We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which invest…
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48 results for “drawdown distributions”
Probability distribution of drawdowns in risky investmentscond-mat.stat-mech
We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investor's risk attitude, thus his risk exposure, we find that the distribution of these drawdowns follows a general power law. In particular, if the risk exposure is Kelly-optimal, the expo…
Bayesian analysis optimizes stop-loss thresholds based on drawdown distributions.
problem Arbitrary stop-loss levels in financial strategies.
method Bayesian analysis of drawdown distributions.
result Systematic selection of optimal stop-loss thresholds.
Drawdowns measuring the decline in value from the historical running maxima over a given period of time, are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focus on the side of severity by studying the first drawdown over certain pre-specified size. In th…
On the maximum drawdown during speculative bubblesphysics.data-an
A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with respect to the bulk of drawdown price movement distribution. This paper goes on dee…
Risk-Constrained Kelly Gamblingq-fin.PM
Develops a method to manage drawdown risk in Kelly gambling.
problem Managing drawdown risk in Kelly gambling with uncertain outcomes.
method Develops a convex optimization problem to bound drawdown probability, trading off growth rate and risk.
result Shows that the convex optimization method outperforms fractional-Kelly bets for the same drawdown risk level or growth rate.
Generalized Expected Discounted Penalty Function at General Drawdown for Lévy Risk Processesq-fin.PR
The paper studies drawdown times in Lévy risk processes, generalizing previous results.
problem Analyzing the time of drawdown in spectrally negative Lévy risk processes.
method Using the joint distribution of drawdown times, maximums, and other related quantities.
result Obtained semi-explicit expressions for the joint distribution in terms of scale functions and Lévy measure.
The paper quantifies when a trading strategy's drawdown becomes a cause for concern.
problem Detecting when a profitable trading strategy starts to degrade over time.
method Quantitative analysis of drawdown length and depth for upward drifting Brownian motions.
result Drawdowns lasting too long or being too deep indicate a need to revise the strategy's Sharpe ratio.
Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum dr…
Study portfolio optimization with partial info and drawdown constraints using deep learning.
problem Optimizing portfolios with partial information and maximum drawdown constraints.
method Bayesian framework, dynamic programming, semi-explicit solutions, deep learning for stochastic control.
result Numerical solutions and performance analysis with deep learning, convergence to Merton problem.
Leptokurtic Portfolio Theoryphysics.soc-ph
The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurti…
New method generates realistic financial price paths with drawdowns.
problem Lack of realistic drawdown scenarios in financial simulations.
method Variational autoencoder with drawdown reconstruction loss and path signatures.
result Simulated paths closely match empirical drawdown data.
This paper studies the stochastic modeling of market drawdown events and the fair valuation of insurance contracts based on drawdowns. We model the asset drawdown process as the current relative distance from the historical maximum of the asset value. We first consider a vanilla insurance contract whereby the protectio…
The paper optimizes portfolios to minimize drawdown, outperforming market indices.
problem Minimizing drawdown in financial portfolios.
method Formulated as a nonlinear program, partially linearized, solved using SCIP.
result Minimal drawdown portfolios outperform market indices in return, Sharpe ratio, maximum and average drawdown.
Paper adds a restart mechanism to a drawdown control policy for better trading performance.
problem Missed profitable opportunities when drawdown limit is close to reality.
method Integrates a data-driven restart mechanism into the drawdown modulation trading system.
result The restart mechanism improves trading performance even with transaction costs.
New control strategy mitigates stock trading drawdowns.
problem Mitigating drawdowns in stock trading.
method Drawdown-modulated feedback control using control theory.
result Optimal investment strategy that maximizes logarithmic growth.
This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …
Develops a new framework for drawdown risk beyond Gaussian assumptions.
problem Understanding drawdowns in systematic trading strategies.
method Monte-Carlo simulation, non-Gaussian extensions, fractional Brownian motion.
result Drawdowns and related measures vary differently under non-Gaussian assumptions.
Fair valuation of Lévy-type drawdown-drawup contracts with general insured and penalty functionsq-fin.PR
The paper calculates fair premiums and optimal stopping rules for equity-linked contracts tied to drawdown and drawup events.
problem Fair valuation of equity-linked contracts tied to drawdown and drawup events.
method Fluctuation theory of Lévy processes and optimal stopping theory.
result Calculation of fair premiums and optimal stopping rules for equity-linked contracts.
Modeling Maximum drawdown Records with Piecewise Deterministic Markov Processe in Capital Marketsq-fin.RM
Modeling maximum drawdown records in capital markets using PDMP.
problem Capturing the statistical properties of maximum drawdown records in financial markets.
method Piecewise Deterministic Markov Process (PDMP) for modeling, statistical analysis of mean and variance, simulation study, parameter estimation techniques.
result Derivation of statistical results including mean and variance of maximum drawdown records.
Paper improves fractional trading for risk-averse investors by considering current drawdowns.
problem Optimizing trading strategies for risk-averse investors.
method Reconsidered fractional trading ansatz with current drawdown risk measure.
result Optimal fraction solutions better reflect risk-averse investor needs.
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
Unified approach for drawdown and drawup of Markov processes.
problem Study of drawdown and drawup in time-homogeneous Markov processes.
method Short-time pathwise analysis, integral equation solution.
result Unified approach to study various drawdown quantities.
The paper calculates premiums and optimal stopping rules for insurance contracts with Lévy assets.
problem Calculating fair premiums and optimal stopping rules for insurance contracts with Lévy assets.
method Solving two-sided exit problems related to drawdown and drawup of spectrally negative Lévy processes, and optimal stopping theory.
result Fair premiums and optimal stopping rules identified for various insurance contracts.
Paper builds risk measures for portfolio theory, focusing on drawdown risk.
problem Calculating efficient portfolios with drawdown risk constraints.
method Develops convex risk measures for portfolio theory, including drawdown-based measures.
result Calculates efficient portfolios using drawdown risk constraints.
Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial modelq-fin.PM
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We wor…
Unified framework for drawdown risk computation under Markov models.
problem High computational challenges in drawdown risk metrics.
method Unified framework for computing five drawdown quantities under general Markov models, using linear systems and efficient algorithms.
result Efficient algorithms achieve same complexity as path-independent problems, validated by rigorous convergence analysis and extensive experiments.
In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…
The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distrib…
Study optimizes portfolio to minimize relative drawdown duration, penalizing unfavorable performance states.
problem Minimizing relative drawdown duration in portfolio optimization relative to a benchmark.
method Introduces a benchmark-relative drawdown-duration criterion penalizing unfavorable performance states. Uses a one-dimensional Markovian representation and Hamilton-Jacobi-Bellman equation.
result Derives explicit projection-based characterization of the optimal feedback control and identifies geometric settings for unique strong solutions.
Paper calculates perpetual put option pricing with drawdown cap.
problem Pricing perpetual American put options with drawdown constraints.
method Derives explicit formula using Black-Scholes model and martingale theory.
result Optimal exercise occurs at first drawdown below a threshold.
Investors with anxiety about drawdowns may use stop-loss and trailing stops as optimal selling strategies.
problem Investors' anxiety about drawdowns affects optimal selling strategies.
method Mathematical analysis of optimal stopping with random discounting.
result Stop-loss and trailing stops can be optimal selling strategies under anxiety about drawdowns.
Endogenous versus Exogenous Crashes in Financial Marketscond-mat.stat-mech
We perform an extended analysis of the distribution of drawdowns in the two leading exchange markets (US dollar against the Deutsmark and against the Yen), in the major world stock markets, in the U.S. and Japanese bond market and in the gold market, by introducing the concept of ``coarse-grained drawdowns,'' which all…
This paper shows Markowitz-style strategies are inefficient when considering drawdown risk.
problem Inefficiency of Markowitz-style investment strategies in recursive betting scenarios.
method Use of drawdown as risk metric, time-varying linear feedback block K(k) called the drawdown modulator.
result Classical Markowitz-style strategies are inefficient when considering drawdown risk.
The study characterizes honest times and extends semimartingale class for option pricing.
problem Characterizing honest times and extending semimartingale class for option pricing.
method Characterization of honest times using drawdown and relative drawdown representations, extending semimartingale class to include jumps.
result Established Madan-Roynette-Yor option pricing formula for a broader class of processes.
The field of risk theory has traditionally focused on ruin-related quantities. In particular, the socalled Expected Discounted Penalty Function has been the object of a thorough study over the years. Although interesting in their own right, ruin related quantities do not seem to capture path-dependent properties of the…
Optimal dividend strategy with constraints on drawdown and ratcheting rates.
problem Maximizing discounted utility of dividends until bankruptcy with drawdown and ratcheting constraints.
method Formulated as a stochastic control problem, solved via Hamilton-Jacobi-Bellman variational inequality.
result Optimal dividend rate depends on current surplus and historical maximum of dividend rate, with specific rules for different surplus levels.
Paper calculates perpetual American put option pricing with drawdown event in Lévy market.
problem Pricing perpetual American put options with a drawdown event in a Lévy market.
method Derives explicit price using geometric Lévy process with downward jumps, optimal stopping rule, and martingale arguments.
result Optimal stopping rule is the first time asset price falls below a specific value.
The study identifies factors predicting stock returns and maximum drawdown using various models.
problem Predicting stock returns and maximum drawdown in the US equity market.
method Supervised learning with multiple models (OLS, penalized linear regressions, tree-based models, neural networks) over 49 years of data.
result Non-linear models outperformed linear models in predicting stock returns and maximum drawdown, especially during calm periods.
A modular cash-overlay rule for allocating between a fixed growth-defensive risky sleeve and interest-bearing cash.
problem Drawdown control
method Continuous cash-overlay filters
result Earnings an 18.83% CAGR versus 16.62% for 100% R
We study the class of Azéma-Yor processes defined from a general semimartingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. Solutions of the latter have the drawdown…
We determine the optimal amount to invest in a Black-Scholes financial market for an individual who consumes at a rate equal to a constant proportion of her wealth and who wishes to minimize the expected time that her wealth spends in drawdown during her lifetime. Drawdown occurs when wealth is less than some fixed pro…
We consider the portfolio choice problem for a long-run investor in a general continuous semimartingale model. We suggest to use path-wise growth optimality as the decision criterion and encode preferences through restrictions on the class of admissible wealth processes. Specifically, the investor is only interested in…
Investors optimize their portfolios to maximize utility under drawdown constraints and stochastic volatility.
problem Maximizing utility relative to maximum performance under drawdown constraints and stochastic volatility.
method Approximations through coefficient expansion and nonlinear transformations, numerically computed.
result Investors need a different portfolio strategy in stochastic volatility compared to constant volatility.
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
Parisian excursion below a fixed level from the last record maximum of Levy insurance risk processmath.PR
This paper studies Parisian ruin in insurance risk processes below a fixed level from the last record maximum.
problem Parisian ruin in insurance risk processes below a fixed level from the last record maximum.
method Using recent developments on fluctuation theory of drawdown of spectrally negative Levy process, the paper presents identities for the law of ruin-time and the position at ruin.
result Identities for the law of ruin-time and the position at ruin are given in terms of their joint Laplace transforms.
Optimal dividend payout strategies with drawdown constraint identified.
problem Optimal dividend payout strategies under a drawdown constraint.
method Solving a two-dimensional optimal control problem using viscosity solutions and calculus of variations.
result A two-curve strategy is optimal for sufficiently large initial and maximum dividend rates, with a surprising limit result for large maximum dividend rates.
New f-Betas for portfolio optimization using f-divergence risk measures.
problem Optimizing portfolio performance under varying market conditions.
method Derive f-Betas and Hellinger-Betas, using f-divergence risk measures.
result Demonstrated new Beta metrics provide better performance under stress.