From Markowitz to Fractal Market Cycles

I started out as a traditional quant, schooled in capital market theory tied to the Sharpe/Lintner/Mossin Capital Asset Pricing Model.

At Rutgers grad school in 1980 I was lucky enough to study with Dr. Harry Markowitz, Nobel laureate and the father of Modern Portfolio Theory. Dr. Markowitz required his classes to optimize portfolios using the most advanced portable technology available to us, a hand calculator. It was a tedious process, but it did have one advantage. You needed to know all the assumptions underlying that now common process. As a practitioner I found many of those assumptions to be pretty heroic. Particularly the assumption that stock returns were a random walk (and so could be modeled with the normal distribution, that old “bell shaped curve”) and also that these characteristics averaged out over the long run. Finally, the assumption added by others to justify using the normal distribution: that investors were rational players in aggregate and current prices reflected (at least) all public information making markets “efficient.” At the time thinking otherwise was heretical in academic and quant-investing circles, but I found that theory rarely met with practice. The same was true of the Sharpe-Lintner-Mossin Capital Asset Pricing Model (CAPM), the Black-Scholes model of option pricing, and the Engle auto-regressive- conditional-heteroskedastic model (ARCH) all of whom later won Nobel Prizes. As important as these models were to developing quantitative finance they all depended upon efficient markets. It appeared that “market efficiency” rationalized using the normal distribution to make the math easier and cleaner. Reality was being made to fit the model rather than the other way around.

In the late 1980s I came across chaos theory and fractals which seemed to offer dynamical and statistical properties that better described markets especially when combined into complexity theory. For instance fractals explained why the realized distribution of market returns had “fat tails” rather than the theoretical bell shape of the normal distribution. Chaos theory explained how you could have non-periodic cycles and how randomness could coexist with determinism. The math was messier and you couldn’t solve for a single “optimal” answer to many problems, but it seemed more realistic. After extensive personal study and research, I published a series of books on the topic and formulated the Fractal Market Hypothesis. In later research I found evidence of two distinct periods where market uncertainty was high or low. The risk/return trade-off in those periods was quite different. In the “resilient” lower uncertainty state, risk was rewarded with return. That relationship did not appear to exist in the high uncertainty “fragile” state. More risk did not mean more return. In the resilient state market returns were close to normally distributed. In the fragile state tails became “fat” as more extreme events happened. The distinct risk/return trade-off for each period is shown in this graph:

The first real evidence I found of a market cycle was this shift in uncertainty accompanied by changes in market characteristics. The results also suggested that the markets are in many ways too complex to be modeled using either traditional linear quant or newer non-linear methods, especially since markets shifted between many states over time. These market uncertainty cycles lasted for a few years on average but were embedded in longer waves of inflation and financial instability which could last for decades. This made me realize that complexity theory applied to climatology and meteorology was a better model than physics for the interaction of these systems.

Market Climatology: Cycles Within Regimes

Market climatology not only to explains the past, but also gives insight into the present that hopefully helps us prepare for the future.? Cycles and regimes happen for underlying fundamental reasons combined with the behavioral reaction of investors and economic players.? And while the set of causes is fairly consistent over time, the interactions of these four systems make each turn around the fish bowl different:

• Market Uncertainty Cycles - Risk, return and correlation characteristics change both within and across asset classes as uncertainty rises and falls. Though risk is a symptom of uncertainty, they are not the same thing.
• Short-term Reflation Cycles - The near term trend in inflation expectations drives central bank policy which in turn influences market and economic activity.
• Financial Instability ("Minsky") Regimes - Levels of financial leverage increase with the business cycle while the financial system plants the seeds of its own destruction as postulated by Hyman Minsky.
• Long-Term Inflation Regimes - Investors and economic players behave very differently when inflation is 2% or less, or 6% and more. Accordingly, asset class behavior changes too.

Market climatology links these four fundamental systems to determine the market and economic environment.? Since each system has its own duration there are many possible combinations depending on how they are synchronizing across their cycles. I have created indicators for the systems and will share them with you along with implications for the current market environment.

Because the full market climatology is a complex, dynamical, and fractal most traditional methods of analysis only give a partial picture. My approach is comprehensive but also quite simple in order to keep the flexibility needed to track such a process while still allowing for the complexity of each system’s interaction with the others.

Please comment on this post if you're so inclined. And feel free to forward this post to anyone you think would find it interesting. Thanks for reading!

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