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Leveraged exchange traded funds (ETFs) have become increasingly popular since their introduction in 2006. In recent years, options on leveraged ETFs have been promoted as a means of enhancing returns and reducing risk. The purpose of this paper is to examine the interchangeability of S & P 500 ETF options with leveraged S & P 500 ETF options and to what extent these options allow investors to manage their risk exposure.

With increasing liquidity for these fund’s options, simple option strategies such as covered calls and protective puts can be implemented. This study derives call-call and put-put parity between options on the underlying index and the associated leveraged ETFs. The paper examines comparative measures of return and risk on the underlying indices, along with covered call and protective put positions.

Using the formulations derived, this study shows options on non-leveraged ETFs or on the underlying index can be substituted for leveraged ETF options. Empirical results suggest substituting options on leveraged ETFs with options on the underlying index or index ETF give comparable results, but can differ as the realized leverage ratio over time differs from projected values.

This study is the first to the authors’ knowledge that investigates option strategies on leveraged and inverse ETFs of equity indices. It is also the first to derive call-call and put-put parity relations between options on ETFs and related leveraged and inverse ETFs. The results contribute to securities issuance, investment strategies, and option parity relations.

This paper attempts to establish the conceptional and computational systems of grey determinant and apply it to solve n grey equations with n grey linear equations, which can be viewed as the important parts of grey mathematics.

Starting from the fact that missing information often appears in complex systems, the true values of elements when constructing a determinant and of coefficients when solving n equations with n linear equations cannot be obtained, so they are uncertain. However, their ranges can be obtained by using correct investigation methods. The uncertain elements and coefficients are grey and their ranges are number‐covered sets. On the basis of the results of Li and Wang, the paper systematically proposes the definition system of grey determinant and n grey linear equations, and utilizes the computational rules of grey determinant to solve the n grey equations with n grey linear equations. Some numerical examples are computed to illustrate the results in this paper.

The results show that the ranges of grey value of grey determinant and grey solutions of grey equations with n grey linear equations can be obtained by using computational rules proposed.

Because the determinant and the linear equations have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey determinant and grey linear equations may have great potential application in the real world. The method realizes the feasibility of system analysis under uncertain situations.

The paper succeeds in providing systematic results of computation of uncertain determinant and n linear equations by using grey systems theory and enriches the contents of grey mathematics.

This paper aims to explore the potential use of a dividend capture strategy by individual investors. This strategy arises from the 2003 tax law changes which lowered tax rates on dividends received, while leaving the short‐term tax rates on capital losses unchanged. In addition, leverage can be used in combination with an aggressive call‐writing strategy to receive a multiple of the tax‐advantaged dividend yield without a corresponding increase in risk.

In addition to illustrating how the dividend capture strategy works, a new method of comparing returns between strategies is developed. This method does not rely on a particular risk‐return model, such as is used by the Sharpe ratio or Jensen's alpha methodologies. Finally, a formula is derived which computes the borrowing (margin loan) rate that makes the aggressive call‐writing strategy profitable.

The 2003 changes in US tax laws provide individuals with an opportunity to apply dividend capture techniques similar to those which have been available to corporations for many years. However, corporations use dividend capture techniques to lower risk, while individuals require risk exposure to keep the possibility for capital gains. Thus, a method is developed for capturing an enhanced tax refund on the drop in stock price caused by the stock going ex‐dividend without giving up the potential for capital gain. A byproduct of this method is a straightforward means to measure risk‐adjusted returns for the covered call strategy. The aggressive call‐writing strategy described in this paper is found to offer enhanced returns without an increase in risk for those in the top individual tax brackets.

The specific level of additional risk‐adjusted returns available depends on the tax rates and interest (margin loan) rates facing the investor.

Following the 2003 tax law changes, individuals can receive returns on stocks higher than implied by the statutory tax rate on dividends by employing a dividend capture strategy which involves writing call options on dividend‐paying stocks. This paper also demonstrates that the risk exposure necessary to obtain full capital gains potential can be maintained with an aggressive strategy. This strategy inherently provides a method to judge the extent of improvement without having to rely on questionable assumptions of any specific asset‐pricing model.

The paper provides an alternative to conventional covered call‐writing strategies which reduce exposure to capital gains. Individual investors and their advisors will find a method to maintain exposure to market risk and therefore the full potential for capital gains, while receiving preferential tax treatment on dividends received. Researchers will find a method to directly compute risk‐adjusted return for covered call‐writing strategies without having to rely on assumptions made in the asset‐pricing models underlying the Sharpe ratio and Jensen's alpha.

The use of improved storage procedures for route generation for demand actuated systems is necessary for practical implementation of many routing systems. Neighborhood Storage is a method of storing the system information which requires a covering to be generated for a number of sets of points which are generated by the method. The set covering problem is important to the overall practical implementation of the method. The method requires M coverings to be generated for each application. Thus, computational efficiency is of considerable importance in obtaining the required coverings. The problem is defined and formulated as a set covering problem. Solutions are carried out for a number of examples and the results for the optimum covering are reported. An algorithm is then presented for obtaining a suboptimum covering with considerable efficiency in computation and overall data manipulation. The example results are also included. The algorithm presented is applicable to any (V;A,B) modeled in R2.

Short option positions carry significant risk of losses well in excess of 100 per cent of the initial option price. Margin requirements associated with such positions are therefore considerable. The purpose of this paper is to develop a methodology for calculating margin requirement‐based option portfolio returns that realistically represent the returns realized by investors, and to demonstrate the effects of this methodology on analyses of option returns.

A methodology is developed for calculating margin requirement‐based short option portfolio returns.

Accounting for margin requirements reduces the returns of simple short option strategies by up to 92 per cent compared to the price return. In long/short portfolio analyses, use of margin requirement returns necessitates additional methodological adjustments to ensure that unwanted volatility risk is properly hedged.

The result is a portfolio return that more accurately represents the return realized by investors, and increased power to detect cross‐sectional patterns in option returns.