Publications: Gavekal Portfolio Solutions

Bonds. Which Bonds? - by Didier Darcet


Unconventional monetary policy has led to the largest bond bubble in history; some 15 trillion dollars’ worth of debt globally, now providing negative yields. Bond holders from developed economies may have reason to worry about the future of their savings. History tells us, however, that perhaps they should simply put their feet up, and take a look at less crowded bond markets for inspiration.

Genesis - by Didier Darcet


Fragility in finance is equivalent to mass in physics.


To understand the analogy, one must go back to the origin of time itself. Crucially, the genesis of our universe is remarkably similar to the genesis of finance.


This claim shall lead us to a better understanding of what antifragility means. Antifragility in finance is equivalent to antimass in physics, the hypothetical ‘dark energy’ that has eluded cosmologists for so long.



GOLD and the Chinese Yuan - by Didier Darcet


As the year draws to a close, we have taken time to reflect on our Theory of Financial Fragility. As its track record develops day by day, it has highlighted certain lessons. In the new year, we recommend paying close attention to the two best-remunerating currencies of the past twenty years; Gold, and the Chinese Yuan. Their leadership will soon become particularly symbiotic.


Financial ‘Time’ - by Didier Darcet


Science and philosophy have debated the significance (and even the existence) of ‘Time’ since ancient Greece. Finance, however, is the only discipline providing a market price for the uncertainty of the future, which means ‘Time’. Resultingly, it deserves a seat in the debating chamber.


There are two ‘clocks’ in Finance, turning at different speeds. The first one synchronizes market trading and option values. It provides the tempo of the inherent random variability of asset prices. Only the second clock controls the directionality in ‘Space’, i.e. the expected drift of an asset.


The Theory of Fragility provides the missing link between the two clocks, which reconciles most of the scientific interpretations of ‘Time’.


Unlike ‘Traders’, ‘Investors’ should ignore the first clock and focus on the second.


Wealth and Money - by Didier Darcet


We cannot fill our car tanks with letters of credit, and we can’t have banknotes for dinner. This is because ‘Wealth’, and ‘Money’, are fundamentally different. This is an issue we have considered in many of our papers, defining asset value and wealth out of free energy, not money.


Today, we argue that cash rates set at artificially low levels by major Central Banks for too long deeply affect developed economies’ wealth creation.

Antifragile Gold - by Didier Darcet


Gold is the ultimate antifragile asset. Unlike fragile assets such as equity indices, antifragile assets react positively to stress. Does it make sense to constantly hold gold in a diversified investment portfolio? ‘No’, is the answer.


50% of the time, when currencies act as stores of value, gold is a useless asset. However, the other 50% of the time, when currencies are debased, gold is a vital asset, insofar as it is the centre of pricing of all other financial assets. This paper will take the former 50% of the time to be ‘Wicksellian times’, while the latter 50% to be ‘Keynesian times’.


World economies re-entered ‘Keynesian times’ on January 31st, 2019, following the monetary policy reversal of the FED. Statistics on portfolio allocation advocate a switch in these periods: from bonds to gold, from developed economy equities to emerging equities, and from cash to real estate.


Gold, however, is not antifragile by nature; it has only turned antifragile since the end of the Gold Standard in 1971 because of its pricing in currencies. And currencies are fragile assets…

Theory of Financial Fragility-Free Energy Arbitration - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


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.

Critical Variance - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


‘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 - by Didier Darcet


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 - by Didier Darcet


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 - by Didier Darcet


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

Equities in a Society of Control - Part II (July 2020) - by Didier Darcet

Equities in a Society of Control - Part I (July 2020) - by Didier Darcet

The Liquifity Rule Boosts EM Equities (June 2020) - by Michael Du Jeu

Timing the Peaks - Update (April 2020) - by Didier Darcet

Timing the Peaks (April 2020) - by Didier Darcet

Covid_prediction_ETH_SUSTech_GIS (March2020) - by Didier Darcet

COVID-19 Projections - (March 2020) - by Didier Darcet

SUSTech-ETH-Gavekal COVID-19 (March2020) - by Didier Darcet

COVID-19- The Power of NIMBY (March2020) - by Didier Darcet

Quarantine (February 2020) - by Didier Darcet

Hedge Funds: Oasis in View? (January 2020) - by Didier Darcet

Trade Rebound vs USD Shortage (December 2019) - by Didier Darcet

Antifragile Assets - Select Bonds or Gold (November 2019) - by Didier Darcet

Wealth Transfer to Emerging Markets (October 2019) - by Didier Darcet

Gold Is Money. Eveything Else Is Credit (September 2019) - by Didier Darcet

Is the USA Losing Momemtum? (August 2019) - by Didier Darcet

'Summer Body' for Equity Portfolios: Lose the Weight and Keep it Off! (July 2019) - by Didier Darcet

Best of the Cash and Equity Breed (June 2019) - by Didier Darcet

Lessons From Experience (May 2019) - by Didier Darcet

Asia First! (April 2019) - by Didier Darcet

Two Meanings of Risk (March 2019) - by Didier Darcet

The Broken Window Fallacy (February 2019) - by Didier Darcet

Mission Impossible (January 2019) - by Didier Darcet

Casino Roulette (December 2018) - by Didier Darcet

The Penultimate One (November 2018) - by Didier Darcet

Energy, Power, and the Price of Oil (October 2018) - by Didier Darcet

The Oxymoron of World Trade (September 2018) - by Didier Darcet

In TrackMacro, the Ordinal Rules (August 2018) - by Didier Darcet

Flashback (July 2018) - by Didier Darcet

The Bayesian Surprize (May 2018) - by Didier Darcet

Wisdom of Crowds-or Madness (April 2018) - by Didier Darcet

The Mirror Crack’d (March 2018) - by Didier Darcet

Al Stands for Amazing Intelligence! (August 2017) - by Didier Darcet

World Equity Risks in A One Shot View (February 2017) - by Didier Darcet

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