A General Theory Of Market Behaviour

In 2013 the Nobel Prize committee gave the economics prize to two academics with fundamentally opposite beliefs. On one side they gave Eugene Fama the award for his work developing and expanding the efficient market theory. And on the other side, Robert Shiller won the award for effectively disproving the efficient market theory.

In many ways Dr. Fama and Dr. Shiller created the two leading financial economic theories. One theory believes the markets are efficient. They incorporate all available information into their prices, and in doing so, behave rationally. The other believes investors act irrationally, causing inefficiency in market prices. Available information can not possibly justify stock’s volatile price action (think fall 1987 or 2008), leading to the creation of behavioral finance to explain investors’ irrational behavior. No one has ever unified these two theories, until now.

This article will explain, rationally, why markets behave as they do. They are efficient, but not in the way the efficient market school believes; they are geometrically efficient. Geometric efficiency explains why markets shoot up to into “bubbles”, and why they “crash”. And it explains, with indisputable mathematical concepts, that these “bubbles and crashes” are totally rational, actually proving market efficiency.

What are Efficient Markets?

The efficient market theory says that stocks always trade at their fair value, that all information available to investors is incorporated into the price of the stocks immediately. It’s not possible to find mispriced securities unless one has inside information. Stocks are never under priced or over priced – they are always correctly priced. And changes in security prices are always justified by known information. As such, an investor can’t pick stocks and outperform the “market” because there isn’t any inefficiency to exploit.

The leading theory from Fama’s day explained a market gets “efficient” across all assets by equalizing risk adjusted returns. The more risky an investment, the more the investment should expect to return. Investments that don’t rest on the “security market line”, are in the process of quickly moving towards the line.

Furthermore, under this framework an investor can’t use leverage alone to create a better investment. Leveraging up a lower returning asset just creates the same expected return as a riskier asset. The market is therefore “efficient” as no asset provides a risk adjusted return superior to another.

Shiller’s Insight on Efficient Markets.

Robert Shiller didn’t believe in efficient markets. Dr. Shiller in 1981 wrote a seminal paper showing that markets do not behave rationally and efficiently. The variation in stock fundamentals, aka the “available information”, do not vary enough to justify the amount of price volatility actually seen in the market.

He analyzed the belief that asset prices should reflect the value of all future cash payments, and concluded that if prices acted efficiently they would fluctuate far less than they do in the real world. Bubble and Crashes would not exist.

Put bluntly, the stock market information available to investors does not explain the wild swings in stock prices. Therefore markets continuously overshoot and undershoot fair value. This realization lead to the creation of behavioral finance to explain the clear discrepancy between efficient markets and actual investor behavior.

Based on the framework given for the efficient market hypothesis, Dr. Schiller was mostly right. But his ultimate conclusion that markets are inefficient and investors irrational is misguided. Instead, his work disproved the current framework describing the markets construction, not their efficiency or rationality.

The Problem With the Efficient Market Theory

Let’s think again about the the working framework of asset price falling along uniform risk/return security market line. Which return becomes efficient along this line, the arithmetic or the geometric? They both can’t be efficient can they?

Most efficient market theories assume markets get efficient across the the arithmetic return. Researchers, such as Markowitz pay lip service to the geometric return, but never in the core parts of their theories. CAPM is entirely based around the arithmetic return, and so are most other asset pricing models. Over very short time frames that are not repeated, this model of the markets works.

It's fundamentally known, everything in investing repeats. The arithmetic return is meaningless. The geometric return is hence all that matters.

Efficient Theory of Geometric Markets

Calculating the geometric return of assets on the theoretical “security market line” gives a much different picture. The long term returns become curved. There is a peak. The end of the security market line is no longer efficient at all. The whole concept breaks.

The proper framework states markets aim to maximize their long term geometric return. Geometrically, there is an optimal portfolio for all assets, and the market will try and efficiently move toward this portfolio at all times.

We’re going to stick with a very simple two asset stocks/cash portfolio to walk through the philosophy. A portfolio of two assets (stocks and cash) will have a curved long term expected return.

There is a clear maximum point showing there is a singular superior portfolio composition. The equation for determining the maximum portfolio is:

% Stocks in Portfolio = (Asset Return – Risk Free Rate) / (Asset Variance)

The rational investor in this market should try and invest at this maximum point. A truly efficient market doesn’t organize itself around a securities line, it organizes itself around the maximum return point on a geometric return curve. This is the correct framework for testing the efficient market theory.

Lets Evaluate the Model for Expected Volatility.

So lets walk through a simple thought experiment, and you check for any irrational decisions. We’re going to assume 7% risk free rate, 10% risky asset rate, and 20% volatility (uncertainty) for the thought experiment .

1. I recognize that geometric return is what matters to my future wealth.
2. Therefore I decide to structure my portfolio to maximize my geometric return through this method and hold 75% of my portfolio in stocks and 25% cash.
3. All is well in the market, nothing new changes. I keep the portfolio the same.
4. Suddenly a major financial company goes bankrupt. I believe the uncertainty in the market increases due to this event. Lets say the uncertainty (volatility) is now estimated at 25%.
5. My portfolio needs to change because the properties of the market have changed. What is the right portfolio now?
6. Based on the math of maximizing the geometric return, my new portfolio should be:

(10%-7%)/ (25%^2) = 48% Stocks

Wait a second. A 5% change in uncertainty (volatility) should cause the percentage portfolio to drop by 36%? . That's stunning.

And what if Everyone did this?

Mathematically, the value of the risky asset in your portfolio should fall from 75% to 48%, a 36% drop in allocation to the risky asset. It is perfectly rational for your own value of stocks to fall by 36%. So, by extension, doesn’t this also mean it’s perfectly rational for the market value to fall by 36% as well? If everyone is being rational, then the market (everyone) should also act to reduce their exposure to stocks until the percentage of stocks in their portfolio also falls to 48%, correct?

Since there is a buyer of a stock for ever seller, the only way for the average investor (the market) to reduce their stock exposure by 36% is for the PRICE TO FALL by 36%. Therefore, rationally, a 5% increase in expected volatility of the market, should cause the price of the market to fall by 36%. A geometric view of the markets explains why prices crash, efficiently.

Large Fluctuations in Price are PERFECTLY Rational.

This rational six step thought experiment was loosely based on the 2008 crash and Lehman Brothers failure. And I ask you again, did any action described seem irrational? Isn’t that exactly how an intelligent investor should invest? Mathematically, it is. If we are going to say markets are efficient, incorporate all information, and act rationally, the crash is the only logical outcome. Markets organize themselves around maximizing their geometric return. When viewed through a geometric lens the crash is actual proof the markets are rational and efficient.