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. ^

A study of stock market fluctuations and their relation to business conditions

Most research on stock prices is based on the present value model or the more general consumption-based model. When applied to real economic data, both of them are found unable to account for both the stock price level and its volatility. Three essays here attempt to both build a more realistic model, and to check whether there is still room for bubbles in explaining fluctuations in stock prices. In the second chapter, several innovations are simultaneously incorporated into the traditional present value model in order to produce more accurate model-based fundamental prices. These innovations comprise replacing with broad dividends the more narrow traditional dividends that are more commonly used, a nonlinear artificial neural network (ANN) forecasting procedure for these broad dividends instead of the more common linear forecasting models for narrow traditional dividends, and a stochastic discount rate in place of the constant discount rate. Empirical results show that the model described above predicts fundamental prices better, compared with alternative models using linear forecasting process, narrow dividends, or a constant discount factor. Nonetheless, actual prices are still largely detached from fundamental prices. The bubblelike deviations are found to coincide with business cycles. The third chapter examines possible cointegration of stock prices with fundamentals and non-fundamentals. The output gap is introduced to form the nonfundamental part of stock prices. I use a trivariate Vector Autoregression (TVAR) model and a single equation model to run cointegration tests between these three variables. Neither of the cointegration tests shows strong evidence of explosive behavior in the DJIA and S&P 500 data. Then, I applied a sup augmented Dickey-Fuller test to check for the existence of periodically collapsing bubbles in stock prices. Such bubbles are found in S&P data during the late 1990s. Employing econometric tests from the third chapter, I continue in the fourth chapter to examine whether bubbles exist in stock prices of conventional economic sectors on the New York Stock Exchange. The ‘old economy’ as a whole is not found to have bubbles. But, periodically collapsing bubbles are found in Material and Telecommunication Services sectors, and the Real Estate industry group.

A Study of Stock Market Fluctuations and their Relations to Business Conditions

Most research on stock prices is based on the present value model or the more general consumption-based model. When applied to real economic data, both of them are found unable to account for both the stock price level and its volatility. Three essays here attempt to both build a more realistic model, and to check whether there is still room for bubbles in explaining fluctuations in stock prices. In the second chapter, several innovations are simultaneously incorporated into the traditional present value model in order to produce more accurate model-based fundamental prices. These innovations comprise replacing with broad dividends the more narrow traditional dividends that are more commonly used, a nonlinear artificial neural network (ANN) forecasting procedure for these broad dividends instead of the more common linear forecasting models for narrow traditional dividends, and a stochastic discount rate in place of the constant discount rate. Empirical results show that the model described above predicts fundamental prices better, compared with alternative models using linear forecasting process, narrow dividends, or a constant discount factor. Nonetheless, actual prices are still largely detached from fundamental prices. The bubble-like deviations are found to coincide with business cycles. The third chapter examines possible cointegration of stock prices with fundamentals and non-fundamentals. The output gap is introduced to form the non-fundamental part of stock prices. I use a trivariate Vector Autoregression (TVAR) model and a single equation model to run cointegration tests between these three variables. Neither of the cointegration tests shows strong evidence of explosive behavior in the DJIA and S&P 500 data. Then, I applied a sup augmented Dickey-Fuller test to check for the existence of periodically collapsing bubbles in stock prices. Such bubbles are found in S&P data during the late 1990s. Employing econometric tests from the third chapter, I continue in the fourth chapter to examine whether bubbles exist in stock prices of conventional economic sectors on the New York Stock Exchange. The ‘old economy’ as a whole is not found to have bubbles. But, periodically collapsing bubbles are found in Material and Telecommunication Services sectors, and the Real Estate industry group.

Essays on investment, growth and income distribution

In this dissertation, I examine both theoretically and empirically the relationship between stock prices and income distribution using an endogenous growth model with social status impatience.^ The theoretical part looks into how status impatience and current economic status jointly determine time preference, savings, future economic status, stock prices, growth and wealth distribution in the steady state. This work builds on Burgstaller and Karayalcin (1996).^ More specifically, I look at (i) the effects of the distribution of status impatience levels on the distribution of steady state assets, incomes and consumption and (ii) the effects of changes in relative levels of status impatience on stock prices. Therefore, from (i) and (ii), I derive the correlation between stock prices, incomes and asset distribution. Also, the analysis of the stack market is undertaken in the presence of adjustment costs to investments.^ The empirical chapter looks at (i) the correlation between income inequality and long run economic growth on the one hand and (ii) the correlation between stock market prices and income inequality on the other. The role of stock prices and social status is examined to better understand the forces that enable a country to grow overtime and to determine why output per capita varies across countries. The data are from Summers and Heston (1988), Barro and Wolf (1989), Alesina and Rodrik (1994), Global financial Database (1997) and the World Bank. Data for social status are collected through a primary sample survey on the internet. Twenty-five developed and developing countries are included in the sample.^ The model developed in this study was specified as a system of simultaneous equations, in which per capita growth rate and income inequality were endogenous variables. Additionally, stock price index and social status measures were also incorporated. The results indicate that income inequality is inversely related to economic growth. In addition, increase in income inequality arising from higher stock prices constrains growth. Moreover, where social status is determined by income levels, it influences long run growth. Therefore, these results support findings of Persson and Tabellini (1994) and Alesina and Rodrik (1994). ^

Essays on financial crises

This dissertation analyzes recent financial crises in developed and developing countries. The research emphasizes the effects of institutional factors on the international banking and currency crises and their output losses. ^ Chapter two examines the roles of regulation, supervision, and countries' institutional environment in determining the probability of banking crises for a panel of fifteen developed countries from 1975 to 1998. The results from a multivariate logit model indicated that countries with greater government involvement, less capital standard requirements, and lower lending limits on a single borrower are associated with a higher probability of banking crises. ^ Chapter three studies whether output loss in banking crisis differs in market-based or bank-based financial systems. Using existing banking crisis data for sixty-nine countries during 1970–1999, we investigate whether the underlying financial system affects the output loss. The results show that output losses are more serious in market-based economies than those in bank-based economies. Longer crisis duration tends to increase the output losses in banking crises. Finally, countries with deposit insurance and strict law enforcement have less output losses. ^ Chapter four uses macroeconomic and institutional measures to explain the extent of exchange rate depreciation and the decline in stock prices for emerging countries affected by the Mexican currency crisis of 1994–95. The results show that countries with more government budget deficits, and worse reserve adequacies tend to experience large exchange rate depreciation. The institutional measures do not explain much the extent of both the exchange rate depreciation and the decline in stock prices. ^

Essays on the impact of stakeholders' sentiment on the financial decision making process

The most important factor that affects the decision making process in finance is the risk which is usually measured by variance (total risk) or systematic risk (beta). Since investors’ sentiment (whether she is an optimist or pessimist) plays a very important role in the choice of beta measure, any decision made for the same asset within the same time horizon will be different for different individuals. In other words, there will neither be homogeneity of beliefs nor the rational expectation prevalent in the market due to behavioral traits. This dissertation consists of three essays. In the first essay, “ Investor Sentiment and Intrinsic Stock Prices”, a new technical trading strategy was developed using a firm specific individual sentiment measure. This behavioral based trading strategy forecasts a range within which a stock price moves in a particular period and can be used for stock trading. Results indicate that sample firms trade within a range and give signals as to when to buy or sell. In the second essay, “Managerial Sentiment and the Value of the Firm”, examined the effect of managerial sentiment on the project selection process using net present value criterion and also effect of managerial sentiment on the value of firm. Final analysis reported that high sentiment and low sentiment managers obtain different values for the same firm before and after the acceptance of a project. Changes in the cost of capital, weighted cost of average capital were found due to managerial sentiment. In the last essay, “Investor Sentiment and Optimal Portfolio Selection”, analyzed how the investor sentiment affects the nature and composition of the optimal portfolio as well as the portfolio performance. Results suggested that the choice of the investor sentiment completely changes the portfolio composition, i.e., the high sentiment investor will have a completely different choice of assets in the portfolio in comparison with the low sentiment investor. The results indicated the practical application of behavioral model based technical indicator for stock trading. Additional insights developed include the valuation of firms with a behavioral component and the importance of distinguishing portfolio performance based on sentiment factors.

Essays on the Impact of Stakeholders' Sentiment on the Financial Decision Making Process

The most important factor that affects the decision making process in finance is the risk which is usually measured by variance (total risk) or systematic risk (beta). Since investors' sentiment (whether she is an optimist or pessimist) plays a very important role in the choice of beta measure, any decision made for the same asset within the same time horizon will be different for different individuals. In other words, there will neither be homogeneity of beliefs nor the rational expectation prevalent in the market due to behavioral traits. This dissertation consists of three essays. In the first essay, Investor Sentiment and Intrinsic Stock Prices, a new technical trading strategy is developed using a firm specific individual sentiment measure. This behavioral based trading strategy forecasts a range within which a stock price moves in a particular period and can be used for stock trading. Results show that sample firms trade within a range and show signals as to when to buy or sell. The second essay, Managerial Sentiment and the Value of the Firm, examines the effect of managerial sentiment on the project selection process using net present value criterion and also effect of managerial sentiment on the value of firm. Findings show that high sentiment and low sentiment managers obtain different values for the same firm before and after the acceptance of a project. The last essay, Investor Sentiment and Optimal Portfolio Selection, analyzes how the investor sentiment affects the nature and composition of the optimal portfolio as well as the performance measures. Results suggest that the choice of the investor sentiment completely changes the portfolio composition, i.e., the high sentiment investor will have a completely different choice of assets in the portfolio in comparison with the low sentiment investor. The results indicate the practical application of behavioral model based technical indicators for stock trading. Additional insights developed include the valuation of firms with a behavioral component and the importance of distinguishing portfolio performance based on sentiment factors.