Publications: Gavekal Portfolio Solutions

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.

Critical Variance


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

Best of the Cash and Equity Breed (June 2019)

Lessons From Experience (May 2019)

Asia First! (April 2019)

Two Meanings of Risk (March 2019)

The Broken Window Fallacy (February 2019)

Mission Impossible (January 2019)

Casino Roulette (December 2018)

The Penultimate One (November 2018)

Energy, Power, and the Price of Oil (October 2018)

The Oxymoron of World Trade (September 2018)

In TrackMacro, the Ordinal Rules (August 2018)

Flashback (July 2018)

The Bayesian Surprize (May 2018)

Wisdom of Crowds-or Madness (April 2018)

The Mirror Crack’d (March 2018)

Al Stands for Amazing Intelligence! (August 2017)

World Equity Risks in A One Shot View (February 2017)

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