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In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. The second derivative is the derivative of the first derivative. &nbsp... the geometric meaning of the second derivative relates to the curvature of the function displayed graphically, the  most commonly related function of the second derivative applies to the concept of acceleration.  The first derivative of a trajectory relates velocity. The derivative of velocity relates acceleration. The second derivative as applied to our view of economics relates the rate of change of acceleration of a phenomenon we observe.  &n... point where the second derivative of a function changes sign is called an inflection point.
Ok, ok I know you didn’t sign up for a calculus course. Why does any of this matter today? It matters because the markets are focused on this morning’s employment report. In our second derivative world, the experts will try to explain the meaning of the rate of change of the acceleration of layoffs.   The 539,000 jobs lost reported this morning means we are firing people at a significantly decelerating rate. So what’s next? Next the experts will try to extrapolate this data point to predict when the inflection point will occur.    At the inflection point we’ll stop laying people off and start hiring people again. 
This will be used to predict the beginning of a recovery. Unfortu... the market watchers, who love a story, have it backwards.   The economy bottoms before the rate of change of layoffs begins. The market bottoms before the economy bottoms. It’s always been this way and it will always be this way.
On Wednesday a person from ADP went so far as to say that the rate of change of the ADP survey had bottomed last November and that the market bottomed a few months later. Nope.&nbsp... guy is promoting his survey too much. He doesn’t understand that the market is always ahead of the fundamentals. &nb... will continue to have layoffs for the next several months. The rate of change of the layoffs next month may accelerate from the rate witnessed this month. In fact, with the digestion of the auto bankruptcies and the financial industry restructuring going on that is likely. It won’t mean that the recovery is aborted. It won’t mean that the stock market must now go back down and make a new low. It will simply mean that as the economy bottoms companies continue to cut back just to be safe, and that when their orders pick up they will drag their feet hiring back workers until they are sure that the recovery is real. It’s always been this way and it will always be this way.
The stock market has been on quite a tear since the bottom was put in on March 9th. Everyone thought that we had begun a dead cat bounce or a rally in a bear market. I was quite skeptical about the unanimous negative opinion after four up days in a row. Everyone may be right, but that usually doesn’t happen. Usually when everyone thinks something will happen, it doesn’t.”&...(The Little Rally That Could! – March 19, 2009)
That “little rally” now appears to have predicted that the rate of change in many things economic would get better. The “green shoots” everyone are now talking about relates to the deceleration of several  declining data series. If we have further economic disruption that will cause the market to go down again? It might. Will we make a new bottom and be again squarely thrust into a bear market? This is highly unlikely! The market has always been ahead of the economy. People say it is ahead of the economy by 6-9 months. This is actually too simplistic. The market is ahead of the real economy by somewhere between 3 to 18 months. It is highly likely that the market has already forecast a recovery in 2010 with this rally.   The bumpy bottom in economic activity that is likely this summer and into the fall, has already been discounted. The market is now looking into the recovery. We probably can find a 9000-9500 Dow in that recovery.  &... The real question to watch is whether or not we can move back toward old highs in a world where government involvement has increased dramatically and the resulting deficits crowd out the private sector.
The real second derivative to watch is the rate of acceleration of government influence. If that continues to increase it will lead to real trouble, if it evens off a better market awaits us over the next few years. 
Fred S. Fraenkel
Vice Chairman and
Chairman of Investment Policy
Beacon Trust Company
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