41 Example: Investment Banking

From this physical reason we may now have a less indoctrinate look at the special role of the banks own business, also called investment-banking, for the growth of an economy. For this we go back to the basic nonlinear equation

,

resort and express it in some more commonly known phrases

    (41.1)

where RoI is the return on investment (absolute) and CPI the consumer price index (absolute), whereas they are here used in absolute instead of the usual relative (%-) values. But because of the division, also the relative values can be used here (written in small letters cpi and roi).

It should be remarked here, that this here is no explicit solution of the NLDQE but a structural analysis of the differential equation, which can give some deeper insights in special cases in consideration. We will give one example here. Despite that, the full solution needs at least three more equations out of three more symmetries, as we have to solve in principle for four unknown functions, which are the four pseudo-complex vectors in use.

So we may express here an implicit partial solution by pseudo-riemanian-complex vectors simply as

    (41.2)

which means the net compound complex business

    (41.3)

is the complex⁸² Cashflow times the complex interest ratedivided by the complex rate of inflation. It just tells⁸³ us: No complex interests, no complex cashflow, no additional real(!) business. The growth rate of GDP g can now be calculated, but first we get the volume of merchandise by:

    (41.4)

The term under the square root should be positive to get a real tradein real number space, so this restriction results in:

    (41.5)

Then the GDP is:

(41.6)

And the relative GDP growth g is:

    (41.7)

We can rewrite the last equation as:

Now every of the involved function are functions of time, such asand so on. The numerator is thus:

...*()

Dividing this by  results in: 

which may be shortened by suitable abbreviations to:

    (41.8)

with

  and 

and also

  and   

(41.9).

By virtue of this abbreviations we come from nonlinear DQE finally to some defining equations of the limits of investment trade to the possible growth rateof GDP:

With       (41.10)

we get the growth rate

    (41.11).

by definition of inflation rate.

So GDP growth rate g equals inflation I plus/minus some terms, depending on the differences between real returns on investment banking and real returns of loans to the economy and their time-derivatives, in a very complex way. Equation (41.10) demands some restrictions to Banks own business (investment banking) to sustain real economic growth. For the root to deliver real values, we have the restriction, that the three terms under the root have to have some dependent signs:

 

Case of signs
A 1 (bullish)	+	+	+
A 2 (bearish)	-	-	+
B 3 (ind. loss)	-	+	-
B 4 (ind. win)	+	-	-

Case A: clear markets

Case 1: bullish market for investments

Case 2: bear market for investments

In both cases the net inflow of money to the stock marketsshould be high, to sustain real growth. The reason is, that in both cases the implied money is bound in the stock markets instead of influencing (eventually badly) the real economy. Especially this means, that the idea of bets on indexes going down, so called “bear raiding”, can indeed be an objective to stabilize the otherwise negative influenced real economy.

Case B: indifferent markets

Case 3: indifferent market, mostly losses

Case 4: indifferent market, mostly wins

In both cases we see that should be negative. This means, instead of gambling, one should better invest money into the real economy. Which indeed means to do this to stabilize the real economy, but which means not necessarily to get a good return on investment.