Using extreme value theory to value stock market returns

Extreme stock price movements are of great concern to both investors and the entire economy. For investors, a single negative return, or a combination of several smaller returns, can possible wipe out so much capital that the firm or portfolio becomes illiquid or insolvent. If enough investors experience this loss, it could shock the entire economy. An example of such a case is the stock market crash of 1987. Furthermore, there has been a lot of recent interest regarding the increasing volatility of stock prices. ^ This study presents an analysis of extreme stock price movements. The data utilized was the daily returns for the Standard and Poor's 500 index from January 3, 1978 to May 31, 2001. Research questions were analyzed using the statistical models provided by extreme value theory. One of the difficulties in examining stock price data is that there is no consensus regarding the correct shape of the distribution function generating the data. An advantage with extreme value theory is that no detailed knowledge of this distribution function is required to apply the asymptotic theory. We focus on the tail of the distribution. ^ Extreme value theory allows us to estimate a tail index, which we use to derive bounds on the returns for very low probabilities on an excess. Such information is useful in evaluating the volatility of stock prices. There are three possible limit laws for the maximum: Gumbel (thick-tailed), Fréchet (thin-tailed) or Weibull (no tail). Results indicated that extreme returns during the time period studied follow a Fréchet distribution. Thus, this study finds that extreme value analysis is a valuable tool for examining stock price movements and can be more efficient than the usual variance in measuring risk. ^

The men behind the market: Merchants, the Atlantic slave trade, and the shaping of South Carolina plantation society, 1700–1756

The purpose of this dissertation is to examine the role played by merchants in the shaping of South Carolina plantation society in its early stages of development. In 1700 South Carolina was on the fringes of the British Empire. By mid-century the colony had become an integral part of the British Atlantic system. This dissertation addresses merchants' activity in the shaping of plantation society through their involvement in the Atlantic slave trade. Records of the British and South Carolina governments, and petitions from merchants on both sides of the Atlantic have been extremely valuable in understanding the complex and rapidly changing political affiliations of merchants on both sides of the Atlantic. These sources are valuable to this study since they illustrate the merchants' strategy of utilizing government policies to acquire the absolute best terms of trade. Records such as wills and inventories yielded valuable information on merchants' economic portfolios and provided valuable insight into their personal lives. The data shows that the integration of Colonial South Carolina into the global economy can be attributed to its merchant class, who actively sought out business opportunities in the global economy while working within the framework of British mercantilism.

Essays on international lending and increasing returns to scale

Standard economic theory suggests that capital should flow from rich countries to poor countries. However, capital has predominantly flowed to rich countries. The three essays in this dissertation attempt to explain this phenomenon. The first two essays suggest theoretical explanations for why capital has not flowed to the poor countries. The third essay empirically tests the theoretical explanations.^ The first essay examines the effects of increasing returns to scale on international lending and borrowing with moral hazard. Introducing increasing returns in a two-country general equilibrium model yields possible multiple equilibria and helps explain the possibility of capital flows from a poor to a rich country. I find that a borrowing country may need to borrow sufficient amounts internationally to reach a minimum investment threshold in order to invest domestically.^ The second essay examines how a poor country may invest in sectors with low productivity because of sovereign risk, and how collateral differences across sectors may exacerbate the problem. I model sovereign borrowing with a two-sector economy: one sector with increasing returns to scale (IRS) and one sector with diminishing returns to scale (DRS). Countries with incomes below a threshold will only invest in the DRS sector, and countries with incomes above a threshold will invest mostly in the IRS sector. The results help explain the existence of a bimodal world income distribution.^ The third essay empirically tests the explanations for why capital has not flowed from the rich to the poor countries, with a focus on institutions and initial capital. I find that institutional variables are a very important factor, but in contrast to other studies, I show that institutions do not account for the Lucas Paradox. Evidence of increasing returns still exists, even when controlling for institutions and other variables. In addition, I find that the determinants of capital flows may depend on whether a country is rich or poor.^