The attraction of symmetry has long had a powerful impact on what we see and what we wish to see in the world and in the heavens, affecting everything from the sciences to mathematics to the arts. Despite its allure, attempts to impose symmetry on inherently asymmetrical realities can severely distort truth and create significant risk, particularly when analyzing complicated systems such as markets.
Symmetry and Human Thought
Symmetry has long held a powerful influence over humanity’s efforts to understand the universe. Based on the Greek polymath Ptolemy’s views, for centuries it was believed that the southern hemisphere of the earth must balance the land mass in the northern hemisphere; this belief had a major impact on the efforts of adventurers across the ages to map the dark area of the globe. This imagined land mass was referred to as Terra Australis Incognita.
In addition to serving as the basis for assumptions about the natural world, the search for and the creation of symmetry has had a major impact on many elements of human existence. In architecture, for example, the vast majority of structures are built with one side being an exact replica of the other. Aesthetic predispositions play an important role in this repetition.
If we look at the Taj Mahal, for example, we are immediately striken by symmetry of the monument, with the central dome flanked by two chattri (domed kiosks) and four towering minarets. Another important example of symmetry in architecture is found in Palladio’s Villa Capra “La Rotonda” in Vicenza. This building, which was influenced by the Pantheon in Rome, is completely symmetrical, with four identical facades.
The search for symmetry can be seen in many components of music, from rhythm to harmony and even in the relationship between sound and silence. If we listen to the music of baroque musicians such as Johann Sebastian Bach we can hear layers and layers of symmetical melodies and harmonies that move back and forth across points of tonal balance and ultimately lead to resolution.
Symmetry in Economics
The search for symmetry also plays an important role in business and economics, particularly with respect to our expectations about market relationships and movements. These expectations are the basis for many vital elements of market analysis, including forecasting, valuation and the quantification of risk.
One of the most common expressions of the search for symmetry is in regard to asset pricing which is heard in the phrase “what goes up must come down.” This expresses the view that somehow a movement up in prices must be balanced by a corresponding movement downwards, as if a movement in one direction was naturally subject to an unseen force pulling it back to a center.
The concept of symmetry also plays an important role in more sophisticated theories of how markets work. One area where symmetry is present is in the concept of market equilibrium, a state which represents the exact point at which the demand for a product equals supply. This conception of a market serves as the basis for setting what is called an equilibrium price. According to this view of price dynamics, if demand remains constant and supply falls, prices must rise. Conversely, if demand falls and supply remains constant prices must fall. The geometric assumptions underlying Ptolemy’s cartography are not far from these views.
The Reality of Market Asymmetries
Despite the simplicity and attractiveness of symmetry as a predictive and explanatory framework, attempts to impose symmetry on a world which is characterized by significant amounts of disorder can be very dangerous when it comes to economic and business analysis.
To begin with, if we start by revisiting the assumption that “what goes up must come down” we can immediately see that this is often not only not the case but more importantly has very little to do with basic principles of economics. Setting aside the impact of market expectations, prices can continue to rise for very long periods of time and when they fall fall not to the level where they started but at progressively higher price points. These pricing movements are a function not of an overarching geometric form but rather a large set of asset intrinsic and asset extrinsic variables.
Considering downside scenarios, the fact that prices for a certain asset have fallen does not by any means mean that they will rise again. Whether they will rise again does not depend on an unseen force that brings all things into symmetrical balance but rather a series of market factors which, depending on the circumstances, can cause prices to rise, remain the same or fall further. Further, while not always the case, falling prices often set in motion a chain of events that increase the likelihood that prices will continue to drop; in other words asymmetries can create additional asymmetries.
Reasons for Market Asymmetries
Market factors such as prices are often far from symmetrical because the variables that drive these factors are also not symmetrical. The following are three of the many reasons for this.
The first reason is unequal and imperfect access to information. As the core of an equilibrium view of markets is the assumption that market participants have perfect knowledge of the market; this is because if they did not they would not be able to adjust their purchasing and buying decisions to react to market realities. A more accurate statement of market participants is that they make decisions in the face of high degrees of uncertainty about levels of market supply and demand. While it may seem counterintuitive, this degree of uncertainty is generally the highest at the exact point in time when a pricing decision is made.
Rather than having perfect market knowledge at the time of making a purchasing decision, market knowledge tends to move to essentially zero as the time for making a decision comes closer.
The second reason is the dynamics of pricing negotiations. Equilibrium models assume that pricing negotiations are carried out with reference to market supply and demand levels. Depending on the nature of the product, however, pricing negotiations can be more heavily based on asset-specific and transaction-specific factors. This is particularly true for products that are not commodities.
The third reason is market drags on price fluidity. Equilibrium models assume that prices are relatively fluid and can react quickly to changes in supply and demand In reality, there are number of factors which tend to hold prices in place regardless of short-term supply and demand movements, including prices that are fixed for certain time periods by contract, limited bands of cost structure fluidity, limited bands of ability to change prices that are paid for goods and services and even psychological factors that impact price horizon perspectives.
Conclusion
Keeping in mind the centuries of fruitless searches for the Terra Australis Incognita, it is important to be wary of the dangers involved in searching for symmetry in areas of economics or business that are inherently assymetrical, such as markets. Rather than trying to fit data into preconceived and attractive shapes, one should approach market analysis and decisions through a careful consideration of the underlying relationships that drive markets, regardless of how messy and contradictory they actually are. This leads to conclusions that are perhaps less elegant but more likely to avoid the whirlpools that markets put in the path of individuals who set out to discover their mysteries and return with their treasures.