International stock portfolio selection and performance measures recognizing higher moments of return distributions

Since the seminal works of Markowitz (1952), Sharpe (1964), and Lintner (1965), numerous studies on portfolio selection and performance measure have been based upon the mean-variance framework. However, several researchers (e.g., Arditti (1967, and 1971), Samuelson (1970), and Rubinstein (1973)) argue that the higher moments cannot be neglected unless there is reason to believe that: (i) the asset returns are normally distributed and the investor's utility function is quadratic, or (ii) the empirical evidence demonstrates that higher moments are irrelevant to the investor's decision. Based on the same argument, this dissertation investigates the impact of higher moments of return distributions on three issues concerning the 14 international stock markets.^ First, the portfolio selection with skewness is determined using: the Polynomial Goal Programming in which investor preferences for skewness can be incorporated. The empirical findings suggest that the return distributions of international stock markets are not normally distributed, and that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of his optimal portfolio. The evidence also indicates that an investor will trade expected return of the portfolio for skewness. Moreover, when short sales are allowed, investors are better off as they attain higher expected return and skewness simultaneously.^ Second, the performance of international stock markets are evaluated using two types of performance measures: (i) the two-moment performance measures of Sharpe (1966), and Treynor (1965), and (ii) the higher-moment performance measures of Prakash and Bear (1986), and Stephens and Proffitt (1991). The empirical evidence indicates that higher moments of return distributions are significant and relevant to the investor's decision. Thus, the higher moment performance measures should be more appropriate to evaluate the performances of international stock markets. The evidence also indicates that various measures provide a vastly different performance ranking of the markets, albeit in the same direction.^ Finally, the inter-temporal stability of the international stock markets is investigated using the Parhizgari and Prakash (1989) algorithm for the Sen and Puri (1968) test which accounts for non-normality of return distributions. The empirical finding indicates that there is strong evidence to support the stability in international stock market movements. However, when the Anderson test which assumes normality of return distributions is employed, the stability in the correlation structure is rejected. This suggests that the non-normality of the return distribution is an important factor that cannot be ignored in the investigation of inter-temporal stability of international stock markets. ^

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.

Seagrass ecosystems as a globally significant carbon stock

The protection of organic carbon stored in forests is considered as an important method for mitigating climate change. Like terrestrial ecosystems, coastal ecosystems store large amounts of carbon, and there are initiatives to protect these ‘blue carbon’ stores. Organic carbon stocks in tidal salt marshes and mangroves have been estimated, but uncertainties in the stores of seagrass meadows—some of the most productive ecosystems on Earth—hinder the application of marine carbon conservation schemes. Here, we compile published and unpublished measurements of the organic carbon content of living seagrass biomass and underlying soils in 946 distinct seagrass meadows across the globe. Using only data from sites for which full inventories exist, we estimate that, globally, seagrass ecosystems could store as much as 19.9 Pg organic carbon; according to a more conservative approach, in which we incorporate more data from surface soils and depth-dependent declines in soil carbon stocks, we estimate that the seagrass carbon pool lies between 4.2 and 8.4 Pg carbon. We estimate that present rates of seagrass loss could result in the release of up to 299 Tg carbon per year, assuming that all of the organic carbon in seagrass biomass and the top metre of soils is remineralized.

A study of stock market linkages between the US and frontier countries

My dissertation investigates the financial linkages and transmission of economic shocks between the US and the smallest emerging markets (frontier markets). The first chapter sets up an empirical model that examines the impact of US market returns and conditional volatility on the returns and conditional volatilities of twenty-one frontier markets. The model is estimated via maximum likelihood; utilizes the GARCH model of errors, and is applied to daily country data from the MSCI Barra. We find limited, but statistically significant exposure of Frontier markets to shocks from the US. Our results suggest that it is not the lagged US market returns that have impact; rather it is the expected US market returns that influence frontier market returns The second chapter sets up an empirical time-varying parameter (TVP) model to explore the time-variation in the impact of mean US returns on mean Frontier market returns. The model utilizes the Kalman filter algorithm as well as the GARCH model of errors and is applied to daily country data from the MSCI Barra. The TVP model detects statistically significant time-variation in the impact of US returns and low, but statistically and quantitatively important impact of US market conditional volatility. The third chapter studies the risk-return relationship in twenty Frontier country stock markets by setting up an international version of the intertemporal capital asset pricing model. The systematic risk in this model comes from covariance of Frontier market stock index returns with world returns. Both the systematic risk and risk premium are time-varying in our model. We also incorporate own country variances as additional determinants of Frontier country returns. Our results suggest statistically significant impact of both world and own country risk in explaining Frontier country returns. Time-variation in the world risk premium is also found to be statistically significant for most Frontier market returns. However, own country risk is found to be quantitatively more important.