Quantifying Diversification Effects of A Portfolio Using the Generalised Extreme Value Distribution- Archimedean Gumbel Copula Model

This paper uses the Generalized Extreme Value Distribution - Archimedean Gumbel copula modelling approach to quantify diversification effects in a bivariate portfolio of financial asset returns. This paper estimates Value at Risk (VaR) and Expected Shortfall (ES) of a portfolio consisting of the South African Industrial and Financial Indices using Monte-Carlo simulation. Results show that the portfolio risks are smaller than the sum of the individual component risks, indicating diversification benefits for investors. This approach is valuable for assessing, preparing, and mitigating risks in investment decisions, particularly for international investors considering cross-market diversification

On Volatility, Outliers, and Uncertainty

This dissertation is composed of three loosely related chapters, all of which are empirical.In Chapter 1, I examine whether expectations are formed in a systematically different manner during periods of low volatility versus periods of high volatility. I achieve this by measuring non-linearities in relationship between the SP 500 and the VIX across different market regimes. Three distinct market regimes are identified through a Markov Process, allowing for the capture of non-constant behavior in the relationship between contemporaneous price changes and future volatility expectations. The results indicate that the effect of the underlying asset on the supply and demand dynamics of its derivative is strongest during periods of low volatility and weakest during periods of high volatility. The decrease in magnitude of the SP 500 coefficient as the market switches from low volatility to high, suggests that information scarcity (low volatility) makes additional data (price changes) more impactful. Measures to limit market volatility may make market participant prone to expect changes in the state of the system. The purpose of Chapter 2 is to draw inference from the tail behavior of financial market price volatility in order to compare and contrast volatility expectations with volatility realizations. In doing so, I discuss the implications of slowly decaying tails as they relate to systems susceptible to unpredictable and consequential events. In such cases where fat tails are identified, typical values such as the average and variance, do not properly characterize the risk and unpredictability of the dynamic process under study. Prior research has identified asset prices and asset volatility as being drawn from a power law distribution. This paper aims to quantitatively confirm this characterization, specifically for market volatility. Further, this paper identifies whether or not volatility expectations exhibit similar power law characteristics. Goodness of fit and log likelihood tests indicate that most realized volatility series are plausibly drawn from a power- law distribution. However, none of the studied implied volatility series show evidence of power-law behavior, suggesting that risk premia may exist for lower levels of volatility but does not scale proportionally to the more extreme crisis events. That is, risk premia does not scale proportionally as values move farther into the tail. In Chapter 3, co-authored with Minh Pham, we investigate how economic uncertainty, specifically stock market uncertainty, correlates to individuals\u27 life-satisfaction. Using expected price volatility (VIX) as our anticipatory indicator and life-satisfaction as our measure of utility, our hypothesis is built on the Anticipatory Utility framework, which suggests that people also derive utility from their beliefs. After accounting for associations with the unemployment rate and stock ownership, we find a positive relationship between the VIX and low self-reported life- satisfaction. This analysis captures the contemporaneous effects of future beliefs and indicates that economic sentiment about the future plays an important role in individuals\u27 feelings about the present. This work was inspired by a desire to understand the economic crises that redirect and ultimately redefine our socioeconomic lives, as individuals and as nations. I began my economic studies during one of the most profound crises in recent history, the global financial crisis of the late 2000s. Here again in 2021, as my studies conclude, economies grapple with another, albeit different crisis. Both the Covid-19 pandemic and the subprime financial crisis highlight a salient fact; we never really know when, why, or from where such extreme events arrive. But they do, and do so more frequently than we like or predict. Each of the chapters presented in this dissertation seek to understand the ways in which we anticipate and interact with a characteristic marker of economic and financial crises, uncertainty

Why should we investigate the morphological disparity of plant clades?

Background Disparity refers to the morphological variation in a sample of taxa, and is distinct from diversity or taxonomic richness. Diversity and disparity are fundamentally decoupled; many groups attain high levels of disparity early in their evolution, while diversity is still comparatively low. Diversity may subsequently increase even in the face of static or declining disparity by increasingly fine sub-division of morphological ‘design’ space (morphospace). Many animal clades reached high levels of disparity early in their evolution, but there have been few comparable studies of plant clades, despite their profound ecological and evolutionary importance. This study offers a prospective and some preliminary macroevolutionary analyses. Methods Classical morphometric methods are most suitable when there is reasonable conservation of form, but lose traction where morphological differences become greater (e.g. in comparisons across higher taxa). Discrete character matrices offer one means to compare a greater diversity of forms. This study explores morphospaces derived from eight discrete data sets for major plant clades, and discusses their macroevolutionary implications. Key Results Most of the plant clades in this study show initial, high levels of disparity that approach or attain the maximum levels reached subsequently. These plant clades are characterized by an initial phase of evolution during which most regions of their empirical morphospaces are colonized. Angiosperms, palms, pines and ferns show remarkably little variation in disparity through time. Conifers furnish the most marked exception, appearing at relatively low disparity in the latest Carboniferous, before expanding incrementally with the radiation of successive, tightly clustered constituent sub-clades. Conclusions Many cladistic data sets can be repurposed for investigating the morphological disparity of plant clades through time, and offer insights that are complementary to more focused morphometric studies. The unique structural and ecological features of plants make them ideally suited to investigating intrinsic and extrinsic constraints on disparity