New monotone Sharpe ratio measures investment performance.
problem Investment performance measurement.
method Introducing a new monotone Sharpe ratio and studying its properties.
result Established a connection with coherent risk measures and obtained an efficient representation.
Study optimal portfolio allocation in a general semimartingale model.
problem Dynamic optimal portfolio allocation under monotone mean-variance preferences.
method New results in semimartingale theory applied to Sharpe ratio analysis.
result Characterization of circumstances for improving mean-variance efficiency.
Investments with best performance are not associated with best Sharpe ratios.
problem The relationship between performance and risk-adjusted return (Sharpe ratio) is counterintuitive for heavy-tailed distributions.
method Synthetic and real data analysis of returns distributions.
result The best-performing investments are not the best in terms of Sharpe ratio, and vice versa.
The paper characterizes optimal dynamic portfolios for a modified mean-variance utility.
problem Optimal dynamic portfolio choice for a modified mean-variance utility.
method Complete characterization under minimal assumptions, no restrictions on asset return moments.
result Maximal MMV utility is linked to the monotone Sharpe ratio, with global squared MSR as the nominal yield.
Study causal inference under specific sampling methods with monotonicity assumptions.
problem Causal inference under biased sampling methods.
method Binary-outcome and binary-treatment case study with monotonicity assumptions.
result Monotonicity assumptions yield comparable results to random sampling.
The paper develops methods for conditional inference on the asset with the highest Sharpe ratio.
problem Performing inference on the asset with the highest Sharpe ratio among correlated assets.
method Conditional inference procedure using multivariate Sharpe ratio standard error, alternative tests, and asymptotic adjustments.
result The conditional inference procedure achieves nominal type I rate and maintains near-nominal rejection rates under the conditional null.
Paper extends ranking metrics theory for financial positions.
problem Developing a new class of functionals for evaluating financial positions.
method Axiomatic framework based on monotonicity and cash-quasiconcavity.
result Linking ranking metrics to families of acceptance sets and risk measures.
Paper extends ranking metrics theory for financial positions.
problem Developing a new class of performance evaluation methods.
method Axiomatic framework based on monotonicity and cash-quasiconcavity.
result Linking ranking metrics to families of acceptance sets and risk measures.
Tests Sharpe ratio for skill vs luck in asset management.
problem Accuracy of Sharpe ratio in measuring skill vs luck.
method Statistical tests to assess the significance of Sharpe ratios.
result Tests reveal the statistical significance of Sharpe ratios and their impact of auto-correlation.
GD monotonically decreases GFS sharpness in neural networks and scalar models.
problem Oscillatory behavior of loss in GD training.
method Analysis of GFS sharpness and empirical validation.
result GFS sharpness decreases monotonically during GD training.
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
Omega ratio is shown to be equivalent to Sharpe ratio under certain distributional assumptions.
problem Comparing Omega ratio to Sharpe ratio as performance indicators.
method Computation and analysis of Omega ratio for normal distribution and proof for elliptic distributions.
result Omega ratio is equivalent to Sharpe ratio for returns with elliptic distributions.
Paper connects Sharpe ratio and Student t-statistic, providing exact distribution and asymptotic behavior.
problem Error-prone Sharpe ratio due to statistical estimation of expected returns and volatilities.
method Derive exact distribution of Sharpe ratio for independent normally distributed returns, extend to AR(1) assumptions.
result Empirical Sharpe ratio is asymptotically optimal and achieves Cramer Rao bound.
The Sharpe ratio is a way to compare the excess returns (over the risk free asset) of portfolios for each unit of volatility that is generated by a portfolio. In this paper we introduce a robust Sharpe ratio portfolio under the assumption that the risk free asset is unknown. We propose a robust portfolio that maximizes…
We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schroedinger operators and Schroedinger operators on immersed manifolds. In particular, we prove bounds on the eigenvalue lambda_{N+1} in terms of the lower spectrum, bou…
We discuss - in what is intended to be a pedagogical fashion - generalized "mean-to-risk" ratios for portfolio optimization. The Sharpe ratio is only one example of such generalized "mean-to-risk" ratios. Another example is what we term the Fano ratio (which, unlike the Sharpe ratio, is independent of the time horizon)…
Sharp gradient estimates for positive Ricci curvature manifolds.
problem Understanding geometric properties of manifolds with positive Ricci curvature.
method Proving sharp gradient estimates and monotonicity formulae.
result Sharp gradient estimates and monotonicity formulae for positive Ricci curvature manifolds.
New method to decompose portfolio performance ratios.
problem Understanding the drivers of portfolio performance ratios.
method Using Euler's theorem, decomposes performance ratios into modified ratios.
result Derives condition for new asset to improve portfolio performance.
A new measure, the implied Sharpe ratio, helps investors choose among European options.
problem No concise measure exists to compare different European options.
method Taylor series expansion of state-dependent coefficients in a nonlinear PDE.
result The option with the highest implied Sharpe ratio improves utility the most.
Post hoc test for Sharpe ratio improves pairwise comparisons.
problem Improving pairwise comparisons of Sharpe ratios.
method Analogous to Tukey's test, applied after rejecting equal Signal-Noise ratios.
result Maintains nominal type I rate and is moderately powerful.
Derives new monotone quantities for p-harmonic functions on asymptotically flat 3-manifolds.
problem Estimating the mass of 3-manifolds with non-negative scalar curvature and minimal boundary.
method Derives monotone quantities for p-harmonic functions and applies them to derive a sharp mass-capacity estimate.
result Derives a sharp mass-capacity estimate relating the ADM mass of a 3-manifold to the p-capacity of its boundary.
Estimates true Sharpe ratio of selected assets with various methods.
problem Estimating the true Sharpe ratio of a selected asset with high in-sample ratio.
method Polyhedral lemma, James Stein shrinkage, debiasing, thresholding, empirical Bayes.
result James Stein estimator performs best across various parameter values.
DRCD identifies causal direction between continuous and discrete variables using density ratio monotonicity.
problem Inferring causal direction between continuous and discrete variables from observational data.
method Density Ratio-based Causal Discovery (DRCD) method.
result DRCD identifies causal direction between continuous and discrete variables using density ratio monotonicity.
New method improves submodular maximization for machine learning applications.
problem Inexact monotonicity in submodular functions limits traditional algorithms' performance.
method Introduces monotonicity ratio as a continuous version of monotonicity, leading to improved approximation guarantees.
result Improved approximation ratios for movie recommendation, quadratic programming, and image summarization.
A simple example shows that losing all money is compatible with a very high Sharpe ratio (as computed after losing all money). However, the only way that the Sharpe ratio can be high while losing money is that there is a period in which all or almost all money is lost. This note explores the best achievable Sharpe and …
A new ratio, the Hansen ratio, simplifies mean-variance portfolio theory.
problem Simplifying mean-variance portfolio theory.
method Introducing the Hansen ratio and extending mean-variance theory.
result The Hansen ratio provides a parsimonious description of the mean-variance efficient frontier.
Bayesian Parametric Portfolio Policies corrects overestimation of utility and risk in traditional PPP.
problem Traditional Parametric Portfolio Policies ignore policy risk, leading to overestimation of expected utility and understatement of portfolio risk.
method Developed Bayesian Parametric Portfolio Policies (BPPP) by placing a prior on policy coefficients to correct the decision rule.
result BPPP delivers higher Sharpe ratios, lower turnover, larger investor welfare, and lower tail risk compared to traditional PPP.
When the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space, it is a biased estimator for what can be expected on unseen data (out-of-sample). We derive (1) an unbiased estimator adjusting for both sources of bias: noise fit and estimation error. We then show (2) how to use the adjust…
Study tests whether trade-off functions are above or below benchmarks using finite samples.
problem Testing trade-off functions between unknown distributions.
method Identifies a condition for nontrivial testing, constructs a test with error guarantees, and inverts the test for confidence bands.
result Finite-sample testing is possible under specific structural assumptions about rejection regions.
New method for Sharpe ratio analysis in high dimensions using residual-based nodewise regression.
problem Consistency of Sharpe ratio estimators in high-dimensional portfolios.
method Residual-based nodewise regression for estimating precision matrix of errors and returns.
result Consistent Sharpe ratio estimators in various portfolio settings.
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for markets prohibiting sh…
Sharp gradient estimates extended to surfaces with lower Ricci curvature.
problem Rigidity of Cheng-Yau gradient estimates on surfaces with lower Ricci curvature.
method Extending Cheng-Yau gradient estimates to surfaces with lower Ricci curvature bound and higher-dimensional Riemannian manifolds.
result Pointwise Cheng-Yau gradient estimates for higher-dimensional Riemannian manifolds and monotonicity formulas for positive harmonic functions.
Develops a dynamical method to prove the sharp Berezin-Li-Yau inequality.
problem Proving the sharp Berezin-Li-Yau inequality for convex domains.
method Volume-preserving mean curvature flow and a new monotonicity principle.
result Shows the sharp Berezin-Li-Yau bound for every smooth convex domain.
Grover search for optimal portfolios based on Sharpe ratio.
problem Finding optimal portfolios with specific risk-return characteristics.
method Grover's algorithm applied to portfolio selection with oracles.
result Quantum algorithms can efficiently find optimal portfolios.
Double descent in portfolio optimization shows improved performance with complexity, then declines, due to overfitting.
problem Improving portfolio optimization performance with model complexity.
method Investigates the relationship between model complexity and out-of-sample performance in mean-variance portfolio optimization.
result Performance of low-dimensional models initially improves with complexity but declines due to overfitting. High-dimensional models show double ascent Sharpe ratio curve.
We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov-Hausdorff distance to the neare…
The paper proposes an asset allocation strategy using the Sortino ratio for better performance.
problem Traditional asset allocation methods like the Sharpe ratio do not penalize negative returns adequately.
method The Sortino ratio is used to maximize asset allocation, penalizing only negative return variances.
result The Sortino ratio-based strategy outperforms traditional methods like the Kelly criterion.
The paper examines the unexpected losses and risk ratios for co-monotonic alternatives in large portfolios.
problem Understanding the unexpected losses and risk ratios for large portfolios with co-monotonic alternatives.
method Analyzes the asymptotic behavior of unexpected losses and risk ratios for co-monotonic alternatives using monotone cash-additive risk measures and Choquet insurance premia.
result Unexpected losses of large weighted portfolios are of order o(nλn), where λn is the average weight. Monotonicity formulae play a crucial role for many geometric PDEs, especially for their regularity theories. For minimal submanifolds in a Euclidean ball, the classical monotonicity formula implies that if such a submanifold passes through the centre of the ball, then its area is at least that of the equatorial disk. R…
The paper describes a method to infer the signal-to-noise ratio in portfolio optimization.
problem Estimating the signal-to-noise ratio in portfolio optimization problems.
method A statistic similar to the Sharpe Ratio Information Criterion is used for inference.
result The method works well for reasonable sample and asset universe sizes.
The Sharpe ratio is the most widely used risk metric in the quantitative finance community - amazingly, essentially everyone gets it wrong. In this note, we will make a quixotic effort to rectify the situation.
New quantity helps map homotopy classes in complex spaces.
problem Understanding homotopic classes of maps between complex spaces.
method Identified a new monotone quantity in mean curvature flows of maps between Riemannian manifolds.
result Sharp criteria for homotopic classes of maps between complex projective spaces and spheres.
The paper optimizes portfolios using clustering and Sharpe ratio-based optimization.
problem Optimizing portfolio performance in financial modeling.
method Combines K-Means clustering for asset segmentation and Sharpe ratio-based optimization.
result Optimized portfolios outperform traditional equal-weighted benchmarks.
The VIX is used to enhance quantitative trading strategies.
problem Improving Sharpe ratio and reducing trading risks in quantitative strategies.
method Postprocessing quantitative strategies with VIX signals.
result Increased Sharpe ratio and reduced trading risks.
The paper optimizes dynamic portfolios using utility maximization and risk measures.
problem Maximizing expected utility in dynamic stochastic portfolio optimization.
method Solves a dynamic stochastic portfolio optimization problem numerically using evolutionary Hamilton-Jacobi-Bellman equations and Riccati transformations.
result Defines and computes the Conditional Value-at-Risk deviation (CVaRD) based Sharpe ratio for risk-adjusted performance.
Adaptive learning rate improves FTRL's performance in online learning.
problem Optimizing FTRL's learning rate for competitive regret in online learning.
method Formulated as a sequential decision-making problem, introduced competitive analysis framework, and proposed stability-penalty matching update rules.
result Achieved a constant competitive ratio under specific conditions, enabling Best-Of-Both-Worlds algorithms.
The paper studies Steklov eigenvalues in space forms and warped product manifolds, deriving bounds and monotonicity results.
problem Estimating Steklov eigenvalues in space forms and warped product manifolds.
method Monotonicity results for Steklov eigenvalues in geodesic disks and warped product manifolds with non-negative Ricci curvature.
result Sharp bounds and monotonicity results for Steklov eigenvalues on warped product manifolds.