-regional diversification of share portfolios, diminish proportionately.

To put this into perspective: Intra-regional diversification of share portfolios, in an environment of increasing regional (political and economic) integration, is akin to loading different egg-filled baskets onto the same haulage truck.

Although your eggs are in different baskets, they still have a common environment...

What happens to your precious eggs, when another haulage truck crashes into your egg-carrying-truck
?

Your attempt to limit risks by diversifying your eggs into different baskets, would have been an exercise in futility!

...Now think about mutual funds with a European Union listed-equity focus: What does this say about their risk management practices?

You have been warned! :-)