style="text-align: justify;">The current behavior of financial markets may seem paradoxical and irrational. It can be explained by a change in sentiment about the likely evolution and future of the global economy. The prevailing sentiment until mid March was rather that of an entry in a long phase of depression, resulting in several years of negative growth, a collapse of the banking system and a sustainable price deflation.

The recent publication of leading indicators of the economy and for elements as important as the price of real estate transactions, retail sales and slowing down the production of bank loans has changed the analysis investors about the likely evolution of the macroeconomic environment and financial.

The slowdown in the deterioration of fundamentals can be measured and explained in the magic of the second derivative finance.

We can here make the following reminders:

In mathematics, a function is differentiable if and only if the function x-> F (x) - F (a) has a limit point has

F '(x) = lim f (x) - f (a) / xa and F' (x) = DF / Dx x-> a

The second derivative is denoted F''(F second x) D F ² / dx ²

The second derivative indicates the change in slope. If it is positive on a given interval, the slope increases, the curve is directed upward, the function is called concave. If it is negative on an interval, the slope decreases, the curve is downwards, the function is called convex. If it is zero, the curve is locally straight. If the second derivative vanishes and changes sign, there was a point of inflection and the curvature of the curve is inverted.

As the first derivative indicates the slope of the function, the second derivative indicates the slope of the first derivative. When the second derivative is positive, the first derivative is increasing. A curve whose second derivative is always positive or zero, is convex. This kind of curve has a single minimum.

We can apply this reasoning to the development anticipated by the stock exchange operators of the world economy since the end of first quarter 2009. From the moment we consider that today's world knows no lasting depression (depression type of Nippon 90s), one is clearly in a recession scenario, albeit violent and unprecedented in recent economic history, but should be completed in a relatively short time.

This change of sentiment regarding the form and nature of the current financial crisis significantly alter the range of possibilities regarding the likely profile of the market on the horizon 6-8 months.

A question comes to mind: Why are stock traders they become less pessimistic? In addition to improving leading indicators already mentioned, it can be several factors to explain this change in behavior.

The recovery plans initiated by the States everywhere have been massive and have already helped restore some confidence to investors and other economic agents in general. The addition of a massive public spending to private spending (consumption and investment) has begun to slow the collapse of production.

In addition, the support plan for banks (reaffirmation of guarantee deposits, guarantee bank refinancing, recapitalizing lending institutions through programs in equity or quasi-equity by the government allowed the release of the money markets). The role of central banks has also been instrumental in providing liquidity and lowering interest rates which are now in Europe and the United States close to zero.

All these elements have allowed the return to a degree of confidence although it is not yet back to pre-crisis situation (before June 2007). Credit spreads between maturities and issuers were particularly relaxed and the yield curve of interest was normalized by repentifiant thereby promoting the recovery of margins for banks. It remains to solve the problem of illiquid assets and / or depreciate by forming ad hoc structures cantonment guaranteed by the public.

One can also argue that contrary to previous financial crises (eg crisis countries of Southeast Asia in 97 - 98), emerging countries have some of them could face crisis with more flexibility because they had been built up large foreign exchange reserves (eg China).

One can think of is that although emerging markets suffered from capital flight since last October could quickly find a significant rate of growth in economic development based not only on exports but also in promoting their domestic consumption (the savings rate in his country was particularly high given the weakness of social protection systems).

For all these reasons, investor sentiment is moving toward a stop or a gradual reduction of deterioration of economic statistics in the coming quarters, thereby stabilizing the fundamental end of 2009 or during 2010.