Serial Correlation of Asset Returns and Optimal Portfolios for the Long and Short Term

Optimal portfolios differ according to the length of time they are held without being rebalanced. For the case in which asset returns are identically and independently distributed, it has been shown that optimal portfolios become less diversified as the holding period lengthens.We show that the anti-diversification result does not obtain when asset returns are serially correlated, and examine properties of asymptotic portfolios for the case where the short term interest rate, although known at each moment of time, may change unpredictably over time. The theoretical results provide no presumption about the effects of the length of the holding period on the optimal portfolio. Using estimated processes for stock and bill returns, we show that calculated optimal portfolios are virtually invariant to the length of the holding period. The estimated processes for asset returns also imply very little difference between portfolios calculated ignoring changes in the investment opportunity set and those obtained when the investment opportunity set changes over time.

Height-resolved Scaling Properties of Tropospheric Water Vapour based on Airborne Lidar Observations

Two-dimensional vertical water vapour cross sections of the free troposphere between altitudes of 2 and 10 km, measured by nadir-viewing airborne differential-absorption lidar with high spatial resolution, were analyzed using structure functions up to the fifth order. We found scale invariance, i.e. a power-law dependency of structure function on length scale, for scales between 5 and 100 km, for the horizontal time series of water vapour mixing ratio. In contrast to one-dimensional in situ measurements, the two-dimensional water vapor lidar observations allow height-resolved analyses of power-law scaling exponents at a vertical resolution of 200 m. The data reveal significantly different scaling properties above and below an air-mass boundary. They stem from three very dissimilar aircraft campaigns: COPS/ETReC over middle and southern Europe in summer 2007, T-PARC around Japan mostly over sea in late summer 2008, and T-IPY around Spitsbergen over sea in winter 2008. After discarding flight segments with low lidar signals or large data gaps, and after averaging horizontally to a resolution of between 1 and 5 km to obtain a high signal to noise ratio, structure functions were computed for 20 flights at various heights, adding up to a length of more than 300,000 km. The power-law scaling exponents of the structure functions do not show significant latitudinal, seasonal or land/sea dependency, but they do differ between air masses influenced by moist convection and air masses aloft, not influenced. A classification of the horizontal water vapour time series into two groups according to whether the series occurred above or below the level of nearby convective cloud tops could be performed by detecting the cloud top height from the lidar backscatter signal in the corresponding flight segment. We found that the scaling exponents can be divided into two groups depending on the respective air mass: The smoothness of the time series, expressed by the first-order scaling exponent, varies from less than 0.5 in the low-level convectively influenced air masses to values greater than 0.5 and most frequently near 0.6 in the higher-level air above the convective cloud tops. The time series’ intermittency, expressed by the variation of the scaling exponent with increasing order, is larger in convectively influenced air masses. These differences in variability strongly suggest that convection provides a source of moisture variability on small scales. Our results show that the high horizontal and vertical resolution of lidar observations allows a characterisation of the scale dependency of the water vapour field at scales close to and smaller than the smallest resolved scales in modern weather and climate models. This provides both a reference for validation of high resolution models and a basis for the design of stochastic or pdf-based parameterisations of clouds and convection

The Mass distribution of the Cluster 0957+561 from Gravitational Lensing

Multiply gravitationally lensed objects with known time delays can lead to direct determinations of H$_0$ independent of the distance ladder if the mass distribution of the lens is known. Currently, the double QSO 0957+561 is the only lensed object with a precisely known time delay. The largest remaining source of systematic error in the H$_0$ determination results from uncertainty in the mass distribution of the lens which is comprised of a massive galaxy (G1) and the cluster in which it resides. We have obtained V-band CCD images from CFHT in order to measure the mass distribution in the cluster from its gravitional distorting effect on the appearance of background galaxes. We use this data to constuct a two-dimensional mass map of the field. A mass peak is detected at the $4.5\sigma$ level, offset from, but consistent with, the position of G1. Simple tests reveal no significant substructure and the mass distribution is consistent with a spherical cluster. The peak in the number density map of bright galaxies is offset from G1 similarly to the mass peak. We constructed an azimuthally averaged mass profile centered on G1 out to 2 \arcmin ($400 h^{-1}$ kpc). It is consistent with an isothermal mass distribution with a small core (r_c \approx 5 \arcsec = 17 h^{-1} kpc). The inferred mass within 1 Mpc is consistent with the dynamical mass estimate but $2\sigma$ higher than the upper limits from a ROSAT X-ray study. We discuss implications for H$_0$ in a future paper.Comment: LaTeX, aas version 4 macros. Calibration error in original led to overestimate of cluster mass. Seven out of twelve figures included. Complete paper is available at: http://www.astro.lsa.umich.edu:80/users/philf

The stem smuts of Stipa and Oryzopsis in North America

Over much of that great natural resource called the Western Range, comprising some 728 million acres (1), species of Stipa and Orysopsis are prominent and important members of the grass cover. These are commonly found affected with stem smut; often as much as 15-20 per cent of the plants are affected, and occasionally as 90 per cent infection is encountered. In view of these grasses as components of the western range, and the general interest manifest in the nature of the stem smuts so common on them, it seemed desirable to make a study of the identity of these smuts

A study of fruit diseases occurring in a mid-western market

Diseases occurring in a market represent to a fair degree the diseases of fruits and vegetables in the field, since, in the majority of cases, the diseases appearing and developing in the markets are but a delayed expression of infection which occurred in the field. Furthermore, since fruits and vegetables in the markets have been shipped in from various sections of the country as well as from foreign lands, the diseases of these plant products represent not only the phytopathological conditions of the local state or country, but also those of any other part of the world whence they came

Interactive design methods in virtual reality with haptics

This research demonstrated the use of virtual reality and related interaction technology, such as haptics, in an immersive virtual design application. The goal was to present an effective methodology for interactive design where engineers alter products and investigate updated analysis results in real-time using a virtual environment. Research was presented as a series of four papers;Chapter 2 covered a history of the interactive design methodology and it\u27s applications followed by the largest hurdles to effective interaction. Solutions where presented and their effectiveness demonstrated;The third chapter examined some limitations of the custom mesh-free analysis method used on the application. A search was performed for suitable replacement software with an emphasis on Open Source applications. The Tahoe program was selected, tested against the custom implementation, and integrated with the application;In Chapter 4 the calculation of shape design sensitivities for stress approximation were examined. Limitations of the existing finite differences technique were explained and a search of available techniques was made. After considering discrete derivatives, continuum derivatives, and automatic differentiation, and discrete derivatives approach with exact numerical differentiation was selected, implemented, and tested. Results indicate the discrete derivatives approach to be a fine replacement;Chapter 5 considered the use of haptic or force feedback as an additional channel of information for the designer. Several haptic devices and their uses were examined, and a PHANTOM 3.0 was selected for use with the immersive design application. Networked haptic feedback was added to the application and several techniques for mapping model stress state to device forces were investigated. Finally, a simple pilot study was conducted to help determine which feedback styles were considered most useful to a potential designer;The area with the greatest potential for future work would seem to be the use of haptics as a design tool in the application. A proper user study should be conducted to sort out which stress-force mapping techniques are the most effective for a designer. One should also try to determine just how useful the additional haptic feedback generally is when working in the virtual environment;A second area worth investigating further is the use of automatic differentiation routines for the computation of shape design sensitivities. Throughout the course of this research automatic differentiation has made many improvements. With programs as large as 400,000 lines and more now being completely differentiated, it appears to be fast becoming a practical analysis option. This would also make implementing additional types of sensitivity analyses much more straightforward, and would be a powerful addition to the methodologies of interactive design in virtual reality