The paper finds the normal distribution unsuitable for modeling daily stock returns and suggests using the Laplace distribution instead.
problem The difficulty in modeling the distribution of daily stock returns, especially for extreme outliers.
method Investigation of daily stock returns of major indices using both normal and Laplace distributions.
result The normal distribution is not a good model for stock returns, even over long periods of data.
Adapts Roy's criterion for non-normal returns using Cornish Fisher expansion.
problem Selecting one risky asset from many when returns are non-normal.
method Adapts Roy's criterion via Cornish Fisher expansion for non-normal returns.
result Investment objective consistent with first order stochastic dominance, equal to Sharpe ratio for normal returns.
Study finds spin model returns align with normal distribution.
problem Understanding return dynamics in financial markets.
method Calculated realized volatility and examined standardized returns.
result Moments of standardized returns match theoretical values.
The vector of periodic, compound returns of a typical investment portfolio is almost never a convex combination of the return vectors of the securities in the portfolio. As a result the ex post version of Harry Markowitz's "standard mean-variance portfolio selection model" does not apply to compound return data. We pro…
The thesis models financial returns using mixtures of generalized normal distributions.
problem Estimation issues in financial return analysis.
method Mixtures of generalized normal distributions (MGND), ECM/GEM algorithms, constrained mixture models (CMGND), GND-HMMs.
result Enhanced accuracy and interpretability in financial return modeling.
Study resolves the Korean LVRP puzzle by showing HVRP exists but is masked by investor heterogeneity and improper intensity normalization.
problem Puzzling Low Volume Return Premium (LVRP) in Korea, contradicting global High Volume Return Premium (HVRP) evidence.
method Used Korean market data (2020-2024) to demonstrate HVRP exists but is masked by investor heterogeneity and improper intensity normalization. Normalized institutional buying intensity by market capitalization rather than trading value.
result Demonstrated a perfect monotonic relationship between highest-conviction institutional buying and positive cumulative abnormal returns, while lowest-intensity trades yield modest returns.
Proposes a method to model financial returns with extreme shocks using flexible tail transformations.
problem Capturing extreme shocks in financial return data.
method Introduces a transformation layer in normalizing flows to model heavy-tailed distributions.
result Trained models can generate synthetic sets of extreme returns.
Derives an approximate solution for power utility optimization under predictable returns.
problem Optimizing portfolios with power utility functions under predictable returns.
method Approximate analytical solution using multivariate normal distribution and gradient descent algorithm.
result Gradient descent method provides a viable alternative to Taylor series expansion for portfolio optimization.
The study explains stock return distributions using reaction functions.
problem Stock return distributions often deviate from normal distributions.
method Assumes normal event/information effects, financial over/underreaction, proposes reaction function model.
result Financial markets often underreact to minor events, overreact to significant ones, and react stronger to positive events.
Paper optimizes international portfolios with new copula-based scenario generation.
problem Optimizing international portfolios with realistic uncertainty models.
method Two-stage stochastic model, regular-vine copula for scenario generation, including transaction costs.
result Proposed method yields better risk-return portfolios than standard approaches.
We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of non-stationary correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains…
Model for equity trading with asynchronous price updates converging to a stationary return distribution.
problem Equity trading dynamics with asynchronous price updates and varying number of participants.
method Modeling agents' adaptive strategies and using numerical simulations to analyze returns.
result The model converges to a stationary return distribution, with mean returns influenced by adaptive mechanisms and agent interactions.
The paper improves asset allocation using a skew-normal distribution in the Black-Litterman model.
problem Improving asset allocation under skewed return distributions.
method Using the Black-Litterman model with hidden truncation skew-normal distribution and Simaan's three-moment risk model.
result Optimal portfolios have less risk and higher skewness compared to classical BL model.
Estimates returns for dollar cost averaging using geometric Brownian motion.
problem Estimating returns for dollar cost averaging investing strategy.
method Uses geometric Brownian motion and log-Normal distribution to construct a lower bound for returns. Computes parameters recursively and in closed form for dollar cost averaging. Compares to lump sum investing for matching wealth distributions.
result Probability of negative returns is less than 2.5% for 40 years of annual dollar cost averaging.
Study examines volatility of Nikkei Stock Average, finding returns follow a Gaussian process.
problem Analyzing volatility of Nikkei Stock Average on Tokyo Stock Exchange.
method Calculated realized volatility in morning and afternoon sessions, investigating return dynamics.
result Return dynamics of Nikkei Stock Average are consistent with Gaussian distribution.
In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-…
The paper models stock returns using q-Gaussians and negative binomials.
problem Modeling stock return distributions and pricing options.
method Proposes a generalized jump-diffusion model and uses q-Gaussians and negative binomial distributions. result An explicit option pricing formula is derived.
ReVol normalizes stock price features to mitigate distribution shifts, improving prediction accuracy.
problem Distribution shifts in stock price data hinder accurate prediction.
method ReVol uses normalization, attention-based estimation, and geometric Brownian motion.
result ReVol achieves an average improvement of more than 0.03 in IC and over 0.7 in SR.
We study the dependence structure of market states by estimating empirical pairwise copulas of daily stock returns. We consider both original returns, which exhibit time-varying trends and volatilities, as well as locally normalized ones, where the non-stationarity has been removed. The empirical pairwise copula for ea…
The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student's t-distribution, which we call a …
The study identifies and analyzes different market regimes in equity markets using advanced signal processing techniques.
problem Understanding and quantifying the dynamics of different market regimes in equity markets.
method Data-driven Hilbert--Huang Transform for regime identification, Holo--Hilbert Spectral Analysis for profiling, and Variable-Length Markov Chains for return dynamics modeling.
result Developed markets normalize more effectively as stress subsides, while developing markets retain residual tail dependence and downside persistence.
A new model forecasts Value-at-Risk using NIG distribution and dynamic scores.
problem Forecasting Value-at-Risk (VaR) in financial markets.
method Proposes a parametric forecasting model based on the normal inverse Gaussian distribution (NIG) incorporating intraday information.
result The model outperforms traditional GARCH models, especially in high-risk scenarios.
We compute the analytic expression of the probability distributions F{AEX,+} and F{AEX,-} of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the αre-scaled AEX daily index positive returns r(t)^αand negative returns (-r(t))^αthat we call, after normalization, the …
Optimizes cryptocurrency portfolios using MNTS GARCH model.
problem Optimizing cryptocurrency portfolios with non-Gaussian return dynamics.
method Multivariate normal tempered stable (MNTS) GARCH model for non-Gaussian returns, Foster-Hart risk optimization.
result Foster-Hart optimization yields a more profitable portfolio with better risk-return balance.
New optimal portfolios derived for power and logarithmic utilities under log-normal returns.
problem Optimal portfolio weights for power and logarithmic utilities under log-normal returns.
method Closed-form expressions derived for optimal portfolio weights, proving mean-variance efficiency.
result Both optimal portfolios are mean-variance efficient and belong to the feasible set.
The Sharpe ratio, which is defined as the ratio of the excess expected return of an investment to its standard deviation, has been widely cited in the financial literature by researchers and practitioners. However, very little attention has been paid to the statistical properties of the estimation of the ratio. Lo (200…
Starting from an exact relationship between news, threshold and price return distributions in the stationary state, I discuss the ability of the Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under normal conditions, this model is not able to transform Gaussian news into fat-tailed price retu…
Proposes a new volatility measure for LETFs.
problem Leveraged Exchange Traded Funds (LETFs) returns do not follow normal distribution and independence.
method Introduces Shortfall from Maximum Convexity (SMC) as a new measure of realized volatility.
result SMC provides a more intuitive interpretation and more statistical information than standard deviation.
We compute the analytic expression of the probability distributions F{FTSE100,+} and F{FTSE100,-} of the normalized positive and negative FTSE100 (UK) index daily returns r(t). Furthermore, we define the alpha re-scaled FTSE100 daily index positive returns r(t)^alpha and negative returns (-r(t))^alpha that we call, aft…
Improves efficiency of simulators that fail to return.
problem Computational inefficiency in simulators that don't return for certain inputs.
method Trains a conditional normalizing flow to propose perturbations.
result Increased computational efficiency of simulators.
The paper optimizes portfolios by measuring randomness in asset returns.
problem Challenges in assessing the risk of portfolios due to non-normal asset returns.
method Uses Rényi entropy, an information-theoretic criterion, to quantify uncertainty in asset returns.
result Minimizing Rényi entropy leads to portfolios with better risk-return trade-offs.
Model monthly VIX and stock returns using log-Heston model.
problem Modeling monthly VIX and stock index returns accurately.
method Log-Heston model applied to logarithm of VIX as an autoregression, normalizing stock returns by VIX.
result Model captures independent, identically distributed Gaussian stock returns after normalization.
Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
problem Modeling correlated volatility in financial time series with heavy tails and long memory.
method Superstatistical dynamics, Bayesian Inference, Metropolis-Hasting sampling.
result The log-Normal model is reliable for short timescales, while inverse-Gamma is preferred for long timescales.
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals this amplitude is proportional to a Cauchy-distribution and satisfies the Schroedi…
Optimal option portfolios under Sharpe Ratio maximization with skew-elliptical t-distributed returns
problem Optimal option portfolios under Sharpe Ratio maximization
method Formulation for explicit portfolio weights
result Different optimal portfolios for Sharpe Ratio and return-to-Value-at-Risk (VaR) ratio
The moments of historic stock returns align with the Heston model, not the multiplicative model.
problem Understanding the distribution of historic stock returns and volatility.
method Comparison of moments with Heston and multiplicative models, analysis of mean realized variance.
result The moments of historic stock returns are better explained by the Heston model than the multiplicative model.
Analyzes GJR-GARCH moments for efficient predictive distributions.
problem Estimating moments of GARCH processes for accurate predictions.
method Derives analytic expressions for GJR-GARCH moments and their limits.
result Analytic moments provide excellent approximate predictive distributions.
A new method tracks market performance without active management.
problem Active portfolio management does not outperform benchmarks.
method Developed a hybrid PCA-based tracking portfolio strategy.
result The hybrid PCA strategy outperforms optimization-based approaches.
We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in normal times. The co-movement of stock returns also increases in panic times. W…
Introduces new financial models using subordinated processes.
problem Modeling asset returns with behavioral finance considerations.
method Introduces multiple internally embedded financial time-clocks, subordinated to Brownian motion, with a behavioral subordinator.
result New log-price process with multiple embedded subordinations, requiring estimation of new parameters.
Study shows big winner stocks significantly impact passive and active investment strategies.
problem Impact of big winner stocks on passive and active investment strategies.
method Numerical and analytical techniques applied to historical stock price data.
result Concentrated portfolios underperform equally weighted indexes due to missing big winner stocks.
Automates size normalization for fashion items.
problem Reduce merchandise returns in e-commerce.
method Uses sales data to automate size mapping.
result Automated size mappings comparable to human-generated ones.
Unified approach to trend-following systems, deriving exact relationships and expected returns.
problem Designing and understanding trend-following systems in financial markets.
method Derive exact relationships, analyze expected returns, and use fractional ARFIMA processes.
result Profitability of trend-following systems depends on positive long-term autocorrelation and excess spectral mass at low frequencies.
We investigate the recently introduced variety of a set of stock returns traded in a financial market. This investigation is done by considering daily and intraday time horizons in a 15-day time period centered at the August 31st, 1998 crash of the S&P500 index. All the stocks traded at the NYSE during that period are …
The herd behavior of returns is investigated in Korean futures exchange market. It is obtained that the probability distribution of returns for three types of herding parameter scales as a power law R−β with the exponents β=3.6(KTB203) and 2.9(KTB209) in two kinds of Korean treasury bond. For our case since the…
This paper compares stationarity in Bitcoin and S&P500 price indices.
problem Comparing stationarity in cryptocurrency and traditional stock market indices.
method Wide sense stationarity defined; Wiener-Khinchin Theorem applied; stationarity achieved through detrending and normalization of price returns.
result S&P500 price return achieves stationarity for 28 years with specific normalization windows, while Bitcoin's stationarity varies by segment and volatility.
The κ-generalised distribution fits daily stock returns well.
problem Stock returns are often heavy-tailed, not normally distributed.
method Used the κ-generalised distribution with a Monte-Carlo goodness of fit test. result The κ-generalised distribution fits historic daily stock returns well for a significant proportion of analyzed stocks. The price of electricity is far more volatile than that of other commodities normally noted for extreme volatility. The possibility of extreme price movements increases the risk of trading in electricity markets. However, underlying the process of price returns is a strong mean-reverting mechanism. We study this featur…