Liquidity and asset pricing: A comparison between three-factor and three-moment capital asset pricing models

Liquidity is an important attribute of an asset that investors would like to take into consideration when making investment decisions. However, the previous empirical evidence whether liquidity is a determinant of stock return is not unanimous. This dissertation provides a very comprehensive study about the role of liquidity in asset pricing using the Fama-French (1993) three-factor and Kraus and Litzenberger (1976) three-moment CAPM as models for risk adjustment. The relationship between liquidity and well-known determinants of stock returns such as size and book-to-market are also investigated. This study examines the liquidity and asset pricing issues for both intertemporal as well as cross-sectional data. ^ The results indicate an existence of a liquidity premium, i.e., less liquid stocks would demand higher rate of return than more liquid stocks. More specifically, a drop of 1 percent in liquidity is associated with a higher rate of return of about 2 to 3 basis points per month. Further investigation reveals that neither the Fama-French three-factor model nor the three-moment CAPM captures the liquidity premium. Finally, the results show that well-known determinants of stock return such as size and book-to-market do not serve as proxy for liquidity. ^ Overall, this dissertation shows that a liquidity premium exists in the stock market and that liquidity is a distinct effect, and is not influenced by the presence of non-market factors, market factors and other stock characteristics.^

The effects of intellectual property rights on knowledge spillovers and innovation: An empirical investigation

FDI is believed to be a conduit of new technologies between countries. The first chapter of this dissertation studies the advantages of outward FDI for the home country of multinationals conducting research and development abroad. We use patent citations as a proxy for technology spillovers and we bring empirical evidence that supports the hypothesis that a U.S. subsidiary conducting research and development overseas facilitates the flow of knowledge between its host and home countries.^ The second chapter examines the impact of intellectual property rights (IPR) reforms on the technology flows between the U.S. and host countries of U.S. affiliates. We again use patent citations to examine whether the diffusion of new technology between the host countries and the U.S. is accelerated by the reforms. Our results suggest that the reforms favor innovative efforts of domestic firms in the reforming countries rather than U.S. affiliates efforts. In other words, reforms mediate the technology flows from the U.S. to the reforming countries.^ The third chapter deals with another form of IPR, open source (OS) licenses. These differ in the conditions under which licensors and OS contributors are allowed to modify and redistribute the source code. We measure OS project quality by the speed with which programming bugs are fixed and test whether the license chosen by project leaders influences bug resolution rates. In initial regressions, we find a strong correlation between the hazard of bug resolution and the use of highly restrictive licenses. However, license choices are likely to be endogenous. We instrument license choice using (i) the human language in which contributors operate and (ii) the license choice of the project leaders for a previous project. We then find weak evidence that restrictive licenses adversely affect project success.^

Development of safety performance functions for empirical Bayes estimation of crash reduction factors

Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.

Surface mean flow and turbulence structure in tropical cyclone winds

Hurricanes are one of the deadliest and costliest natural hazards affecting the Gulf coast and Atlantic coast areas of the United States. An effective way to minimize hurricane damage is to strengthen structures and buildings. The investigation of surface level hurricane wind behavior and the resultant wind loads on structures is aimed at providing structural engineers with information on hurricane wind characteristics required for the design of safe structures. Information on mean wind profiles, gust factors, turbulence intensity, integral scale, and turbulence spectra and co-spectra is essential for developing realistic models of wind pressure and wind loads on structures. The research performed for this study was motivated by the fact that considerably fewer data and validated models are available for tropical than for extratropical storms. ^ Using the surface wind measurements collected by the Florida Coastal Monitoring Program (FCMP) during hurricane passages over coastal areas, this study presents comparisons of surface roughness length estimates obtained by using several estimation methods, and estimates of the mean wind and turbulence structure of hurricane winds over coastal areas under neutral stratification conditions. In addition, a program has been developed and tested to systematically analyze Wall of Wind (WoW) data, that will make it possible to perform analyses of baseline characteristics of flow obtained in the WoW. This program can be used in future research to compare WoW data with FCMP data, as gust and turbulence generator systems and other flow management devices will be used to create WoW flows that match as closely as possible real hurricane wind conditions. ^ Hurricanes are defined as tropical cyclones for which the maximum 1-minute sustained surface wind speeds exceed 74 mph. FCMP data include data for tropical cyclones with lower sustained speeds. However, for the winds analyzed in this study the speeds were sufficiently high to assure that neutral stratification prevailed. This assures that the characteristics of those winds are similar to those prevailing in hurricanes. For this reason in this study the terms tropical cyclones and hurricanes are used interchangeably. ^

Quantifying the effects of temperature and concentration on variable-density flow in numerical modeling of groundwater systems: Implications for predictive uncertainty and data collection

Groundwater systems of different densities are often mathematically modeled to understand and predict environmental behavior such as seawater intrusion or submarine groundwater discharge. Additional data collection may be justified if it will cost-effectively aid in reducing the uncertainty of a model's prediction. The collection of salinity, as well as, temperature data could aid in reducing predictive uncertainty in a variable-density model. However, before numerical models can be created, rigorous testing of the modeling code needs to be completed. This research documents the benchmark testing of a new modeling code, SEAWAT Version 4. The benchmark problems include various combinations of density-dependent flow resulting from variations in concentration and temperature. The verified code, SEAWAT, was then applied to two different hydrological analyses to explore the capacity of a variable-density model to guide data collection. ^ The first analysis tested a linear method to guide data collection by quantifying the contribution of different data types and locations toward reducing predictive uncertainty in a nonlinear variable-density flow and transport model. The relative contributions of temperature and concentration measurements, at different locations within a simulated carbonate platform, for predicting movement of the saltwater interface were assessed. Results from the method showed that concentration data had greater worth than temperature data in reducing predictive uncertainty in this case. Results also indicated that a linear method could be used to quantify data worth in a nonlinear model. ^ The second hydrological analysis utilized a model to identify the transient response of the salinity, temperature, age, and amount of submarine groundwater discharge to changes in tidal ocean stage, seasonal temperature variations, and different types of geology. The model was compared to multiple kinds of data to (1) calibrate and verify the model, and (2) explore the potential for the model to be used to guide the collection of data using techniques such as electromagnetic resistivity, thermal imagery, and seepage meters. Results indicated that the model can be used to give insight to submarine groundwater discharge and be used to guide data collection. ^

Eulerian-Lagrangian two phase debris flow model

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier-Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Integrated surface-ground water modeling in wetlands with improved methods to simulate vegetative resistance to flow

In topographically flat wetlands, where shallow water table and conductive soil may develop as a result of wet and dry seasons, the connection between surface water and groundwater is not only present, but perhaps the key factor dominating the magnitude and direction of water flux. Due to their complex characteristics, modeling waterflow through wetlands using more realistic process formulations (integrated surface-ground water and vegetative resistance) is an actual necessity. This dissertation focused on developing an integrated surface – subsurface hydrologic simulation numerical model by programming and testing the coupling of the USGS MODFLOW-2005 Groundwater Flow Process (GWF) package (USGS, 2005) with the 2D surface water routing model: FLO-2D (O’Brien et al., 1993). The coupling included the necessary procedures to numerically integrate and verify both models as a single computational software system that will heretofore be referred to as WHIMFLO-2D (Wetlands Hydrology Integrated Model). An improved physical formulation of flow resistance through vegetation in shallow waters based on the concept of drag force was also implemented for the simulations of floodplains, while the use of the classical methods (e.g., Manning, Chezy, Darcy-Weisbach) to calculate flow resistance has been maintained for the canals and deeper waters. A preliminary demonstration exercise WHIMFLO-2D in an existing field site was developed for the Loxahatchee Impoundment Landscape Assessment (LILA), an 80 acre area, located at the Arthur R. Marshall Loxahatchee National Wild Life Refuge in Boynton Beach, Florida. After applying a number of simplifying assumptions, results have illustrated the ability of the model to simulate the hydrology of a wetland. In this illustrative case, a comparison between measured and simulated stages level showed an average error of 0.31% with a maximum error of 2.8%. Comparison of measured and simulated groundwater head levels showed an average error of 0.18% with a maximum of 2.9%. The coupling of FLO-2D model with MODFLOW-2005 model and the incorporation of the dynamic effect of flow resistance due to vegetation performed in the new modeling tool WHIMFLO-2D is an important contribution to the field of numerical modeling of hydrologic flow in wetlands.

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Improving Analytical Travel Time Estimation for Transportation Planning Models

This dissertation aimed to improve travel time estimation for the purpose of transportation planning by developing a travel time estimation method that incorporates the effects of signal timing plans, which were difficult to consider in planning models. For this purpose, an analytical model has been developed. The model parameters were calibrated based on data from CORSIM microscopic simulation, with signal timing plans optimized using the TRANSYT-7F software. Independent variables in the model are link length, free-flow speed, and traffic volumes from the competing turning movements. The developed model has three advantages compared to traditional link-based or node-based models. First, the model considers the influence of signal timing plans for a variety of traffic volume combinations without requiring signal timing information as input. Second, the model describes the non-uniform spatial distribution of delay along a link, this being able to estimate the impacts of queues at different upstream locations of an intersection and attribute delays to a subject link and upstream link. Third, the model shows promise of improving the accuracy of travel time prediction. The mean absolute percentage error (MAPE) of the model is 13% for a set of field data from Minnesota Department of Transportation (MDOT); this is close to the MAPE of uniform delay in the HCM 2000 method (11%). The HCM is the industrial accepted analytical model in the existing literature, but it requires signal timing information as input for calculating delays. The developed model also outperforms the HCM 2000 method for a set of Miami-Dade County data that represent congested traffic conditions, with a MAPE of 29%, compared to 31% of the HCM 2000 method. The advantages of the proposed model make it feasible for application to a large network without the burden of signal timing input, while improving the accuracy of travel time estimation. An assignment model with the developed travel time estimation method has been implemented in a South Florida planning model, which improved assignment results.

Factors Controlling Surface Water Flow in a Low-gradient Subtropical Wetland

Surface water flow patterns in wetlands play a role in shaping substrates, biogeochemical cycling, and ecosystem characteristics. This paper focuses on the factors controlling flow across a large, shallow gradient subtropical wetland (Shark River Slough in Everglades National Park, USA), which displays vegetative patterning indicative of overland flow. Between July 2003 and December 2007, flow speeds at five sites were very low (s−1), and exhibited seasonal fluctuations that were correlated with seasonal changes in water depth but also showed distinctive deviations. Stepwise linear regression showed that upstream gate discharges, local stage gradients, and stage together explained 50 to 90% of the variance in flow speed at four of the five sites and only 10% at one site located close to a levee-canal combination. Two non-linear, semi-empirical expressions relating flow speeds to the local hydraulic gradient, water depths, and vegetative resistance accounted for 70% of the variance in our measured speed. The data suggest local-scale factors such as channel morphology, vegetation density, and groundwater exchanges must be considered along with landscape position and basin-scale geomorphology when examining the interactions between flow and community characteristics in low-gradient wetlands such as the Everglades.

Three empirical essays on startups' survival using the Kauffman Firm Survey

This dissertation studies newly founded U.S. firms' survival using three different releases of the Kauffman Firm Survey. I study firms' survival from a different perspective in each chapter. ^ The first essay studies firms' survival through an analysis of their initial state at startup and the current state of the firms as they gain maturity. The probability of survival is determined using three probit models, using both firm-specific variables and an industry scale variable to control for the environment of operation. The firm's specific variables include size, experience and leverage as a debt-to-value ratio. The results indicate that size and relevant experience are both positive predictors for the initial and current states. Debt appears to be a predictor of exit if not justified wisely by acquiring assets. As suggested previously in the literature, entering a smaller-scale industry is a positive predictor of survival from birth. Finally, a smaller-scale industry diminishes the negative effects of debt. ^ The second essay makes use of a hazard model to confirm that new service-providing (SP) firms are more likely to survive than new product providers (PPs). I investigate the possible explanations for the higher survival rate of SPs using a Cox proportional hazard model. I examine six hypotheses (variations in capital per worker, expenses per worker, owners' experience, industry wages, assets and size), none of which appear to explain why SPs are more likely than PPs to survive. Two other possibilities are discussed: tax evasion and human/social relations, but these could not be tested due to lack of data. ^ The third essay investigates women-owned firms' higher failure rates using a Cox proportional hazard on two models. I make use of a never-before used variable that proxies for owners' confidence. This variable represents the owners' self-evaluated competitive advantage. ^ The first empirical model allows me to compare women's and men's hazard rates for each variable. In the second model I successively add the variables that could potentially explain why women have a higher failure rate. Unfortunately, I am not able to fully explain the gender effect on the firms' survival. Nonetheless, the second empirical approach allows me to confirm that social and psychological differences among genders are important in explaining the higher likelihood to fail in women-owned firms.^

A tidal creek water budget: Estimation of groundwater discharge and overland flow using hydrologic modeling in the Southern Everglades

Taylor Slough is one of the natural freshwater contributors to Florida Bay through a network of microtidal creeks crossing the Everglades Mangrove Ecotone Region (EMER). The EMER ecological function is critical since it mediates freshwater and nutrient inputs and controls the water quality in Eastern Florida Bay. Furthermore, this region is vulnerable to changing hydrodynamics and nutrient loadings as a result of upstream freshwater management practices proposed by the Comprehensive Everglades Restoration Program (CERP), currently the largest wetland restoration project in the USA. Despite the hydrological importance of Taylor Slough in the water budget of Florida Bay, there are no fine scale (∼1 km2) hydrodynamic models of this system that can be utilized as a tool to evaluate potential changes in water flow, salinity, and water quality. Taylor River is one of the major creeks draining Taylor Slough freshwater into Florida Bay. We performed a water budget analysis for the Taylor River area, based on long-term hydrologic data (1999–2007) and supplemented by hydrodynamic modeling using a MIKE FLOOD (DHI,http://dhigroup.com/) model to evaluate groundwater and overland water discharges. The seasonal hydrologic characteristics are very distinctive (average Taylor River wet vs. dry season outflow was 6 to 1 during 1999–2006) with a pronounced interannual variability of flow. The water budget shows a net dominance of through flow in the tidal mixing zone, while local precipitation and evapotranspiration play only a secondary role, at least in the wet season. During the dry season, the tidal flood reaches the upstream boundary of the study area during approximately 80 days per year on average. The groundwater field measurements indicate a mostly upwards-oriented leakage, which possibly equals the evapotranspiration term. The model results suggest a high importance of groundwater contribution to the water salinity in the EMER. The model performance is satisfactory during the dry season where surface flow in the area is confined to the Taylor River channel. The model also provided guidance on the importance of capturing the overland flow component, which enters the area as sheet flow during the rainy season. Overall, the modeling approach is suitable to reach better understanding of the water budget in the mangrove region. However, more detailed field data is needed to ascertain model predictions by further calibrating overland flow parameters.

Development of safety performance functions for SafetyAnalyst applications in Florida

In 2010, the American Association of State Highway and Transportation Officials (AASHTO) released a safety analysis software system known as SafetyAnalyst. SafetyAnalyst implements the empirical Bayes (EB) method, which requires the use of Safety Performance Functions (SPFs). The system is equipped with a set of national default SPFs, and the software calibrates the default SPFs to represent the agency's safety performance. However, it is recommended that agencies generate agency-specific SPFs whenever possible. Many investigators support the view that the agency-specific SPFs represent the agency data better than the national default SPFs calibrated to agency data. Furthermore, it is believed that the crash trends in Florida are different from the states whose data were used to develop the national default SPFs. In this dissertation, Florida-specific SPFs were developed using the 2008 Roadway Characteristics Inventory (RCI) data and crash and traffic data from 2007-2010 for both total and fatal and injury (FI) crashes. The data were randomly divided into two sets, one for calibration (70% of the data) and another for validation (30% of the data). The negative binomial (NB) model was used to develop the Florida-specific SPFs for each of the subtypes of roadway segments, intersections and ramps, using the calibration data. Statistical goodness-of-fit tests were performed on the calibrated models, which were then validated using the validation data set. The results were compared in order to assess the transferability of the Florida-specific SPF models. The default SafetyAnalyst SPFs were calibrated to Florida data by adjusting the national default SPFs with local calibration factors. The performance of the Florida-specific SPFs and SafetyAnalyst default SPFs calibrated to Florida data were then compared using a number of methods, including visual plots and statistical goodness-of-fit tests. The plots of SPFs against the observed crash data were used to compare the prediction performance of the two models. Three goodness-of-fit tests, represented by the mean absolute deviance (MAD), the mean square prediction error (MSPE), and Freeman-Tukey R2 (R2FT), were also used for comparison in order to identify the better-fitting model. The results showed that Florida-specific SPFs yielded better prediction performance than the national default SPFs calibrated to Florida data. The performance of Florida-specific SPFs was further compared with that of the full SPFs, which include both traffic and geometric variables, in two major applications of SPFs, i.e., crash prediction and identification of high crash locations. The results showed that both SPF models yielded very similar performance in both applications. These empirical results support the use of the flow-only SPF models adopted in SafetyAnalyst, which require much less effort to develop compared to full SPFs.

Globalization and the public provision of higher education: Empirical evidence from selected countries

This research study was designed to examine the relationship between globalization as measured by the KOF index, its related forces (economic, political, cultural and technological) and the public provision of higher education. This study is important since globalization is increasingly being associated with changes in critical aspects of higher education. The public provision of education was measured by government expenditure and educational outcomes; that is participation, gender equity and attainment. The study utilized a non-experimental quantitative research design. Data collected from secondary sources for 139 selected countries was analyzed. The countries were geographically distributed and included both developed and developing countries. The choice of countries for inclusion in the study was based on data availability. The data, which was sourced from international organizations such as the United Nations and the World Bank, were examined for different time periods using five year averages. The period covered was 1970 to 2009.^ The relationship between globalization and the higher education variables was examined using cross sectional regression analysis while controlling for economic, political and demographic factors. The major findings of the study are as follows. For the two spending models, only one revealed a significant relationship between globalization and education with the R 2 s ranging from .222 to .448 over the period. This relationship was however negative indicating that as globalization increased, spending on higher education declined. However, for the education outcomes models, this relationship was not significant. For the sub-indices of globalization, only the political dimension showed significance as shown in the spending model. Political globalization was significant for six periods with R2 s ranging from .31 to .52.^ The study concluded that the results are mixed for both the spending and outcome models. It also found no robust effects of globalization on government education provision. This finding is not surprising given the existing literature which sees mixed results on the social impact of globalization.^

Foundations of quantitative information flow: Channels, cascades, and the information order

Secrecy is fundamental to computer security, but real systems often cannot avoid leaking some secret information. For this reason, the past decade has seen growing interest in quantitative theories of information flow that allow us to quantify the information being leaked. Within these theories, the system is modeled as an information-theoretic channel that specifies the probability of each output, given each input. Given a prior distribution on those inputs, entropy-like measures quantify the amount of information leakage caused by the channel. ^ This thesis presents new results in the theory of min-entropy leakage. First, we study the perspective of secrecy as a resource that is gradually consumed by a system. We explore this intuition through various models of min-entropy consumption. Next, we consider several composition operators that allow smaller systems to be combined into larger systems, and explore the extent to which the leakage of a combined system is constrained by the leakage of its constituents. Most significantly, we prove upper bounds on the leakage of a cascade of two channels, where the output of the first channel is used as input to the second. In addition, we show how to decompose a channel into a cascade of channels. ^ We also establish fundamental new results about the recently-proposed g-leakage family of measures. These results further highlight the significance of channel cascading. We prove that whenever channel A is composition refined by channel B, that is, whenever A is the cascade of B and R for some channel R, the leakage of A never exceeds that of B, regardless of the prior distribution or leakage measure (Shannon leakage, guessing entropy leakage, min-entropy leakage, or g-leakage). Moreover, we show that composition refinement is a partial order if we quotient away channel structure that is redundant with respect to leakage alone. These results are strengthened by the proof that composition refinement is the only way for one channel to never leak more than another with respect to g-leakage. Therefore, composition refinement robustly answers the question of when a channel is always at least as secure as another from a leakage point of view.^