Optimal leverage from non-ergodicity

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loosely or too tightly constraining investors' risk preferences, from their respective perspectives. The conflict can be understood on the basis that the multiplicative models used in both approaches are non-ergodic which leads to ensemble-average returns differing from time-average returns in single realizations. The classic treatments, from the very beginning of probability theory, use ensemble-averages, whereas the Kelly-result is obtained by considering time-averages. Maximizing the time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage. The latter measure can thus incentivize investors to maximize leverage, which is detrimental to time-average growth and overall market stability. The Sharpe ratio is insensitive to leverage. Its relation to optimal leverage is discussed. A better understanding of the significance of time-irreversibility and non-ergodicity and the resulting bounds on leverage may help policy makers in reshaping financial risk controls.Comment: 17 pages, 3 figures. Updated figures and extended discussion of ergodicit

Binary systems and their nuclear explosions

Peer ReviewedPreprin

A targeted metabolomic protocol for short-chain fatty acids and branched-chain amino acids

Research in obesity and metabolic disorders that involve intestinal microbiota demands reliable methods for the precise measurement of the short-chain fatty acids (SCFAs) and branched-chain amino acids (BCAAs) concentration. Here, we report a rapid method of simultaneously determining SCFAs and BCAAs in biological samples using propyl chloroformate (PCF) derivatization followed by gas chromatography mass spectrometry (GC-MS) analysis. A one-step derivatization using 100 µL of PCF in a reaction system of water, propanol, and pyridine (v/v/v = 8:3:2) at pH 8 provided the optimal derivatization efficiency. The best extraction efficiency of the derivatized products was achieved by a two-step extraction with hexane. The method exhibited good derivatization efficiency and recovery for a wide range of concentrations with a low limit of detection for each compound. The relative standard deviations (RSDs) of all targeted compounds showed good intra- and inter-day (within 7 days) precision (< 10%), and good stability (< 20%) within 4 days at room temperature (23–25 °C), or 7 days when stored at −20 °C. We applied our method to measure SCFA and BCAA levels in fecal samples from rats administrated with different diet. Both univariate and multivariate statistics analysis of the concentrations of these target metabolites could differentiate three groups with ethanol intervention and different oils in diet. This method was also successfully employed to determine SCFA and BCAA in the feces, plasma and urine from normal humans, providing important baseline information of the concentrations of these metabolites. This novel metabolic profile study has great potential for translational research

Developing an evidence-based clinical pathway for the assessment, diagnosis and management of acute Charcot Neuro-Arthropathy: a systematic review

Background: Charcot Neuro-Arthropathy (CN) is one of the more devastating complications of diabetes. To the best of the authors' knowledge, it appears that no clinical tools based on a systematic review of existing literature have been developed to manage acute CN. Thus, the aim of this paper was to systematically review existing literature and develop an evidence-based clinical pathway for the assessment, diagnosis and management of acute CN in patients with diabetes