Wednesday, April 1, 2009

Origins of Chaos

In the last post the conceptual framework for seeing some bits of order in apparent disorder. This post will focus on the sources of disorder in the stock market. Many of the concepts will apply readily to financial markets of all types. What you should take home from this post is that there is no clear-cut way to determine the value of a stock, and even if there was, there are plenty of reasons why it can't be traded at that value consistently. However, a greater question is, can a stock trade at any price? This post will answer this question with a degree of certainty that seasoned traders and new traders alike may find surprising.

To start, let's imagine a market established solely to determine the value of shares while paying no attention to whether they can be bought or sold in volume at that price. Looking back at the relationship between fundamental analysis and technical analysis, since fundamental analysis is the only avenue for information to enter the market through trading while technical analysis is effectively blind without some fundamental analysis or an existing trading pattern, it's clear that fundamental analysis is the only technique that would be able to determine the value of shares in the absence of trading and market data. Therefore we need to look more closely at what fundamental analysis is and where it loses traction in order to find out why stocks seem to trade so erratically sometimes.

The goal of the fundamental analyst should be to determine the price of the stock based on equity per share and future earnings. Equity per share is just an acknowledgment that the corporation does indeed have assets, cash and non-cash, that if liquidated will be worth an approximate value per share, effectively establishing a certain amount of "hard" value to the share. That is, the share is representative to a certain extent of at least that amount of real assets.

The value of future earnings is much trickier. For one, the value one should pay for earnings that have yet to be booked isn't well agreed upon. Good measures are usually derived from other more stable investments such as CD's and bonds. The value of potential earnings can be benchmarked against relatively guaranteed earnings and using various approximations for risk, the price one is willing to pay for future earnings can be obtained.

However, analysts don't always agree about their earnings predictions, growth rates, and the equity in a corporation. Depending on their models, the data their using, how they interpret it, their instincts through experience and hunches, and even whether or not the investment bank they work for is trying to get a banking deal with the corporation, their earnings estimates and target prices will differ. Different analysts will apply different growth models and will make approximations using different methods. This alone is enough to tell us that the problem of establishing the price a stock should trade at is not straightforward.

Two issues are responsible for most of the difficulty in calculating future earnings, which is a big part of the value per share. The first is that earnings is the difference between revenue and expenses per share. If revenue and expenses are relatively large compared to their difference, then relatively minor fluctuations in either revenue or expenses can produce huge percentage differences in the earnings. This is a condition known as low-margin, and it just means that there is little separation between revenue and expenses. Wall street likes the sound of high-margin because it means that earnings are much less sensitive to minor fluctuations in revenue and costs.

The second challenge to accurately predicting future earnings is the growth rate of the market or markets the corporation does business in. Growth has the most dramatic effect on long-term profitability. If one analyst predicts 5% earnings growth year-on-year and another predicts 10% growth, at the end of ten years the first analyst will expect 63% higher earnings while the second will be looking for 159% higher earnings. Clearly, in any situation where growth is exponential on a long time-scale, minute differences in the estimation of growth can lead to very large divergences in the valuation of a stock by different analysts.

This situation can be exacerbated even further if the net worth of the corporation is small compared to the expected value of future earnings. In this case, the future earnings are the dominant component of the value of the stock, and differences in the predictions of future earnings will create a high degree of uncertainty in the price of the stock.

This illustration shows the assets and liabilities, both hard items on a corporation's balance sheet, as metal coins since the value is very real. The revenue and expenditures are represented by the paper bills. The change in value of the corporation is a result of all of these numbers, and is usually small in comparison. From this chart, it's easy to see how minor fluctuations in these large numbers will produce large percentage changes in profit, causing profit and growth forecasts to vary greatly.

The big picture is starting to take shape, and it's obvious that fundamental analysis has a lot of room for error, particularly in situations where there a corporation has a small amount of assets relative to the size of its expected earnings or where the profit margin is tiny and very susceptible to minor fluctuations in revenue or expenses. What this tells us is that even in an imaginary stock market where the price is set solely by fundamental analysis, there is no perfect price to trade at, leading to the conclusion that fundamentals cannot be the end-all be-all of stock valuations.

This moves us to a second question of interest: Can a stock even trade at a theoretical best price if it exists? To begin answering this, take not that equity markets were originally conceived to facilitate capitalization and to alleviate supply-demand imbalances. Corporations obtain capital through Initial Public Offerings and other secondary offerings, and the market is where they go to sell those shares. Also, traders occasionally wish to move their assets and the market is what provides the medium of liquidity so that they can buy and sell when they need to. Managing supply and demand is a fundamental role of any market.

First to answer the question, supply-demand imbalances exist because not everyone wants to buy or sell at the same time even if they do know what price they would buy or sell at. To make this very clear, let's imagine that Leeroy Jenkens is a day trader worth millions of dollars and also likes to play World of Warcraft. One day Leeroy gets distracted while playing and realizes he's missing out a move he expects from BEBE. He hurriedly enters in an order, but due to carpal tunnel and the rush of the moment, accidentally enters in a few extra zeroes on the number of shares of his market order. Because he has enough cash on hand, the order goes live and wipes out all of the sell orders on the market, eating into higher and higher priced orders up to a theoretical infinity until other computer trading systems quickly catch on and cash in on poor Leeroy. This wouldn't likely happen in real life due to market makers managing such orders to give liquidity a hand, but the point is clear. If someone is buying or selling and has unlimited funds, anything is possible. Clearly the potential exists for localized supply imbalances, whatever the cause, to drive the price far from any expected best price.

To begin illustrating the extent to which these imbalances can affect the trading price, let's consider a different example. A village is visited by two trucks every six months. One is full of bread and the other is full of sneakers. At the day of their arrival, there is simply too much of both bread and sneakers for all of it to be sold. Being the clever merchant, you would look at the cheap prices and realize the opportunity for profit in the future when the demand recovered. However, you wouldn't be willing to accept the same discount on both products. Bread is a staple. It's necessity is guaranteed, so there is a high likelihood that the price will recover. Sneakers are discretionary, so there is a chance that people won't be willing to spare enough income for the prices to fully recover. By the time the price would have recovered, they may be out of style. You would only accept a large discount on the sneakers in order to reduce your exposure to risk. With bread, the price difference quickly becomes like arbitrage, where you trade an asset at a better price on another market. In this case, it's more like time-arbitrage. You just wait for the market to recover. However, with sneakers, the price changes involve more risk, which means it takes a deeper discount for the discount to translate to a sure profit. It takes longer for sneakers to become arbitrage-like than bread.

Turning back to the inaccuracy of fundamental analysis, the role of certainty of fundamentals in determining the sensitivity of the supply-demand relationship to price fluctuations can be made clear. A corporation whose earnings have more potential to fluctuate wildly and has a small amount of hard assets per share will require deeper discounts to attract more dollars. Every buy or sell order will require a large relative price change to succeed in executing a trade. Corporations with lots of hard assets, consistent earnings, and high margins will become arbitrage-like very quickly. In short, the uncertainty of fundamental analysis has a dominant effect on the supply-demand relationship.

The big picture is nearly finished. Not only is there no exact best price, but even if there was a theoretical best price, due to supply-demand imbalances this price can't always be traded at. Furthermore, the potential for valuation to fluctuate due to uncertainty in earnings has a direct effect on how powerful supply-demand imbalances will be in determining what price shares ultimately change hands at.

The last question is, does the theoretical best price stay constant over time? To answer this, we can simply look at what drives fundamental analysis. Existing and emerging financial data, news breaks with relevant impact on expectations, and insider information etc are all used to create the fundamental analysts estimates. In the case of existing data, it exists and won't change over time. This would form a static picture of the stock's valuation. However, the fact that there is emerging financial news will produce changes in this picture, making it dynamic as new data or news emerges.

To integrate this all into a single model, turn back to the idea that all information enters the market via fundamental analysis of some sort, be it insider information or SEC filings becoming expressed in expectations, followed by trading activity. We would expect that due to variations in expectations, that there is in fact no best price, but instead a range of plausible prices, with fundamentals creating a containment effect whereby supply-demand imbalances are evened out whenever the trading price becomes a less plausible valuation, attracting more counteracting trades. Near the edges of the range of plausible prices, supply-demand imbalances will be corrected more quickly. In regions where prices changes all result in plausible valuations, there is little sensitivity to price changes and other mechanisms are dominant. As new information becomes available one way or another, the range of plausible valuations is changed, giving us new locations to expect resistance to supply-demand imbalances to exist.

To visualize this, recall the cigarette diagrams. While turbulent smoke can take many paths, the underlying physics always act to ensure that the path that any particular smoke plume takes is going to fall within a certain range of likelihood. Within this range, the particular shape is more dominated by chaotic effects. If the cigarette was inside a region of slowly churning air, the range the smoke would exist in would so migrate, taking the smoke with it. This should start to seem very familiar to any seasoned trader. The range of likelihoods of smoke is analogous to the range of plausible valuations. The turbulent path within this range is analogous to the trading price as it ultimately exists at any given time. The migration of the smoke plume caused by tiny winds is analogous to the changes in plausible valuations that occurs as new information becomes available.

Turning back to the million dollar question of whether a stock can trade at any price, it's already been made clear that extreme supply-demand imbalances can exist and can severely impact the stock price one way or another. Upon first inspection, this would seem to suggest that it is in fact possible for any price to exist at any time. Internet stocks and the recently failed bank stocks are two examples where valuations can seem to indeed demonstrate that any price is possible. However, lets look at what the model says about these two situations. With internet stocks, they had low assets, high expected earnings growth, and little or no current earnings, all factors which increased the uncertainty in valuations and thereby decreased the response to supply-demand imbalances. Thus we saw the stocks trading at very generous valuations even if they were to ultimately fail. The potential earnings were so high that there was little to rein in the price at the top end. In the case of failed banks, it could be said that the banks had low volatility in earnings predictions leading up to the collapse of the stock price, but they also were affected considerably by emerging news. Lehman Brother announcing bankruptcy was a major change to the set of existing data, which facilitated a huge move in the stock price. What we begin to see in these examples is that, while at first glance almost any stock price does seem possible, extreme valuations and changes to valuations will only occur in the presence of large uncertainty in fundamentals or when those fundamentals themselves have been greatly modified by new data. What this says is that, while any stock price can be possible over time, at any one given time, only certain stock prices are likely. In short, $60 Lehman would never have traded at $2. It was emerging news that facilitated this price. It can and did trade that way over time, but these valuations are not plausible for every stock at any time.

The keen scholar would say that the potential for supply-demand imbalances to move a stock to any price would negate the assertion that there is such a thing as a trading range. However, consider a different field of study that can and does tolerate such local variance. Quantum physics, in stark contrast to classical physics, only requires that things are conserved on the average. Essentially, there is a finite chance that particles can appear out of absolute total nothing, but the chance is small and, on average, the balance of particles just randomly appearing and disappearing out of thin nothing is zero. To get a better idea of why this doesn't break the model, consider the recent popular movie, The Watchmen, in which a main character, Dr. Manhattan, declares he longs to see oxygen turn into gold. While theoretically possible with a finite chance that is about as close to zero as it can get, Dr. Manhatten should be disappointed to find out that his one atom of gold, while worth nearly $1000 per ounce, is almost worthless. To rephrase this, likely events will happen with great effect and are very tradable while small variances are not tradable and will happen with fleeting effect on the larger market.