Approximating the numéraire portfolio by naive diversification

Estimation theory has shown, owing to the limited estimation window available for real asset data, that the sample-based Markowitz mean-variance approach produces unreliable weights that fluctuate substantially over time. This article proposes an alternate approach to portfolio optimization, being the use of naive diversification to approximate the numéraire portfolio (NP). The NP is the strictly positive portfolio that, when used as benchmark, makes all benchmarked non-negative portfolios either mean decreasing or trendless. Furthermore, it maximizes expected logarithmic utility and outperforms any other strictly positive portfolio in the long run. The article proves for a well-securitized market that the naive equal value-weighted portfolio converges to the NP when the number of constituents tends to infinity. This result is model independent and, therefore, very robust. The systematic construction of diversified stock indices by naive diversification from real data is demonstrated. Even when taking transaction costs into account, these indices significantly outperform the corresponding market capitalization- weighted indices in the long run, indicating empirically their asymptotic proximity to the NP. Finally, in the time of financial crisis, a large equi-weighted fund carrying the investments of major pension funds and insurance companies would provide important liquidity. It would not only dampen the drawdown of a crisis, but would also moderate the excesses of an asset price bubble. © 2012 Macmillan Publishers Ltd

Quasi-exact approximation of hidden Markov chain filters

This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper proposes a quasi-exact approximation method for hidden Markov chain filters, which can be applied when discrete time approximations, such as the Euler scheme, may fail in practice

Atomic structure of granulin determined from native nanocrystalline granulovirus using an X-ray free-electron laser

To understand how molecules function in biological systems, new methods are required to obtain atomic resolution structures from biological material under physiological conditions. Intense femtosecond-duration pulses from X-ray free-electron lasers (XFELs) can outrun most damage processes, vastly increasing the tolerable dose before the specimen is destroyed. This in turn allows structure determination from crystals much smaller and more radiation sensitive than previously considered possible, allowing data collection from room temperature structures and avoiding structural changes due to cooling. Regardless, high-resolution structures obtained from XFEL data mostly use crystals far larger than 1 μm3 in volume, whereas the X-ray beam is often attenuated to protect the detector from damage caused by intense Bragg spots. Here, we describe the 2 Å resolution structure of native nanocrystalline granulovirus occlusion bodies (OBs) that are less than 0.016 μm3 in volume using the full power of the Linac Coherent Light Source (LCLS) and a dose up to 1.3 GGy per crystal. The crystalline shell of granulovirus OBs consists, on average, of about 9,000 unit cells, representing the smallest protein crystals to yield a high-resolution structure by X-ray crystallography to date. The XFEL structure shows little to no evidence of radiation damage and is more complete than a model determined using synchrotron data from recombinantly produced, much larger, cryocooled granulovirus granulin microcrystals. Our measurements suggest that it should be possible, under ideal experimental conditions, to obtain data from protein crystals with only 100 unit cells in volume using currently available XFELs and suggest that single-molecule imaging of individual biomolecules could almost be within reach

APPROXIMATING THE GROWTH OPTIMAL PORTFOLIO AND STOCK PRICE BUBBLES

In practice, optimal portfolio construction for large stock markets has never been conclusively resolved because estimating the required means of returns with sufficient accuracy is a highly intractable task. By avoiding estimation, this paper approximates closely the growth optimal portfolio (GP) for the stocks of developed markets with a well-diversified, hierarchically weighted index (HWI). For stocks denominated in units of the HWI, their current value turns out to be strictly greater than their future expected values, which indicates the existence of stock price bubbles that could be systematically exploited for long-term asset management. It is shown that the HWI does not leave much room for significant performance improvements as proxy for the GP. </jats:p