The Geometry of Markets
Empirical evidence does not exist for the notion that supply has ever equaled demand in any market. If it did, there would cease to be a market. That is until demand increased beyond supply again or vice versa. In either case, measuring it would be impossible.
Consider a road-side farmer selling produce. This person is standing behind a pick-up truck loaded with peaches and a sign that reads, “Peaches: $10 per dozen”. Those wanting the product, stop and purchase the fruit. As demand is realized, the farmer has less-and-less peaches to sell.
After sometime, all of the peaches have sold. At this point supply and demand may be equal or demand may be greater than supply. Since there is no more supply, it is very difficult to know. However, if people continue to stop and ask the farmer for peaches, demand is greater than supply. Otherwise, the farmer will have to return later with a fresh supply of peaches to find out.
Complexities of Measuring Supply and Demand
For a road-side stand, the notion of supply and demand is simple. If upon returning with peaches, the farmer is able to continuing selling, he or she has not reached the demand. Otherwise, if they return and only sell a few dozen, then it is highly probably that supply is greater than demand. The point is that the exact point of supply meeting demand is impossible to measure.
More complex markets like a modern exchange poise a greater set of complexities in determining supply and demand. These type of markets have third-party participants called market makers whose job it is to buy and sell any asset listed at a specific price. The sell price is higher than the buy price, giving them the profit from the bid / ask spread regardless of market conditions. Their purpose is to ensure liquidity.
In a natural market, one with only buyers and sellers, there are times when supply and demand are far apart. For example, consider a real estate market where home sales are slow. This may be the result of reduced demand or it could be due to a decrease in supply. Either way, it is impossible for supply and demand to be in equilibrium.
The reason it could be a decrease in supply, something usually related to higher demand, is the supply available may not match the specific demand. Just because homes are for sale, does not mean those homes are what is wanted by the buyers currently in the market. Perhaps only homes at the top-end of the market are available with the majority of buyers being young families.
If supply and demand become in equilibrium then the market is over. That means everyone wanting to sell has sold while all the people wanting to buy has purchased. Until someone else is willing to sell and another is willing to buy, the market is closed.
Market Momentum
Market pricing does ebb and flow. Anyone trying to sell a home realizes this. In a sellers market, homes sell quickly and at a premium. Buyers markets means home either sell slower and/or for less money. However, there is no time when the number of houses for sell equal the number of buyers. This holds true for any market.
This ebb and flow of price is known as Market Momentum and is a measurement of price difference between now and sometime in the past. The idea being a positive difference points to a bullish trend while a negative one signifies a bearish trend.
Pinpointing a timeframe that supply and demand are in equilibrium is like trying to forecast the exact moment it will rain. A meteorologist can determine the likelihood for rain over a few hours. However, there is yet a means to determine an exact moment for the phenomenon.
Stephen Wolfram, founder of Wolfram Alpha, explained in his controversial book, A New Kind of Science, that even simple systems can generate complexity. This applies to the issue of measuring supply and demand. Wolfram concludes that the only means of determining the full effects of even simple systems is to simulate them.
Borrowed Models
In a given market, pricing signals are created as a result of changing supply and demand. This is known as market dynamics. In determining a subtle model, the number of factors makes it difficult. Using only price and demand, it is complicated enough. Adding to that, the human emotional element with ensuing volatility, and it becomes near impossible to simulate.
One of the best means to measure difficult things is to borrow solutions from other disciplines. For example, Leon Battista Alberti, a 15th century Italian Architect, formulated the idea that “vision makes a triangle, and from this it is clear that a very distant quantity seems no larger than a point.”
Battista made representing three-dimensional objects in two-dimensional space a matter of simple geometry. The theoretical point at which supply and demand meet is similar to the point in a painting where two parallel lines come together. In both markets and paintings, the meeting point of these lines is just a representation.
In the diagram above is an illustration of two-point perspective. The vanishing points are lines that do not actually exist but are used as guides for the artist. Think of the left vanishing point as supply and the right vanishing point as demand. Coming down from the center to a point where both meet forming a cube is the theoretical moment when price causes supply and demand to equal.
Financial models begin with a deep study of market behavior. Only after gaining an understanding of the subject is a mathematical model attempted. In constructing a mathematical model, one must do 4 things: formulate a problem, outline the model, determine if it is useful, and test it.
So far, the problem has been discussed and a model outlined. However, it’s practicality is not very useful due to being impossible to solve. This means a better model is needed and/or more study of the market needs to occur.
Hopefully, one is not disappointed that measuring supply and demand is impossible for now. The entire exercise was to introduce the complexities of creating accurate market models. As the history of this topic is filled with being fooled by simple systems creating complex behavior.
Black-Shoals-Merton and Einstein
Prior to the global market crash of 1987, option valuation was considered a solved problem. The Black-Shoals-Merton (BSM) model seemed to be a good-enough model for the purpose. This model assumes the price of exchange traded assets follows a geometric Brownian motion with constant drift and volatility.
Brownian motion is one of those borrowed models applied to finance. Robert Brown, a Scottish botanist, discovered the phenomenon when he noticed a “rapid oscillatory motion” of the microscopic particles within pollen grains suspended in water under the microscope.
Later, Albert Einstein used the findings for his study of atoms. Applying the bell-shape Gaussian curve that arises from the sum of many independent, statistically identical random variables. Later, proving the existence of atoms and molecules with the study.
After the crash of 1987, it became clear that the BSM model was not an accurate depiction of option pricing. The models since have displayed a volatility smile. A curved line that looks like a person smiling. Something very much in contrast to the BSM theory that assumes the price curve is flat.
Conclusion
Over the past few decades, financial modeling has become increasingly formal. It is steadily shifting focus from mathematical methods to engineering ones.
As a Software Engineer, this is a familiar evolution. In the 1950’s, creating software was a mathematical endeavor. During the 1970’s and 80’s, the focus shifted to the application of engineering principals. In the 1990’s, the profession borrowed heavily from architecture.
Regardless of the method, markets are a deceptively complex subject with multiple hidden variables. Machine Learning should help clarify with many new answers. However, it will take multiple advancements in the field before anything close to an accurate market model is realized.
Thank you for reading.
