Mapping the Advantage to a Curve

The advantage is a ratio that can be dynamically used as a control measure to limit participation to the most optimal situation or environment. It’s highly favorable properties are described in this blog here. The purpose of this article is to explain how mapping the advantage to a particular environment called a patch — can give you a powerful performance edge — which will compound money faster than alternative approaches.

The normal curve and the two diagrams below have in common a single peak that is labeled as point c below. The adjacent theorems explain the features that will occur when such peaks or valleys exist. A generalized measure of performance that can be mapped to almost any situation or environment by assuming that favorable performance occurs before c and unfavorable after it.

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Diagram 1The shape of curve could be as shown or inverted dependent on usage. What counts is the order and location of points a,b and c and their representation of performance on a closed interval. We can represent the advantage on the curve so positive mathematical expectation will occur between a to c and negative afterward.

To do this we need to be able to extract the information that will enable us to determine when assets will accumulate faster (same as compounding) in the specific environment of interest. Here extract means to reduce those factors into a concise formula suitable for determining whether we do or do not have an advantage. This process becomes simple after we are able to repeatedly use the same measure to give us a clear advantage.

Mapping Wealth Distribution to a Curve

In reward to risk related situations — when the advantage is higher the reward will also be higher while the risk will be lower. This recurrent theme is easily applicable to physical models where the ratio and magnitude of wins and losses are measurable between two intervals such as a and b described above. What makes this model attractive is the simplicity with which information between the interval points can be dynamically measured.

Much of the power in the model has to do with the volume of evidence related to human conflict to capture and secure the most favorable land masses to grow their societies. In short, military conflicts have typically been a key factor in determining how societies obtain and/or keep various land patches. We now turn to wealth building within societies which can also be defined as patches — typically protected by military powers — as proved by historical evidence.

Human competition to gather wealth is different from — animal foraging as discussed in Marginal Value Theorem. As our societies have evolved — those focused on risk taking situations have sequentially dominated both local and world economic wealth. What is known as the Pareto principle is often used to imply that approximately 80% of wealth as defined by land ownership and/or income growth is controlled by just 20% of the population. Partitioning the 80/20 relationship with the same points as labeled in Diagram 1 — gives us a similar curve that we will use to illustrate concepts related to the advantage and patch dynamics.

Diagram 2How to Move toward the top 20% of the Curve

Assume points a to c represents the top 20% as shown in Diagram 2 which is called Optimal Accumulation Theorem (OAT). The curve is the same as that of the Marginal Value Theorem — but you can not wander freely due to what is explained above — about how such patches are protected within our human societies.

You don’t get to pick the street you are born on — which could determine your initial place on the wealth distribution curve. However, after birth what you learn about risk taking — combined with your focus on taking smart risk — will typically be the determining factor where you end up on the curve. Most people never accumulate the interest or skill sets — which is part of the reason for the disparity. This can be remedied by increasing risk taking skills and using a credible process that works no matter what part of the curve you are born on — or are on now.

Let’s say you are at point b on the OAT patch. Here’s our big idea. We show you a risk taking process in which you can learn how to use the advantage to trade a wide variety of markets. Obviously, a serious effort would be needed to accumulate and convert your knowledge into cash — but you would have a huge edge — with the capacity to do that. Your challenge would be to understand the math behind the physical model, how to properly use it — and to develop a team to make money using the advantage in trading markets.

What’s the logic behind the math?

Liquid market assets typically have highly fluctuating values. The nature of the fluctuations create such visual problems that most existing mathematical models and/or traders do not know how to calculate or use an actual advantage. Most have to estimate it — or use other means. Both these attempts will distort points a, b and c. The missing link is in the logic not the math. Same reason brilliant mathematicians failed to solve blackjack over the centuries until the 1960′s. This presents limitless potential — because it’s like being in a world where the game of blackjack exist — but card counting as the solution has not been discovered yet.

Sure, it possible to make money in the markets without using an actual advantage, but the performance would be less attractive than if it were precisely calculated. Additionally, because of how market information fluctuates — defining and using the advantage on a similar basis as casinos requires reducing the level of non-redundant factors so that the outcomes can be dynamically controlled.

Map Extraction is a way to dynamically value information streams so that money can be extracted via a compounding process without complex assumptions. Information is partitioned into equivalent sets like a deck of cards. Hence, higher levels of disorder and randomness in markets — are physical dynamics which appear in the same region after c in Diagram 1.

Point d which exist if point c does and arrives after it — can be used as an optimal control point to maximize positive and minimize negative compounding. If you learn how to repeatedly use it to profit and to exploit enough favorable opportunities — to move toward the top 20% of the curve as shown in Diagram 2. What follows in subsequent articles will be more details on how you can use knowledge of these concepts to navigate that journey.

by Harry Edwards
Mathematical expectation depends on the situation and environment

The advantage is ratio of mathematical expectation that can be dynamically used as a control measure to limit participation to the most optimal situation or environment. This makes it a crucial variable for summarizing all sorts of risk taking situations especially in military and business environments.

• The higher the magnitude of the advantage — the more favorable will be the outcome and the lower the risk of loss.
• The reverse is also true — which means that the advantage can be used as both a profit and loss function.

The following animation depicts this relationship with the variation around the normal curve — which reflects on the magnitude of risk as shown by the vertical bar adjacent to it.

Figure 1

In business situations — when the advantage is higher money is compounding at a faster rate and with lower variability. This means that if you know the advantage — and how to use it to dynamically value information — you would be able to make make money over the long haul with fewer assumptions than is otherwise possible.

Additionally, the advantage can be used across all asset classes, values and time frames — typically with only dozen or so advantage values. The benefit in having this level of simplicity is that more people can easily evaluate and use the measure to make smarter decisions with markets, business ventures and/or reward to risk situations.

One of the key purposes of this blog is to explain and demonstrate why and how the advantage can typically be generalized to help you capture the competitive advantage in almost any situation and environment more efficiently than other decision making factors.

And what would life be like without it?
by Harry Edwards

The causes of the drunkard’s walk are market noise, randomness and murky market dynamics. But how would you define it mathematically? Take a look at the diagram below. It’s not typically obvious which points peak — then start a decline or bottom and then start and advance with market prices. Smoothing markets introduces time lags — while traditional representations leaves the points labeled as a, b and c camouflaged. In this article — I’m going to show you the solution and the limitless potential of it.

Diagram 1

The above diagram illustration of Rolle’s Theorem was offered by Michel Rolle in 1691. At the peak, the first derivative between the two distinct points A and B is zero. But the peaks and valleys in market prices are confusing. Can’t see point c. You can’t repeatedly determine points a, b and c without distorting those points — which smoothing does by introducing a time lag. Life with the drunkard’s walk means attempting to determine point c — which is useful for optimal stopping — is an unsolved problem. Given the high variability nature of market dynamics — it’s no wonder most people have difficulty finding a simple market theory that works consistently enough for them. The simplest and most powerful solution has remained hidden due to the drunkard’s walk.

Time Value of Money Theorem (TVM)

The Time Value of Money dates at least to Martín de Azpilcueta (1491–1586) and is the central concept in finance theory. The concept allows the valuation of a likely stream of income and/or cash flows — both even and variable in nature between specific points in time. Variable sources can also be considered such as interest, projects cash flows and so forth.

Liquid market assets have fluctuating values. The key is to be able to dynamically value information streams so that money can be extracted via a compounding process without complex assumptions. This requires a unique solution that determines when the time lines should start, stop and when a shift of position should occur. This is the case because to know whether money is compounding for — rather than against you — requires a timeline so that the two points defined as a and b in Diagram 1 exist. Point b always unfolds sequentially in time — and positive compounding occurs naturally between points a and c. I will summarize a theorem and process that makes it possible to optimize TVM via the identification of the crucial points on timelines including market information streams.

Optimal Accumulation Theorem (OAT)

After point c in Diagram 1 dimensioning returns will occur — followed by negative returns. The challenge is to be able to classify system dynamics so that as little time as possible is spent attempting to accumulate resources after point c. Our theorem states: “In system dynamics which vary from favorable to unfavorable as defined by point a to b — there is some point called d — beyond c which presents an unacceptable risk.”

In order to optimize the rate of asset accumulation — the identification of point d is required to sequentially convert market information into variable returns streams. While the returns will contain both positive or negative results — classification for the information also enables strategy to limit the negative return streams. With fixed rate compounding — what is called a periodic “accumulator factor” is static and so is the conversion frequency of the compounding period.

The optimal accumulation theorem is an umbrella theorem which covers risk /reward conflicts in human and animal domains. While the scope of this article does not permit its discussion in more detail — readers will grasp the details in the examples that follow using Marginal Value Theorem and Information Foraging which are related concepts. MVT says a marginal rate forager should leave the current path once the marginal rate decreases pass point c in the diagram 1.

A typical illustration is competitive apple picking by humans. On each new apple tree, the number of apples picked per minute is high but decreases fast with time. Continuing to pick apples until the last few apples can be shown to be quantitatively suboptimal by the MVT. In OAT, the competition can take place on protected patches involving human conflicts that can have an extended range of position or negative outcome. It’s a completely general framework applicable where system dynamics as sequential patches can be mapped by partitioning as shown in Diagram 1.

Accumulation Rate Optimization (ARO)

Instead of a fixed accumulation factor — Accumulation Rate Optimization (ARO) uses a variable accumulation factor in an optimal compounding process. Point d as well as the classification of points between a to b are used to maximize performance by decreasing the time spent after the accumulator factor passes point c. Of course point c remains unknown until after it has occurred. An exit in the area of d is practical without prediction or probability estimates. The solution to drunkard’s walk makes discovering c and d simple classification problem. Optimizing positive and negatives returns is therefore a matter of maximizing time in partitions with a positive accumlation factor and minimizing time in those where it is negative.

The MVT implies that a forager should leave the current patch once the marginal rate decreases pass point c in the diagram 1 (which is similar to an MTV diagram). In ORA, optimizing the rate asset accumulation — is an optimal compounding process in which the patches resemble Diagram 1 — where a to b represent the timeline. The best accumulation factor for optimal compounding is the same advantage formula used in blackjack — as it defines mathematical expectation.

Hence, the advantage is able to confirm the correct mapping from a to b. How? Positive and negative return streams appear in their appropriate location in each patch is shaped as redundant curve. Each point exist within partition that makes it easier to determine point d. Additionally, each market patch is self-organized so that both the timeline and time spent in each is optimized by an actual — rather than estimated advantage.

What would life — be like — without the drunkard’s walk?

Imagine your financial life changed by a solution that enables you to use an optimal compounding process. Instead of debating or protesting about the inequalities in the financial industry — you could level the playing field. What makes our solution potential limitless is the ease which those without finance or math background — can do exactly that. How? Perceive how the concept works — then as our affiliate — learn to use it to control your financial destiny by helping a world full of people looking to do the same.