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Thesis (doctoral)--Universität St. Gallen, 2001.

Virginia's regional grain prices exhibit high volatility due to the state's unique spatial variability and supply and demand fundamentals. This study explains Virginia's basis patterns for corn, soybeans, and wheat. Discussion of times when there were outstanding economic or fundamental market movers that affected basis in Virginia is also offered. The feasibility and process of hedging using futures is explained and evaluated in a case study. Possible marketing decisions based on the findings are presented in an easy and accessible manner, so that producers and extension agents can use this information to make real-time grain marketing decisions. / Master of Science / Virginia's regional grain prices exhibit high volatility due to the state's unique spatial variability and supply and demand fundamentals. This study explains Virginia's basis patterns for corn, soybeans, and wheat. Discussion of times when there were outstanding economic or fundamental market movers that affected basis in Virginia is also offered. The feasibility and process of hedging using futures is explained and evaluated in a case study. Possible marketing decisions based on the findings are presented in an easy and accessible manner, so that producers and extension agents can use this information to make real-time grain marketing decisions.

Futures contracts represent a suitable instrument for hedging. One conse- quence of their standardized nature is the presence of basis risk. In order to mitigate it an agent might aim to minimize Value at Risk or Expected Shortfall. Among numerous approaches to their modelling, CAViaR models which build upon quantile regression are appealing due to the limited set of assumptions and decent empirical performance. We propose alternative specifications for CAViaR model - power and exponential CAViaR, and an alternative, flexible way of computing Expected Shortfall within CAViaR framework - Implied Expectile Level. Empirical analysis suggests that ex- ponential CAViaR yields competitive results both in Value at Risk and Ex- pected Shortfall modelling and in subsequent Value at Risk and Expected Shortfall hedging. 1

This thesis includes three chapters regarding influence functions, higher moments, and futures hedging. In Chapter 2, the objective is to use an influence function to better understand semi-kurtosis for use in analyzing peakedness and tail heaviness on one side of a distribution. Also, it is shown that both the right side semi-kurtosis and left side semi-kurtosis summed together, equal kurtosis, so the ratio of semi-kurtosis to kurtosis can be used to analyze asymmetry, as an alternative to skewness. In Chapter 3, the objective is to analyze higher moments of daily, weekly, and monthly stock market returns using large stocks, technology stocks, and small cap stocks. Kurtosis is found to be positive (greater than 3) and statistically significant for all of the daily and weekly stock market returns, indicating peakedness and fat tails. Similar to kurtosis, the left side semi-fourth moment (semi-kurtosis) is also found to be positive (greater than 1.5) for all of daily and weekly returns, indicating peakedness and fat tails on the left sides of the distributions. Skewness is found to be both positive and negative in the daily stock returns data, indicating asymmetry but with no consistent patterns. The fifth moment is also used to analyze asymmetry, as an alternative to skewness. The fifth moment and skewness (third moment) sometimes indicate opposite asymmetry results, as evidenced by different signs for the two moments. This is because the exponent of five for the fifth moment amplifies observations further from the mean, more so than the exponent of three for skewness. In Chapter 4, the objective is to analyze research on futures hedging and to identify the major factors affecting the use of futures hedging by commodity producers. A multifactor conceptual model is developed that explains the factors and subfactors that are likely to affect the commodity producers’ hedging decisions. Factors include industry characteristics, business operation characteristics, management characteristics, futures hedging costs, and substitute risk management instruments. This model provides a more complete understanding of the factors and subfactors affecting futures hedging, and should be of interest to academics and practitioners working with hedging models.

This thesis includes three chapters regarding influence functions, higher moments, and futures hedging. In Chapter 2, the objective is to use an influence function to better understand semi-kurtosis for use in analyzing peakedness and tail heaviness on one side of a distribution. Also, it is shown that both the right side semi-kurtosis and left side semi-kurtosis summed together, equal kurtosis, so the ratio of semi-kurtosis to kurtosis can be used to analyze asymmetry, as an alternative to skewness. In Chapter 3, the objective is to analyze higher moments of daily, weekly, and monthly stock market returns using large stocks, technology stocks, and small cap stocks. Kurtosis is found to be positive (greater than 3) and statistically significant for all of the daily and weekly stock market returns, indicating peakedness and fat tails. Similar to kurtosis, the left side semi-fourth moment (semi-kurtosis) is also found to be positive (greater than 1.5) for all of daily and weekly returns, indicating peakedness and fat tails on the left sides of the distributions. Skewness is found to be both positive and negative in the daily stock returns data, indicating asymmetry but with no consistent patterns. The fifth moment is also used to analyze asymmetry, as an alternative to skewness. The fifth moment and skewness (third moment) sometimes indicate opposite asymmetry results, as evidenced by different signs for the two moments. This is because the exponent of five for the fifth moment amplifies observations further from the mean, more so than the exponent of three for skewness. In Chapter 4, the objective is to analyze research on futures hedging and to identify the major factors affecting the use of futures hedging by commodity producers. A multifactor conceptual model is developed that explains the factors and subfactors that are likely to affect the commodity producers’ hedging decisions. Factors include industry characteristics, business operation characteristics, management characteristics, futures hedging costs, and substitute risk management instruments. This model provides a more complete understanding of the factors and subfactors affecting futures hedging, and should be of interest to academics and practitioners working with hedging models.

Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de mean-variance hedging e princípio da programação dinâmica. / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy pure-jump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using mean-variance hedging and dynamic programming.

Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de mean-variance hedging e princípio da programação dinâmica. / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy pure-jump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using mean-variance hedging and dynamic programming.

本論文研究如何建立一個投資組合用來追蹤穩定成長的目標線。我們將這個目標線追蹤問題建構成混合整數非線性數學規劃模型。由於用以追蹤目標線的投資組合，經過一段時間後其追蹤效能可能未如預期，本論文提出調整投資組合的數學規劃模型。這些模型中除了考量實務中的交易成本，亦考慮限制放空股票，所以將期貨加入投資組合中作為避險部位。最後，以台灣股票市場與期貨交易市場作為實證研究對象，探討投資組合建立與調整的表現，亦分析不同成長率設定之目標線與期貨投資比重上限對投資組合價值的影響。 / This thesis studies how to construct a tracking portfolio for the benchmark of a stable growth rate. This tracking problem can be formulated as a mixed-integer nonlinear programming model. Since the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical programming model to rebalance the tracking portfolio. These models not only consider the transaction cost but also take into account of the limitation of shorting a stock; thus the tracking portfolio will include a futures position as a hedging position. Finally, an empirical study will be performed by using the data from the Taiwan stock market and the futures market to explore the performance of the proposed models. We will analyze how the different benchmark settings and the futures position limits will affect the value of the tracking portfolio.

本論文提出追蹤特定目標線的二階段混合整數非線性隨機規劃模型，以建立追蹤目標線的投資組合。藉由引進情境樹(scenario tree)，我們將此類二階段隨機規劃問題，轉換成為等價的非隨機規劃模型。在金融商品的價格波動及交互作用下，所建立的投資組合在經過一段時間後，其追蹤目標線的能力可能會日趨降低，所以本論文亦提出調整投資組合的規劃模型。為符合實務考量，本論文同時考慮交易成本、股票放空的限制，並且加入期貨進行避險。為了反應投資者的預期心理，也引進了選擇權及情境樹。最後，我們使用台灣股票市場、期貨交易市場及台指選擇權市場的資料進行實證研究，亦探討不同成長率設定之目標線與投資比例對於投資組合的影響。 / To construct a portfolio tracking specific target line, this thesis studies how to do it via two-stage stochastic mixed-integer nonlinear model. We introduce scenario tree to convert this stochastic model into an deterministic equivalent model. Under the volatility of price and the interaction of each financial derivatives, the performance of the tracking portfolio may get worse when time elapses, this thesis proposes another mathematical model to rebalance the tracking portfolio. These models consider the transactions cost and the limitation of shorting a stock, and the tracking portfolio will include a futures as a hedge position. To reflect the expectation of investors, we introduce scenario tree and also include a options as a hedge position. Finally, an empirical study will be performed by the data from Taiwan stock market, the futures market and the options market to explore the performance of the proposed models. We will analyze how the different benchmarks settings and invest ratio will affect the value of the tracking portfolio.