## Wednesday, March 20, 2013

### How Algebra Ruined the World Economy

Anyone paying even a little attention knows world economics is somewhere between shambles to devastating depending upon your location and economic status. Historically, what has changed is the fundamental base of international economic understanding. When economies went from tangible to intangible, from riches and product to computer numbers, there was also a fundamental change in computations.

Banking and corporate computations in the past were ledgers of basically addition and subtraction. Values placed on items calculated for their value based on raw material + labor + availability/demand + transportation + profit customarily ranging between 1-10%.

Merchant Companies made their money with a profit which showed an ebb & flow across the world that remained less than five percent for centuries.  From the commencement of the industrial revolution and the stock exchanges it could be said that economic growth expanded exponentially. The most recent change happened with the 1973 introduction of algebra into economics by Black & Scholes.

Just like theoretical mathematics has no practical application, the Black Scholes equation turns a minus into a plus. The unbelievable part is that when applied to economics the equation can turn multi-million dollar losses into stock option plus.  The equation was recently used on a $60 Million Dollar loss to turn it into a$28 Million Dollar Profit, well, on paper anyway.

Here’s a portion of the calculation:

\begin{align} C(F,\tau) &= D \bigl( N(d_+)~F-N(d_-)~K \bigr),\\ d_\pm &= \frac{\ln\left(F/K\right) \pm (\sigma^2/2) \tau}{\sigma\sqrt{\tau}},\\ d_\mp &= d_\pm \mp \sigma \sqrt{\tau} \qquad \bigl( d_- = d_+ - \sigma \sqrt{\tau} \quad\text{and}\quad d_+ = d_- + \sigma \sqrt{\tau} \bigr) \end{align}

Is this really good for business? It depends upon where you are in the business. The derivation calculation covers the fact that the stock is tanking. Options given to early investors are propped up through financial algebra to entice additional investment. The continued investment gives the financially strapped company an influx of money to pay down debt, providing an opportunity to turn things around.

However, the likelihood that there will be enough investment and the will of the executives to change the direction of the company from a cash drain to a cash cow is slim. The truth is that once a company travels into the world of Black Scholes accounting devastatingly large bankruptcy is virtually inevitable.

Obviously, algebra & economics don’t mix, why do it? The answer is time. Nebulous accounting strategies allow early investors to get out of the investment or at least to mitigate their losses. It allows time for patents and assets to be sold. With that time, the company is allowed to fade away from public scrutiny before it crashes into oblivion.

In the end, basic bookkeeping with endless columns of pluses & minuses remains the only way to keep the economy headed in the right direction:  Raw material + labor + overhead + 10%.