Publications: Gavekal Portfolio Solutions
Theory of Financial Fragility-Free Energy Arbitration
In our early letters on “Antifragility Revisited”, we demonstrated evidence of a linear relationship between many financial assets’ excess return and their variance at all probability levels.
Such a relationship was conspicuously absent from the considerations of Modern Portfolio Theories. This required a transgression to Professor Taleb’s description of fragility and anti-fragility.
But where does this relationship come from?
This letter uses physics to explain the concepts of fragility and antifragility from a theoretical standpoint.
Fragility and antifragility emerge as a natural consequence of market competition; they provide a financial variable which discriminates winners and losers in various market regimes.
A few simple equations can be used to highlight the theory, and demonstrate how one calculates the physical variables, such as fragility. Readers who are not familiar with mathematics need not worry. The equations are even simpler than the ones used in traditional portfolio theories − that is to say, very simple!
Theory of Financial Fragility-Conceptual Framework
The Theory of Financial Fragility anticipates the behaviour of financial assets in times of stress. Such anticipation not only requires a new conceptual framework regarding market arbitration, but also the help of modern physics and its understanding of energy transfers.
“Introduction to Financial Entropy” and “The Energy of a Fragile Asset”, published earlier this year, dealt with the financial interpretation of various forms of energy, such as potential energy associated with expected returns, kinetic energy associated with asset variance and “uncontrollable”, “risky”, or “useless” energy associated with entropy.
The Theory of Financial Fragility considers assets as species in an ecological competition vying to access the “useful” part of energy, also known as “free energy”. In other words, finance is no exception. It is governed by physical laws, and by an arbitration principle among strategies competing for survival.
Understanding survival strategies is key to identifying potential winners and losers in periods of stress, and to build investment portfolios with heightened robustness.
This letter focuses on the conceptual framework: the specifics of self-organized structures that ‘dissipate’ energy, such as planet Earth, living organisms, economic systems, financial markets, and many other systems that shape the evolution of mankind and, to a larger extent, the evolution of the universe, in their own way.
The “Energy” of a Fragile Asset
Physics would simply not exist without conservation laws. The conservation of energy in a closed system, for instance, is the first principle of thermodynamics and one of the most important concepts in physics. Does finance follow similar laws? And what would the “energy” of a fragile asset mean?
Quantum-like Market Memory
This letter presents visual analogies between quantum physics and market behaviour with regards to risk memory. As shown in the previous publication, market risk memory exists, which is inconsistent with the theoretical picture proposed by traditional financial mathematics. Such an inconsistency, between theory and reality, is at the heart of quantum physics, known as the wave-particle duality. As for particles, represented by wave functions, market distribution of returns are distorted by intercations, i.e. transactions. Such distortions can be measured, and affect all common financial risk measures, such as Value-at-Risk.
Empirical Evidence of Market Memory
As professor Eugene Fama stated in 1991, “the literature (on potential market memory) is now so large that a full review is impossible”. In this letter, we show empirical evidence of market memory, in a side manner with crucial consequences for fragile assets.
Introduction to Financial Entropy
Our previous letters on “Antifragility Revisited” principally dealt with the economic and financial meanings of fragility. A necessary step to progress on the theory is to now turn to scientific analogies. This letter focuses on the most profound yet troublesome, and contrived concept of modern science: entropy. It introduces the founding ground of a scientific definition of fragility.
The fragility theory might well be the first financial theory providing a rational explanation for critical risks, behavioral irrationality, and market ruptures. In this letter we analyse why “criticality” emerges from fragility, and how to measure it.
The Missing Variable
The previous publication dealt with providing a formal measure of fragility, shown to be the slope of a return to variance graph. In this letter we analyse why this property is a necessary addition to modern portfolio theories (MPTs).
MPTs focus on correlation across assets and on Value-at-Risk. These provide insightful information in calm market phases, but often implode in tails, when they are most needed. The fragility theory introduces a new variable−the fragile or antifragile nature of investment assets−to help capture hidden risks. The missing variable from MPTs is linked to most of the “unexplained” market behaviors described in this publication.
The Formal Measure of Fragility
Our last publication on “Antifragility” proposed a method to verify the fragile or antifragile nature of financial assets. This week’s publication goes one step further and challenges Professor Taleb’s description of fragility. The suggested transgression opens doors for a formal and quantitative measure of fragility, with very high statistical significance, as opposed to a simple verification of the fragile or antifragile nature of any asset; A necessary step to introduce fragility as a new variable in portfolio construction processes.
A Method To Prove Fragility
Professor Taleb’s concept of antifragility was introduced in part I to highlight its potential innovative applications in finance, in terms of portfolio construction as well as single asset analysis.
Stock analysts for instance, scrutinise companies' performance, strategies, managerial abilities etc. to make conclusions on their expected earnings and risks. They then compare their views to the market's implied assumptions. But what about fragility and antifragility? How can one measure what the market thinks?
Part II proposes a method to prove fragility or antifragility, from the market's perspective. It shows as an example that the S&P 500 index is fragile, and explains why the 20% level on the VIX signals potential major market instabilities.
What Antifragility Means
‘Antifragility Revisited’ is a series of publications on the financial, physical, and socio-political concept of antifragility, invented and promoted by Professor Nicolas Nassim Taleb.
Part I introduces the concept and its potentially revolutionary applications in finance. These include the identification of fragile and antifragile assets, the classification of companies by level of market fragility, the measure of critical volatilities and the construction of investment portfolios targeting long-term robustness.
A Simple Rule - PART III - Risk Remuneration
In this publication, we analyse the competition between major economic zones on risk remuneration. Risk remuneration is the excess return of risk assets above cash rates. Similarly to cash remuneration, presented in Part II, flexible investors can generate significant alpha by dynamically allocating risks to the leading zones.
Part III shows evidence of risk allocation opportunities on equity indices, thereby confirming the arbitrage principle. It temporarily closes a first series of three letters on the global competition across zones to attract world savings, and the benefit that a global and flexible investor can take from it.
A Simple Rule - PART II - Cash Remuneration
Monetary zones compete to attract and safeguard excess savings denominated in their own currency. From an investor’s standpoint, the attractiveness of a currency resides in the total remuneration proposed by its monetary zone, i.e. the interest payments on cash deposits and the appreciation or depreciation of the currency vis-à-vis other competitors.
We analyse below this competition over time and show that currency remunerations, or ranking across zones, reveal the ‘Best of Breed’. A simple rule to allocate cash, based on trusting currency leaders over currency losers, generates significant alpha over time.
A Simple Rule - PART I - Arbitrage Principle
There exists a theoretical trade-off between two types of remuneration: cash and risk. An economic and monetary zone cannot simultaneously favour both ‘the rentier’ and ‘the entrepreneur’. However, we believe that a flexible investor can in fact benefit from such a situation. By investing their cash into the best cash-remunerating zone and their risk into the best risk-remunerating zone, the investor can do what has rarely been done before; reap the benefits of both.
The presentation of our model is split into three parts: (I) Arbitrage Principle, (II) Cash Remuneration, (III) Risk Remuneration. Through our new method of analysing global investment portfolios, our model devises a simple rule that leads to the generation of significant long-term alpha
Publications: Quant Corner Notes