## Tuesday, August 18, 2009

### Optimization

Optimization .
Andre Willers
18 Aug 2009

Synopsis :
We look at financial optimization and extrapolate where necessary .

Discussion :
Optimization is hard and usually involves hunting over landscapes of future potentialities , looking for optima and minima . In other words , it involves infinities .

We have already done this for simple entities :
(see http://andreswhy.blogspot.com. "New Tools : Reserves" )

We use the same argument on the remainders to generate degrees of risk .

What can we afford to place at risk ?
Let z = proportion that remains after we have sequestered our fundamental reserve .
Then the remainder at every iteration n where we keep a proportion of z of the remainder as a reserve of lesser importance is
(1) 1-z
(2) 1-2z+z^2 = (1-z)^2
.
.
.
(n) (1-z)^n

n would denote the degree of risk . Note that it is an exponential function . What you can risk decreases very rapidly .

Competition and greed .
Without competition , the optimal n =1 (ie the maximal reserve) .
Z is normally about 1/e (Eulers constant , as discussed) . About 1/3 .

But competition or greed can drive z to a lower value . Riskier business or evolutionary avenues are explored , leading to extinctions due to unexpected big down-turns (as happened in 2008 in Terran economic systems , or numerous dead-ends in evolution of life-forms )

Greed can be seen as internal competition .

The algorithm to reduce risk in competition is as described above : Take a proportion z of each successive remainder for n times .
The proportion you can gamble at degree risk n can be denoted by A(n) = (1-z)^n

We know z should be 1/e +- 1/3 . The rest can be calculated to degree risk n .

We have an objective measurement of A(n) = risk(N) of a portfolio or extra investment (the Margin ) :
N A=(1-1/e)^n = 0.632120588^n

0 1
1 0.63
2 0.40
3 0.25
4 0.16
5 0.10
6 0.06

Example :
You have 100 000 to invest (regardless of previous investments) . (The beauty of this argument : you can sub-section investments) .
Invest 63% in quality shares that you think will outperform cash , or 6% at the casino.
You see how it goes .

An amusing note :
If you expand the term (1-z)^n and sum the positive and negative terms of the result over n , you get a combination of Elliot-waves and Fibonacci numbers .
As suspected , these systems are artifacts of the analyses .
The predictive information content is null .

Genes .
A portfolio and marginal genes can be examined in the same way .Top organisms that have been around for a long time (eg sharks , jellyfish , birds , etc) have large reservoirs of genetic potential and are capable of explosive adaptation . Bacteria sidestep the problem by not having strong identities . Mammals only evolved the ultimate survival mechanism (flight) twice ( bats and humans) . They will have to pull harder at their bootstraps .

Did tropical penguins catch flying fish on the wing underwater ?

Pterodactyls .
Can any be still around ?
The answer is surprisingly , yes .
But they have gone underwater , switched to a sulfur metabolism . The evidence is bats . The genetic bleed-through (via plasmids , et al) . Look in the cavern-complexes of Central-America near the sulfuric volcanoes . They would have had an instinct to return to ancestral breeding grounds . Note Quetzalcoatl . Deep-sea vents . Note the scars on sperm-whales .
And Nessie ?
Loch Ness is very old . The schism dates back to the Cretaceous . It is possible that breeding females returns there , especially if there is volcanic venting in the neighbourhood (cf Surtsey)

Guano , anyone ?

Andre .