Drafts by Nassim Nicholas Taleb
his note corrects Falconer's formula, to account for stochastic --and potentially changing-- envi... more his note corrects Falconer's formula, to account for stochastic --and potentially changing-- environments.
Our probabilistic representation can be generalized to formalize some of the observations in the medical fields; for instance diabetes, cancer, and cardiovascular disease are deemed both heritable and environment dependent but such effects, while casually mentioned, have not been rigorously and quantitatively uncoupled in the research literature.
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The central decision for a pension fund is the allocation between stocks and bonds, often relying... more The central decision for a pension fund is the allocation between stocks and bonds, often relying, for intellectual backup, on metrics and methods from Modern Portfolio Theory (MPT). We show how, historically, such an "optimal" portfolio is in effect the least optimal one, as it fails to protect against tail risk and under-allocates to the high-returning asset class. MPT fails in both risk control and real-world investment optimization.
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Issues in Science and Technology, 2015
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This discussion applies quantitative finance methods and economic arguments to cryptocurrencies i... more This discussion applies quantitative finance methods and economic arguments to cryptocurrencies in general and bitcoin in particular ---as there are about $10,000$ cryptocurrencies, we focus (unless otherwise specified) on the most discussed crypto of those that claim to hue to the original protocol \cite{nakamoto2009bitcoin} and the one with, by far, the largest market capitalization.
In its current version, in spite of the hype, bitcoin failed to satisfy the notion of "currency without government" (it proved to not even be a currency at all), can be neither a short or long term store of value (its expected value is no higher than $0$), cannot operate as a reliable inflation hedge, and, worst of all, does not constitute, not even remotely, safe haven for one's investments, shield against government tyranny, or tail protection vehicle for catastrophic episodes.
Furthermore, there appears to be an underlying conflation between the success of a payment mechanism (as decentralized mode of exchange), which so far has failed, and the speculative variations in the price of a zero-sum asset with massive negative externalities.
Going through monetary history, we also show how a true numeraire must be one of minimum variance with respect to an arbitrary basket of goods and services, how gold and silver lost their inflation hedge status during the Hunt brothers squeeze in the late 1970s and what would be required from a true inflation hedged store of value.
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The Lindy effect (or law) has been investigated through various traditions. In short it correspon... more The Lindy effect (or law) has been investigated through various traditions. In short it corresponds to situations where the conditional expectation of additional life expectancy increases with time, which requires the survival function of survival time to be that of a power law.
This maps to a declining force of mortality under the standard hazard rate representation. Here we model it as the exit time of a stochastic process (arithmetic) with drift µ and show how the force of mortality behaves with respect to the distance from absorption. We show that, while a process with a drift µ = 0 produces a Lindy survival function, any amount of negative drift makes it exit that class.
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We discuss common errors and fallacies when using naive "evidence based" empiricism and point for... more We discuss common errors and fallacies when using naive "evidence based" empiricism and point forecasts for fat-tailed variables, as well as the insufficiency of using naive first-order scientific methods for tail risk management. We use the COVID-19 pandemic as the background for the discussion and as an example of a phenomenon characterized by a multiplicative nature, and what mitigating policies must result from the statistical properties and associated risks. In doing so, we also respond to the points raised by Ioannidis et al.(2020)
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Uncertainty on an exponential rate translates into higher estimates for outcomes. If r is the ave... more Uncertainty on an exponential rate translates into higher estimates for outcomes. If r is the average exponential growth rate of the fatalities , and X the number of fatalities, and r is stochastic, errors on r map to monstrously huge errors on X, to the point that uncertainty on r translates into considerably higher values for X.
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Using methods from extreme value theory, we examine the major pandemics in history, trying to und... more Using methods from extreme value theory, we examine the major pandemics in history, trying to understand their tail properties. Applying the shadow distribution approach developed by the authors for violent conflicts [5], we provide rough estimates for quantities not immediately observable in the data. Epidemics and pandemics are extremely heavy-tailed, with a potential existential risk for humanity. This property should override conclusions derived from local epidemiological models in what relates to tail events.
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Problems with Ferguson et al, owing to scaling and granularity.
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Using the metadistribution of possible distributions for a given measure, we define a condition u... more Using the metadistribution of possible distributions for a given measure, we define a condition under which it is possible to make a decision based on the observation of random variable, which we call "statistical decidability".
We provide a sufficient condition on the metadistribution for the decision to be "statistically decidable" and conjec- ture that decisions based on a metadistribution with non compact support are always "statistically undecidable".
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Explaining the Precautionary Principle and the need for overreaction under certain classes of mul... more Explaining the Precautionary Principle and the need for overreaction under certain classes of multiplicative systemic risk.
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Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden ... more Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of n. Using extreme value theory, we examine the properties of the hidden tail and calculate its moments of order p.
The method is useful in showing how large a bias one can expect, for a given n, between the visible in-sample mean and the true statistical mean (or higher moments), which is considerable for alpha close to 1.
Among other properties, we note that the "hidden" moment of order 0, that is, the exceedance probability for power law distributions, follows an exponential distribution and has for expectation 1/n regardless of the parametrization of the scale and tail index.
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We discuss the inadequacy of covariances/correlations and other measures in L-2 as relative dista... more We discuss the inadequacy of covariances/correlations and other measures in L-2 as relative distance metrics. We propose a computationally simple heuristic to transform a map based on standard principal component analysis (PCA) (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information.
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We present consequential mistakes in uses of correlation in social science research, particularly... more We present consequential mistakes in uses of correlation in social science research, particularly psychology
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We build a heuristic that takes a given option price in the tails with strike K and extends (for ... more We build a heuristic that takes a given option price in the tails with strike K and extends (for calls, all strikes > K, for put all strikes < K) assuming the continuation falls into what we define as "Karamata Constant" over which the strong Pareto law holds. The heuristic produces relative prices for options, with for sole parameter the tail index α under some mild arbitrage constraints.
Usual restrictions such as finiteness of variance are not required.
The heuristic allows us to scrutinize the volatility surface and test theories of tail option mispricing and overpricing usually built on thin tailed models and modification of the Black-Scholes formula.
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What do binary (or probabilistic) forecasting abilities have to do with overall performance? We ... more What do binary (or probabilistic) forecasting abilities have to do with overall performance? We map the difference between (univariate) binary predictions, bets and "beliefs" (expressed as a specific "event" will happen/will not happen) and real-world continuous payoffs (numerical benefits or harm from an event) and show the effect of their conflation and mischaracterization in the decision-science literature. We also examine the differences under thin and fat tails. The effects are:
A- Spuriousness of psychological results} particularly those documenting that humans overestimate tail probabilities and rare events, or that they overreact to fears of market crashes, ecological calamities, etc. Many perceived "biases" are just mischaracterizations by psychologists. There is also a misuse of Hayekian arguments in promoting prediction markets.
B- Being a "good forecaster" in binary space doesn't lead to having a good performance}, and vice versa, especially under nonlinearities. A binary forecasting record is likely to be a reverse indicator under some classes of distributions. Deeper uncertainty or more complicated and realistic probability distribution worsen the conflation .
C- Machine Learning:} Some nonlinear payoff functions, while not lending themselves to verbalistic expressions and "forecasts", are well captured by ML or expressed in option contracts.
D- Fattailedness:The difference is exacerbated in the power law classes of probability distributions.
The appendix shows the mathematical properties and exact distribution of the various payoffs, along with an exact distribution for the Brier score helpful for significance testing and sample sufficiency.
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Most of the tension resides between
1) Embedded, complexity-minded, multiscale/fractal localis... more Most of the tension resides between
1) Embedded, complexity-minded, multiscale/fractal localism (politics as an ecology/complex adaptive system),
and
2) Abstract one-dimensional universalists and monoculturalism (politics as a top-down engineering project).
We go beyond the verbalism; we rely on information theory, complexity theory, uncertainty approaches (say fragility), and probabilistic rigor to look at politics with the same eyes as we examine highly dimensional interactive elements such as nature, biological systems, internet networks, and medical issues.
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Expression of the error rate for the four populations test.
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—We examine random variables in the power law/slowly varying class with stochastic tail exponent,... more —We examine random variables in the power law/slowly varying class with stochastic tail exponent, the exponent α having its own distribution. We show the effect of stochasticity of α on the expectation and higher moments of the random variable. For instance, the moments of a right-tailed or right-asymmetric variable, when finite, increase with the variance of α; those of a left-asymmetric one decreases. The same applies to conditional shortfall (CVar), or mean-excess functions. We prove the general case and examine the specific situation of lognormally distributed α ∈ [b, ∞), b > 1. The stochasticity of the exponent induces a significant bias in the estimation of the mean and higher moments in the presence of data uncertainty. This has consequences on sampling error as uncertainty about α translates into a higher expected mean. The bias is conserved under summation, even upon large enough a number of summands to warrant convergence to the stable distribution. We establish inequalities related to the asymmetry. We also consider the situation of capped power laws (i.e. with compact support), and apply it to the study of violence by Cirillo and Taleb (2016). We show that uncertainty concerning the historical data increases the true mean.
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Papers by Nassim Nicholas Taleb
The Philosopher's Magazine
Scalability converts qualitative statements into quantitative ones. Without an adequate understan... more Scalability converts qualitative statements into quantitative ones. Without an adequate understanding of scalability, a system of ethics is incomplete, at best.
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Drafts by Nassim Nicholas Taleb
Our probabilistic representation can be generalized to formalize some of the observations in the medical fields; for instance diabetes, cancer, and cardiovascular disease are deemed both heritable and environment dependent but such effects, while casually mentioned, have not been rigorously and quantitatively uncoupled in the research literature.
In its current version, in spite of the hype, bitcoin failed to satisfy the notion of "currency without government" (it proved to not even be a currency at all), can be neither a short or long term store of value (its expected value is no higher than $0$), cannot operate as a reliable inflation hedge, and, worst of all, does not constitute, not even remotely, safe haven for one's investments, shield against government tyranny, or tail protection vehicle for catastrophic episodes.
Furthermore, there appears to be an underlying conflation between the success of a payment mechanism (as decentralized mode of exchange), which so far has failed, and the speculative variations in the price of a zero-sum asset with massive negative externalities.
Going through monetary history, we also show how a true numeraire must be one of minimum variance with respect to an arbitrary basket of goods and services, how gold and silver lost their inflation hedge status during the Hunt brothers squeeze in the late 1970s and what would be required from a true inflation hedged store of value.
This maps to a declining force of mortality under the standard hazard rate representation. Here we model it as the exit time of a stochastic process (arithmetic) with drift µ and show how the force of mortality behaves with respect to the distance from absorption. We show that, while a process with a drift µ = 0 produces a Lindy survival function, any amount of negative drift makes it exit that class.
We provide a sufficient condition on the metadistribution for the decision to be "statistically decidable" and conjec- ture that decisions based on a metadistribution with non compact support are always "statistically undecidable".
The method is useful in showing how large a bias one can expect, for a given n, between the visible in-sample mean and the true statistical mean (or higher moments), which is considerable for alpha close to 1.
Among other properties, we note that the "hidden" moment of order 0, that is, the exceedance probability for power law distributions, follows an exponential distribution and has for expectation 1/n regardless of the parametrization of the scale and tail index.
Usual restrictions such as finiteness of variance are not required.
The heuristic allows us to scrutinize the volatility surface and test theories of tail option mispricing and overpricing usually built on thin tailed models and modification of the Black-Scholes formula.
A- Spuriousness of psychological results} particularly those documenting that humans overestimate tail probabilities and rare events, or that they overreact to fears of market crashes, ecological calamities, etc. Many perceived "biases" are just mischaracterizations by psychologists. There is also a misuse of Hayekian arguments in promoting prediction markets.
B- Being a "good forecaster" in binary space doesn't lead to having a good performance}, and vice versa, especially under nonlinearities. A binary forecasting record is likely to be a reverse indicator under some classes of distributions. Deeper uncertainty or more complicated and realistic probability distribution worsen the conflation .
C- Machine Learning:} Some nonlinear payoff functions, while not lending themselves to verbalistic expressions and "forecasts", are well captured by ML or expressed in option contracts.
D- Fattailedness:The difference is exacerbated in the power law classes of probability distributions.
The appendix shows the mathematical properties and exact distribution of the various payoffs, along with an exact distribution for the Brier score helpful for significance testing and sample sufficiency.
1) Embedded, complexity-minded, multiscale/fractal localism (politics as an ecology/complex adaptive system),
and
2) Abstract one-dimensional universalists and monoculturalism (politics as a top-down engineering project).
We go beyond the verbalism; we rely on information theory, complexity theory, uncertainty approaches (say fragility), and probabilistic rigor to look at politics with the same eyes as we examine highly dimensional interactive elements such as nature, biological systems, internet networks, and medical issues.
Papers by Nassim Nicholas Taleb
Our probabilistic representation can be generalized to formalize some of the observations in the medical fields; for instance diabetes, cancer, and cardiovascular disease are deemed both heritable and environment dependent but such effects, while casually mentioned, have not been rigorously and quantitatively uncoupled in the research literature.
In its current version, in spite of the hype, bitcoin failed to satisfy the notion of "currency without government" (it proved to not even be a currency at all), can be neither a short or long term store of value (its expected value is no higher than $0$), cannot operate as a reliable inflation hedge, and, worst of all, does not constitute, not even remotely, safe haven for one's investments, shield against government tyranny, or tail protection vehicle for catastrophic episodes.
Furthermore, there appears to be an underlying conflation between the success of a payment mechanism (as decentralized mode of exchange), which so far has failed, and the speculative variations in the price of a zero-sum asset with massive negative externalities.
Going through monetary history, we also show how a true numeraire must be one of minimum variance with respect to an arbitrary basket of goods and services, how gold and silver lost their inflation hedge status during the Hunt brothers squeeze in the late 1970s and what would be required from a true inflation hedged store of value.
This maps to a declining force of mortality under the standard hazard rate representation. Here we model it as the exit time of a stochastic process (arithmetic) with drift µ and show how the force of mortality behaves with respect to the distance from absorption. We show that, while a process with a drift µ = 0 produces a Lindy survival function, any amount of negative drift makes it exit that class.
We provide a sufficient condition on the metadistribution for the decision to be "statistically decidable" and conjec- ture that decisions based on a metadistribution with non compact support are always "statistically undecidable".
The method is useful in showing how large a bias one can expect, for a given n, between the visible in-sample mean and the true statistical mean (or higher moments), which is considerable for alpha close to 1.
Among other properties, we note that the "hidden" moment of order 0, that is, the exceedance probability for power law distributions, follows an exponential distribution and has for expectation 1/n regardless of the parametrization of the scale and tail index.
Usual restrictions such as finiteness of variance are not required.
The heuristic allows us to scrutinize the volatility surface and test theories of tail option mispricing and overpricing usually built on thin tailed models and modification of the Black-Scholes formula.
A- Spuriousness of psychological results} particularly those documenting that humans overestimate tail probabilities and rare events, or that they overreact to fears of market crashes, ecological calamities, etc. Many perceived "biases" are just mischaracterizations by psychologists. There is also a misuse of Hayekian arguments in promoting prediction markets.
B- Being a "good forecaster" in binary space doesn't lead to having a good performance}, and vice versa, especially under nonlinearities. A binary forecasting record is likely to be a reverse indicator under some classes of distributions. Deeper uncertainty or more complicated and realistic probability distribution worsen the conflation .
C- Machine Learning:} Some nonlinear payoff functions, while not lending themselves to verbalistic expressions and "forecasts", are well captured by ML or expressed in option contracts.
D- Fattailedness:The difference is exacerbated in the power law classes of probability distributions.
The appendix shows the mathematical properties and exact distribution of the various payoffs, along with an exact distribution for the Brier score helpful for significance testing and sample sufficiency.
1) Embedded, complexity-minded, multiscale/fractal localism (politics as an ecology/complex adaptive system),
and
2) Abstract one-dimensional universalists and monoculturalism (politics as a top-down engineering project).
We go beyond the verbalism; we rely on information theory, complexity theory, uncertainty approaches (say fragility), and probabilistic rigor to look at politics with the same eyes as we examine highly dimensional interactive elements such as nature, biological systems, internet networks, and medical issues.
Many mechanisms have been used to show the emergence of fat tails. Here we follow an alternative route, the epistemological one, using counterfactual analysis, and show how nested uncertainty, that is, errors on the error in estimation of parameters, lead to fattailedness of the distribution.
The results have relevant implications for forecasting, dealing with model risk and generally all statistical analyses. The more interesting results are as follows:
\begin{itemize}
\item The forecasting paradox: The future is fatter tailed than the past. Further, out of sample results should be fatter tailed than in-sample ones.
\item Errors on errors can be explosive or implosive with different consequences. Infinite recursions can be easily dealt with, pending on the structure of the errors.
\end{itemize}
We also present a method to perform counterfactual analysis without the explosion of branching counterfactuals.
PUBLISHED IN "PROCEEDINGS OF THE NOBEL SYMPOSIUM", NOBEL COMMISSION.
P-values are shown to be extremely skewed and volatile, regardless of the sample size n, and vary greatly across repetitions of exactly same protocols under identical stochastic copies of the phenomenon; such volatility makes the minimum p value diverge significantly from the "true" one. Setting the power is shown to offer little remedy unless sample size is increased markedly or the p-value is lowered by at least one order of magnitude.
The formulas allow the investigation of the stability of the reproduction of results and "p-hacking" and other aspects of meta-analysis.
From a probabilistic standpoint, neither a p-value of .05 nor a "power" at .9 appear to make the slightest sense.