Sunday, July 29, 2007

KellyCriteria , MiniMax and BlackScholes

Hi Leslie ,

You have already done this .

Think portfolio management .
How much to invest in every risk bracket to ensure a reasonably smooth total minimum return . (ie minimise risk)

Kelly Criteria is the mathematics behind betting/investing systems that (minimises maximum possible losses) while (maximising average returns) .

(Eg you have R1000 . Flip a 50-50 coin . Heads you double your money . Tails you lose . How much must you bet on every throw to get the most out after 100 throws . Remember , if you go to zero , you are wiped out . Now add a bias to the coin ,say 60-40 .
How much must you bet now ? This is the Kelly Criteria . )

It was the basis of portfolio design (and a lot of Cold War Strategy) until the Black-Scholes Equations came along .

Black-Scholes Equations
This enabled the calculation of the present value of Options in a market that is sophisticated and large enough to support liquidity in both the underlying and the derivitive market . This enabled risk-free investment at the beginning when there were few users of the algorithm .

Hedge Funds were then born in all their glory , and did quite well in a large , liquid , volatile market .

Essentially , they did balancing trades . Think of a balance scale . Add $1 Trillion to each scale , while taking 40% for your trouble . The scale is still in balance . Repeat . It works fine until one arm cannot bear the weight any more . It crashes , then the other arm is unbalanced and crashes as well .

The granddaddy of them all (Long Term Capital Management (LTCM)) crashed spectacularly when the the markets went illiquid .

Russia was a major arm .
Russia essentially reneged on all commitments and told the rest of the world to f***off . Since they had a credible nuclear deterrent , there was no nonsense about seizing assets . Instead , the major parties (mostly US banks) agreed not to call in the counterbalancing obligations . These were securitized and sold to an unsuspecting public via pension funds , insurance funds etc.
The spin was that they saved the World Financial System . So they did .

But Accounting systems are zero-sum systems .

These counterbalance trades had to remain on book as collectible debts (ie assets) .

The amounts are large : about $100 Trillion . About 10 times the US GDP .

This surfaced as asset inflation in the US , especially in the riskier end of the property market .

Fascinating .
This must be the largest con and armed robbery in history .

This is real money we are talking about . The Russian economy bounced back much faster than it should have . Of course .
It had no debts .

Double Fascinating:
This doubled the amount of money in the world !
Russia had $100 trillion in hand . The US had a loss of $100 trillion , but refused to acknowledge it , spreading it out by securitization . At the the moment of collapse , world capital just about doubled ( $100 trillion is just about the Planetary GDP) .

This amounts to an indirect taxation .

Can this happen again?
Yes .

The USA has been outsmarted in a classical Marxist jiu-jitsu maneuvre .Russia gained 10 years of US GDP by manipulating the weaknesses of the US capitalist system (especially the insane deregulation of the 1990's )

The US cannot regain this from Russia , much as they would like to . Instead , China and India are the logical candidates. Both are depending on expected future capital growth . The US is not . It can afford to shut down more than China or India can .


There is no surprise in any of these systems . Some people in the system can see what is coming down , but cannot change it .
It is like war in the age of sail . The enemy ship gets closer every day , but no amount of screaming and shouting is going to change the grinding of combat .

All the major powers know what is coming down the pike .
Will China subsidize the $100 trillion US debt via indirect taxation ?
Maybe if they thought that the US had any money left .
The only asset the US have left is the military .

An aside:

Competition :

The other problem is competition . In a finite market , hedge funds nibble at each other's profit margin .

Entire skyscrapers full of state-of-the-art computers and very expensive brains are devoted to chasing ever smaller margins .

Tyrannosaurus Rexes chasing rabbits . And the surviving rabbits get smaller and scarcer (a well-known evolutionary principle in predator-prey dynamics .)

The end result is predictable : hedge funds start going under (as is the case now , especially if they have been so unwise as to be still exposed to the sub-optimal mortgage and debt market in the US )

Note that the Kelly Criteria can be used in your head , on a piece of paper or on a PC . That is because you can define your risk categories at will over a chosen time interval . Ie it costs little .

But Black-Scholes requires continual monitoring of millions of data-elements , as well as out-guessing the competitors .
When the cost of this exceeds the profits , the funds either go out of business , or cut costs and revert to Kelly Criteria .
(Eg Soros Quantum , etc)

Of course , every major reduction in computing costs gives rise to a flare of hedge funds until the profit margins peter out .


-----Original Message-----From: Leslie [] Sent: 01 July 2007 10:04 PMTo: 'Andre Willers'Subject:
Hi Andre,

What do you think of this? I don't understand the mathematics :-)


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