Meditations on Extremistan - Nassim Taleb

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The authors ran an in-person, proctored experiment inspired by a 2016 tweet from Nassim Nicholas Taleb– “If you give an investor the next day’s news 24 hours in advance he would go bust in less than a year.” The authors called the experiment “The Crystal Ball Challenge.” They gave 118 young adults trained in finance $50 each and the opportunity to grow that stake by trading in the 500 index and 30-year US Treasury bonds with the information on the front page of the Wall Street Journal (WSJ) one day in advance, but with stock and bond price data blacked out. The game covered 15 days, one day for each year from 2008 to 2022. Interested readers can play this game here: https://elmwealth.com/crystal-ball-challenge/ -- though without the pecuniary component. In sum, the players did not do very well. About half of them lost money, and one in six actually went bust. The average payout was just $51.62 (a gain of just 3.2%), which is statistically indistinguishable from breaking even. The poor results were a product of: 1) not guessing the direction of stocks and bonds very well, and 2) poor trade sizing. Many of the players used excessive leverage relative to their exhibited edge in guessing market direction.

To gain further understanding, the authors invited five experienced macro traders - four men, one woman - to play the game, with markedly better results. The group of five consisted of a head of trading at a top-five US bank, a founder of top-ten macro hedge fund, a senior trader at top-ten macro fund, a former senior government bond trader at top-three US primary dealer, and a former senior Jane Street trader. These players all finished with gains. On average, they grew their starting wealth by 130%, with a median gain of 60%. All of the players were selective and highly variable in their trade sizing. These veteran traders predicted the direction of the markets significantly better than the 118 younger, less experienced participants (63% vs 51.5%), but mostly the authors ascribe the dramatically different results to the much more sensible trade sizing displayed by the experienced traders. One conclusion of this experiment and article is that there is little value in a crystal ball without sensible trade-sizing.

Keywords: investment sizing, trade sizing, risk management, macro trading, forecasting, Merton share, Kelly Criterion, Investment Management, Trading Skill

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When a Crystal Ball Isn’t Enough to Make You Rich {quote}{quote} Source: https://papers.ssrn.com/sol3/papers....act_id=4965616 {image}

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{quote} So some standards after: {image}

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We have previously learned about the Kelly formula for optimal lot size; https://www.forexfactory.com/thread/...4#post15095884 {quote}{quote} Now, let's move on to the payout cycle if it can be achieved. In one month, there are typically 20 to 23 trading days, but the 23rd day is usually a holiday, so there are likely only 20 to 22 trading days. If divided into 3 cycles, the average would be 21 trading days, where the cycles could last for 7 days, 14 days or 21 days. The daily risk is as follows: • If a 7-day cycle is selected...

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We have previously learned about the Kelly formula for optimal lot size; https://www.forexfactory.com/thread/...4#post15095884 {quote}{quote} No one thinks that 3% per day or about 10:1 is an optimal size, but let's say 1% per day or 3.33:1 is still acceptable to many traders. Yet, that's just how it is. Now, let's move on to the payout cycle if it can be achieved. In one month, there are typically 20 to 23 trading days, but the 23rd day is usually a holiday, so there are likely only 20 to 22 trading days. If divided into 3 cycles,...

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(Especially) For FX Prop: We have previously learned about the Kelly formula for optimal lot size; https://www.forexfactory.com/thread/...4#post15095884 {quote}{quote} No one thinks that 3% per day or about 10:1 is an optimal size, but let's say 1% per day or 3.33:1 is still acceptable to many traders. Yet, that's just how it is. Now, let's move on to the payout cycle if it can be achieved. In one month, there are typically 20 to 23 trading days, but the 23rd day is usually a holiday, so there are likely only 20 to 22 trading...

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Ergodicity is a foundational concept in models of physical systems that include elements of randomness[1,2]. A physical observable is said to be ergodic if the average over its possible states, is the same as its average over time.

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Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To optimize wealth over time, agents should adapt their utility function according to the dynamical setting they face. Linear utility is optimal for additive dynamics, whereas logarithmic utility is optimal for multiplicative dynamics. Whether humans approximate time optimal behavior across different dynamics is unknown. Here we compare the effects of additive versus multiplicative gamble dynamics on risky choice. We show that utility functions are modulated by gamble dynamics in ways not explained by prevailing decision theories. Instead, as predicted by time optimality, risk aversion increases under multiplicative dynamics, distributing close to the values that maximize the time average growth of in-game wealth. We suggest that our findings motivate a need for explicitly grounding theories of decision-making on ergodic considerations.

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Logarithmic utility

Maximising the expected value of the logarithm of wealth is an established strategy in finance, where it is deployed as part of the Kelly criterion, a formula for sizing bets that leads almost surely to higher wealth compared to any other strategy, in the long run[19]. Though used in practice, it has not been empirically demonstrated whether subjects can naively intuit this strategy. The results of this experiment speak to the plausibility of this idea, insofar as they demonstrate that, at least in the subjects tested here, utility functions under multiplicative dynamics approximated logarithmic utility. Our main result, however, is not simply that logarithmic utility is a good approximation of behavior under multiplicative dynamics, but rather that risk preferences change from ~log utility to ~linear utility, as predicted if agents are maximising time average growth. In effect, ergodic theory can be thought of as providing a generalization of the Kelly criterion by generalising it to a larger class of optimisation behaviors, only two of which we test here. To verify that log utility is time optimal for multiplicative dynamics in this experimental design, we refer the reader to Fig 1G, which shows that with repetitions of this exact experiment, wealth grows fastest for the agent with log utility. The equivalent demonstration for additive dynamics and linear utility is evident in Fig 1F.

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GDP per capita PPP (current international $) {quote} Source: https://www.imf.org/external/datamap...ADVEC/WEOWORLD {image} {file}

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The concept of "cancer clusters" and randomness in patterns is discussed by Nassim Taleb in his works, especially in "Fooled by Randomness" a. Taleb uses the analogy of darts thrown randomly on a board to explain how people can misinterpret randomness as meaningful patterns, such as cancer clusters.

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Average Daily Range (ADR) is a metric used in trading to measure the average movement of a financial instrument (such as a stock, forex pair, or commodity) within a single trading day. It helps traders understand the typical volatility of an asset and can be useful for setting profit targets, stop losses, and identifying potential trading opportunities.

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Average True Range (ATR) is a technical indicator that measures the volatility of a financial instrument by calculating the average of the True Range (TR) over a specified period. Unlike the Average Daily Range (ADR), which only considers the high and low of the day, ATR takes into account gaps between closing prices from previous periods, making it a more comprehensive measure of volatility.