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

Brain energy rescue:an emerging therapeutic concept for neurodegenerative disorders of ageing

The brain requires a continuous supply of energy in the form of ATP, most of which is produced from glucose by oxidative phosphorylation in mitochondria, complemented by aerobic glycolysis in the cytoplasm. When glucose levels are limited, ketone bodies generated in the liver and lactate derived from exercising skeletal muscle can also become important energy substrates for the brain. In neurodegenerative disorders of ageing, brain glucose metabolism deteriorates in a progressive, region-specific and disease-specific manner — a problem that is best characterized in Alzheimer disease, where it begins presymptomatically. This Review discusses the status and prospects of therapeutic strategies for countering neurodegenerative disorders of ageing by improving, preserving or rescuing brain energetics. The approaches described include restoring oxidative phosphorylation and glycolysis, increasing insulin sensitivity, correcting mitochondrial dysfunction, ketone-based interventions, acting via hormones that modulate cerebral energetics, RNA therapeutics and complementary multimodal lifestyle changes

Oxygen regulation of breathing through an olfactory receptor activated by lactate

Animals have evolved homeostatic responses to changes in oxygen availability that act on different timescales. Although the hypoxia-inducible factor (HIF) transcriptional pathway that controls long-term responses to low oxygen (hypoxia) has been established, the pathway that mediates acute responses to hypoxia in mammals is not well understood. Here we show that the olfactory receptor gene Olfr78 is highly and selectively expressed in oxygen-sensitive glomus cells of the carotid body, a chemosensory organ at the carotid artery bifurcation that monitors blood oxygen and stimulates breathing within seconds when oxygen declines. Olfr78 mutants fail to increase ventilation in hypoxia but respond normally to hypercapnia. Glomus cells are present in normal numbers and appear structurally intact, but hypoxia-induced carotid body activity is diminished. Lactate, a metabolite that rapidly accumulates in hypoxia and induces hyperventilation, activates Olfr78 in heterologous expression experiments, induces calcium transients in glomus cells, and stimulates carotid sinus nerve activity through Olfr78. We propose that, in addition to its role in olfaction, Olfr78 acts as a hypoxia sensor in the breathing circuit by sensing lactate produced when oxygen levels decline