It has been prove by simulation (see the book by Bernardo Huberman @The laws of the web@ pages 28-29 chapter 3 http://www.amazon.com/Laws-Web-Patterns-Ecology-Information/dp/0262582252/ref=sr_1_1?s=books&ie=UTF8&qid=1396516209&sr=1-1&keywords=The+laws+of+the+web )
that , if a number of organizations grow multiplicative (in other words exponentially or as logistic growth) , and all have the same growth rate, and start at the same time, then at any time moment, their statistical distribution of sizes, is lognormal. BUT if they start at different times, and/or have different growth rates, then , the resulting distribution, at any time will be a power, or Pareto distribution.
This explains that the enterprises and financial organizations have as statistical distribution of their asset sizes, a power or pareto distribution (in other words that involves a monomial ax^b of probability density, as a function of the size x.) This means also that if we plot the statistical distribution in logarithmic scale both on the x-axis and the statistical density axis y, it will appear as straight line).
This statistical law is inherited to the volumes of transactions, and therefore it creates the momentum conservation, or law of trend, that we have analyzed in other posts.
This inheritance of a power distribution law from the size of the assets, to the volumes of transactions, is the basic mathematical-statistical relation between the fundamental analysis and the technical analysis.
If all the organizations would have the same size, then, the markets would behave as random walk (neutral fluctuations up or down) . This is also a proof why the markets do not behave , as random walk , because, of the law of Pareto of economic inequality. And this is also a proof, that the standard models of Black-Scholes of the Options fair pricing are biased in a systematic way, as their fluctuations are assumed as exponential random walk.
Of course it could not be otherwise! Would the financial status quo elite give a nobel prize, to a model that would allow , smaller or middle players to gain systematically over the large players? Not probable! The model should be so that all players gain zero in the average, and if we consider the transaction costs, would lose systematically.
There are 3 contexts of laws required in trading . The appropriate LAWS OF THINKING for trading, the appropriate LAWS OF FEELINGS for trading , and the appropriate LAWS OF ACTIONS for trading.
The Successful trading is based according to these three laws on
1) POWER OF COLLECTIVE SCIENTIFIC THINKING: A GREAT AND SIMPLE SCIENTIFIC PERCEPTION OF THE FUNCTION OF THE ECONOMY THROUGH SOME GLOBAL STATISTICAL LAW. E.g. The law of Universal attraction in economy: that big money attracts more big money in the capital markets, and this by the balance of demand and supply makes securities indexes of the companies , that are indeed the big money, to have mainly stable ascending trend, whenever one can observe such one. Valid statistical deductions can be obtained with simple statistical hypotheses tests about the existence or not of a trend, with sample size half the period of a dominating cycle). (STABLE GREAT SCIENTIFIC THOUGHT-FORM OR BELIEF FACTOR IN TRADING. )
2) POWER OF COLLECTIVE PSYCHOLOGY: A LINK WITH THE POSITIVE COLLECTIVE PSYCHOLOGY.(E.g. that the growth of security indexes also represent the optimism of the growth and success of real business of the involved companies. And we bet or trade only on the ascension of the index, whenever an ascending trend is observable). (STABLE GREAT POSITIVE COLLECTIVE EMOTIONAL OR PSYCHOLOGICAL FACTOR IN TRADING. )
3) POWER OF INDIVIDUALS SIMPLE , CONSISTENT AND EASY TO CONDUCT PRACTICE. (e.g. a trading system with about 80% success rate that utilizes essentially only one indicator in 3 time frames, simple risk management rules of stop loss, take profit, trailing and escalation, and time spent not more than 20 minutes per day. In this way there are not many opportunities of human errors in the conduction of the trading practice. Failed trades are attributed to the randomness and are not to blame the trader). (STABLE SIMPLE AND EASY PRACTICAL FACTOR IN TRADING)
We may make the metaphor that successful trading is the ability to have successful resonance with the activities of top minority of those who determine the markets.
In trading there are 3 components in the feelings that must be dealt with. 1) The feeling of MONEY itself, 2) The feeling of the UTILITY of the money 3) The feeling of the RISK of the money each time. What is called usually money management in trading is essentially RISK MANAGEMENT.
VALID STATISTICS AND PREDICTABILITY
We must make here some remarks about the robust application of statistical predictions in the capital markets.
1) The theory that the efficient markets and in particular that they follow a pure random walk is easy to refute with better statistical experiments and hypotheses tests. The random walk would fit to a market where the sizes of the economic organizations are uniformly random. But the reality is that they follow a Pareto or power distribution, therefore this is inherited in the distribution of the volumes of transactions and also in the emerging trends or drifts.
2) The statistical models of time series are more robust , when they apply to the entity MARKET as a whole and are better as non-parametric , and not when they apply to single stocks and are linear or parametric. The reasons is that a time series as a stochastic process , requires data of a sample of paths, and for a single stock is available only a single path. While for all the market the path of each stock or security is considered one path from the sample of all paths of all the stocks.
3) The less ambitious the statistical application the more valid the result. E.g. applying a statistical hypothesis test, or analysis of variance to test if there is an up or a down trend (drift) or none, is a more valid statistical deduction , than applying a linear model of a time series and requiring prediction of the next step price.
4) Multivariate statistics, like factor analysis, discriminant analysis , logistic regression, cluster analysis , goal programming etc are possible to utilize for a more detailed theory of predictability and of portfolio analysis, and sector analysis of the market and not only H. Markowitz theory.
5) In applying of the above applications of statistics, the researcher must have at first a very good "feeling" of the data, and should verify rather with statistics the result rather than discover it.
6) The "Pareto rule of complexity-results" also holds here. In other words with less than 20% of the complexity of the calculations is derived more than 80% of the deduction. The rest of the 20% requires more than 80% more complexity in the calculations.
Friday, October 12, 2012
38. RE-POSITIONING THE PORTFOLIO. Optimal adjustments of tradable funds and non-tradable cash.
As I mentioned in the post 3, about the "speculators" they apply an optimal adjustment back-office method that multiplies their profits reduces the risk, and does not need a forecasting of the market. Warren Buffett and many other succesful investors apply this technique as a paramount and basic neccesity in investing and trading.
During 1998 while studying in the University of Portsmouth, I discovered a theorem in the book "Stochastic Differential equations" by B. K.Oksendal (Springer editions) page 223, example 11.5 where he proves through the ITO stochstic calculus that such an adjustment as above is optimal during a constanttrend against just buy-and-hold , and maximizes the probability to have positive profit
We may apply optimal adjustments of tradable funds. This means that we divide the funds in to tradable (e.g. 66%) and non-tradable (33%). Al trading is based only on the tradable funds, which in their turn are divided in to usable for margin, and risked e.g. by stop-loss in a trade or excursions, and those reserved for next trades. Then at the start of the trading we mark the equity level E0. For every dE increase from this E0 level or previous level during trading (e.g. dE=5% over all funds) we adjust by in increasing by 2.5% the non-tradable, and decreasing by 2.5% the tradable, and for every dE decrease from E0 or previous level during trading, we adjust by in decreasing by 2.5% the non-tradable, and increasing by 2.5% the tradable so that the ratio 33% of non-tradable funds to all funds, remains approximately constant.
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