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

Unexpected High Losses of Anopheles gambiae Larvae Due to Rainfall

Background - Immature stages of the malaria mosquito Anopheles gambiae experience high mortality, but its cause is poorly understood. Here we study the impact of rainfall, one of the abiotic factors to which the immatures are frequently exposed, on their mortality. Methodology/Principal Findings - We show that rainfall significantly affected larval mosquitoes by flushing them out of their aquatic habitat and killing them. Outdoor experiments under natural conditions in Kenya revealed that the additional nightly loss of larvae caused by rainfall was on average 17.5% for the youngest (L1) larvae and 4.8% for the oldest (L4) larvae; an additional 10.5% (increase from 0.9 to 11.4%) of the L1 larvae and 3.3% (from 0.1 to 3.4%) of the L4 larvae were flushed away and larval mortality increased by 6.9% (from 4.6 to 11.5%) and 1.5% (from 4.1 to 5.6%) for L1 and L4 larvae, respectively, compared to nights without rain. On rainy nights, 1.3% and 0.7% of L1 and L4 larvae, respectively, were lost due to ejection from the breeding site. Conclusions/Significance - This study demonstrates that immature populations of malaria mosquitoes suffer high losses during rainfall events. As these populations are likely to experience several rain showers during their lifespan, rainfall will have a profound effect on the productivity of mosquito breeding sites and, as a result, on the transmission of malaria. These findings are discussed in the light of malaria risk and changing rainfall patterns in response to climate chang

Moisture Uptake of Polyoxyethylene Glycol Glycerides Used as Matrices for Drug Delivery: Kinetic Modelling and Practical Implications

Gelucire 50/13, a polyoxyethylene glycol glyceride mixture, has been widely used in drug delivery, but its moisture uptake behaviour is still poorly understood. In this study, the effects of relative humidity, temperature, and drug incorporation on the moisture uptake of Gelucire are reported in relation to their practical implications for preparation of solid dispersions using this materialPeer reviewe