Sunday, January 26, 2020

Evidence from International Stock Markets

Evidence from International Stock Markets Portfolio Selection with Four Moments: Evidence from International Stock Markets Despite the international diversification suggested by several researchers (e.g. Grulbel, 1968; Levy and Sarnat, 1970; Solnik, 1974) and the increased integration of capital markets, the home bias has not decreased (Thomas et. al., 2004 and Coeurdacier and Rey, 2013) and there is no complete explanation of this puzzle. Furthermore, there are the fastgrowing concerns of investor for extreme risks[1] and the investors preference toward odd moments (e.g. mean and skewness) and an aversion toward even moments (e.g. variance and kurtosis) considered by numerous studies (e.g. Levy, 1969; Arditti, 1967 and 1971; Jurczenko and Maillet, 2006). According to these reasons, this paper propose to investigate whether the incorporation of investor preferences in the higher moments into the international asset allocation problem can help explain the home bias puzzle. The study will allow investor preferences to depend not only the first two moments (i.e. mean and variance) but also on the higher moments, such as skewness and kurtosis, by using the polynomial goal programming (PGP) approach and then generate the three-dimensional efficient frontier. The main objective of the proposed study is to investigate whether the incorporation of skewness and kurtosis into the international stock portfolio selection causes these issues: The changes in the construction of optimal portfolios, the patterns of relationships between moments, and the less diversification compared to the mean-variance model. Since several researchers (e.g. Grulbel, 1968; Levy and Sarnat, 1970; Solnik, 1974) suggest that investment in a portfolio of equities across foreign markets provide great diversification opportunities, then investors should rebalance there portfolio away from domestic toward foreign equities. However, US investors continue to hold equity portfolios that are largely dominated by domestic assets. Thomas et. al. (2004) reported that by the end of 2003 US investors held only 14 percent of their equity portfolios in foreign stocks. Furthermore, Coeurdacier and Rey (2013) also reported that in 2007, US investors hold more than 80 percent of domestic equities. Many explanations have been recommended in the literature to explain this home bias puzzle include direct barriers such as capital controls and transaction costs (e.g. Stulz, 1981; Black, 1990; Chaieb and Errunza, 2007), and indirect barriers such as information costs and higher estimation uncertainty for foreign than domestic equities (e.g. Brennan and Cao, 1997; Guidolin, 2005; Ahearne et. al., 2004). Nevertheless, several studies (e.g. Karolyi and Stulz, 1996; Lewis, 1999) suggests that these explanations are weakened since the direct costs to international investment have come down significantly overtime and the financial globalization by electronic trading increases exchanges of information and decreases uncertainty across markets. Since the modern portfolio theory of Markowitz (1952) indicates how risk-averse investors can construct optimal portfolios based upon mean-variance trade-off, there are numerous studies on portfolio selection in the framework of the first two moments of the return distributions. However, as many researchers (e.g., Kendall and Hill, 1953; Mandelbrot, 1963a and 1963b; Fama, 1965) discovered that the presence of significant skewness and excess kurtosis in asset return distributions, there is a great concern that highermoments than the variance should be accounted in portfolio selection. The motivation for the generalization to higher moments arises from the theoretical work of Levy (1969) provided the cubic utility function depending on the first three moments. Later, the empirical works of Arditti (1967 and 1971) documented the investors preference for positive skewness and aversion negative skewness in return distributions of individual stocks and mutual funds, respectively. Even Markowitz (1959) himself also supports this aspect by suggesting that a mean-semi-variance trade-off [2], which gives priority to avoiding downside risk, would be superior to the original mean-variance approach. While the importance of the first three moments was recognized, there were some arguments on the incorporation of higher moments than the third into the analysis. First, Arditti (1967) suggested that most of the information about any probability distribution is contained in its first three moments. Later, Levy (1969) argued that even the higher moments are approximately functions of the first moments, but not that they are small in magnitude. Several authors (Levy, 1969; Samuelson, 1970; Rubinstein, 1973) also recommend that in general the higher moments than the variance cannot be neglected, except when at least one of the following conditions must be true: All the higher moments beyond the first are zero. The derivatives of utility function are zero for the higher moments beyond the second. The distributions of asset returns are normal or the utility functions are quadratic. However, ample evidence (e.g., Kendall and Hill, 1953; Mandelbrot, 1963a and 1963b; Fama, 1965) presented not only the higher moments beyond the first and their derivatives of the utility function are not zero, but also the asset returns are not normally distributed. Furthermore, several researchers (Tobin, 1958; Pratt, 1964; Samuelson, 1970; Levy and Sarnat, 1972) indicate that the assumption of quadratic utility function is appropriate only when return distributions are compact. Therefore, the higher moments of return distributions, such as skewness, are relevant to the investors decision on portfolio selection and cannot be ignored. In the field of portfolio theory with higher moments, Samuelson (1970) was the first author who recommends the importance of higher moments than the second for portfolio analysis. He shows that when the investment decision restrict to the finite time horizon, the use of mean-variance analysis becomes insufficient and the higher moments than the variance become more relevant in portfolio selection. Therefore, he developed three-moment model based on the cubic utility function which expressed by Levy (1969)3. Following Samuelson (1970), number of studies (e.g. Jean, 1971, 1972 and 1973; Ingersoll, 1975; and Schweser, 1978) explained the importance of skewness in security returns, derived the risk premium as functions of the first three moments, and generated the three-dimensional efficient frontier with a risk-free asset. Later, Diacogiannis (1994) proposed the multi-moment portfolio optimization programme by minimizing variance at any given level of expected return and skewness. Consequently, Athayde and Flores (1997) developed portfolio theory taking the higher moments than the variance into consideration in a utility maximizing context. The expressions in this paper greatly simplified the numerical solutions of the multi-moment portfolio optimal asset allocation problems4. 23 Levy (1969) defines the cubic utility function as U(x) which has the form: U(x) = ax + bx + cx , where x is a random variable and a,b,c are coefficients. This function is concave in a certain range but convex in another. Jurczenko, E. and Maillet, B. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. xxii. Different approaches have been developed to incorporate the individual preferences for higher-order moments into portfolio optimization. These approaches can be divided into two main groups, the primal and dual approaches. The dual approach starts from a specification of the higher-moment utility function by using the Taylors series expansion to link between the utility function and the moments of the return distribution. Then, the dual approaches will determine the optimal portfolio via its parameters reflecting preferences for the moments of asset return distribution. Harvey et. al. (2004) uses this approach to construct the set of the three-moment efficient frontier by using two sets of returns[3]. The results show that as the investors preference in skewness increases, there are sudden change points in the expected utility that lead to dramatically modifications in the allocation of the optimal portfolio. Jondeau and Rockinger (2003 and 2006) and Guidolin and Timmermann (2008) extend the dual approach in portfolio selection from three- to four-moment framework. A shortcoming of this dual approach is that the Taylor series expansion may converge to the expected utility under restrictive conditions. That is for some utility functions (e.g. the exponential function), the expansion converges for all possible levels of return, whereas for some types of utility function (e.g. the logarithm-power function), the convergence of Taylor series expansion to the expected utility is ensured only over a restricted range6. Furthermore, since Taylor series expansion have an infinite number of terms, then using a finite number of terms creates the truncation error. To circumvent these problems, the primal approach parameters that used to weight the moment deviations are not relate precisely to the utility function. Tayi and Leonard (1988) introduced the Polynomial Goal Programming (PGP), which is a primal approach to solve the goal in portfolio optimization by trade-off between competing and conflicting objectives. Later, Lai (1991) is the first researcher who proposed this method to solve the multiple objectives determining the set of the mean-variance-skewness efficient portfolios. He illustrated the three-moment portfolio selection with three objectives, which are maximizing both the expected return and the skewness, and minimizing the variance of asset returns. Follows Lai (1991) who uses a sample of five stocks and a risk-free asset, Chunhachinda et. al. (1997) and Prakash et. al. (2003) examines three-moment portfolio selection by using international stock indices. Regarding the under-diversification, many studies (e.g. Simkowitz and Beedles, 1978; Mitton and Vorkink, 2004; and Briec et. al., 2007) suggested that incorporation of the higher moments in the investors objective functions can explain portfolio under-diversification. Home bias puzzle is one of the under-diversification. It is a tendency to invest in a large proportion in domestic securities, even there are potential gains from diversification of investment portfolios across national markets. Guidolin and Timmermann (2008)[4] indicate that home bias in US can be explained by incorporate the higher moments (i.e. skewness and kurtosis) with distinct bull and bear regimes in the investors objective functions. Several researchers use the primal and the dual approaches to examine the  international portfolio selection. Jondeau and Rockinger (2003 and 2006) and Guidolin and Timmermann (2008) applied the dual approaches using a higher-order Taylor expansion of the utility function. They provide the empirical evidence that under large departure from normality of the return distribution, the higher-moment optimization is more efficient than the mean-variance framework. Chunhachinda et. al. (1997) and Prakash (2003) applied the Polynomial Goal Programming (PGP), which is a primal approach, to determine the optimal portfolios of international stock indices. Their results indicated that the incorporation of skewness into the portfolio selection problem causes a major change in the allocation of the optimal portfolio and the trade-off between expected return and skewness of the efficient portfolio. Appendix 1 presents methodology and data of the previous papers that study international portfolio selection with higher moments. In the proposed study, I will extend PGP approach to the mean-variance-skewnesskurtosis framework and investigate the international asset allocation problem that whether the incorporation of investor preferences in the higher moments of stock return distributions returns can help explain the home bias puzzle. Since previous research (e.g. Levy, 1972; Singleton and Wingerder, 1986) points out that the estimated values of the moments of the asset return distribution sensitive to the choices of an investment horizon, I will examine daily, weekly, and monthly data sets in the study[5]. The sample data will consist of daily, weekly, and monthly rates of return of five international indices for all available data from January 1975 to December 2016. These five indices cover the stock markets in the main geographical areas, namely the United States, the United Kingdom, Japan, the Pacific region (excluding Japan), and Europe (excluding United Kingdom)[6]. Moreover, the study also use three-month US Treasury bill rates as the existence of the risk-free asset in order that the investor is not restricted to invest only in risky assets. The data source of these indices is the Morgan Stanley Capital International Index (MSCI) who reports these international price indices as converted into US dollar at the spot foreign exchange rate. The MSCI stock price indices and T-bill rates are available in Datastream. The methodology proposed in the study consists of two parts. First, the rate of return distribution of each international index will be tested for normality by using the Shapiro-Wilk test. Then, the PGP approach will be utilized to determine the optimal portfolio in the fourmoment framework. 4.1 Testing for normality of return distribution At the beginning of the empirical work, I will test the normality of return distributions of international stock indices and the US T-bill rates. This test provides the foundation for examine the portfolio selection problem in the mean-variance-skewness-kurtosis framework. Although several methods are developed, there is an ample evidence that the ShapiroWilk is the best choice for evaluating normality of data under various specifications of the probability distribution. Shapiro et. al. (1968) provide an empirical sampling study of the sensitivities of nine normality-testing procedures and concluded that among those procedures, the Shapiro-Wilk statistic is a generally superior measure of non-normality. More recently, Razali and Wah (2011) compared the power of four statistical tests of normality via Monte Carlo simulation of sample data generated from various alternation distributions. Their results support that Shapiro-Wilk test is the most powerful normality test for all types of the distributions and sample sizes. The Shapiro-Wilk statistic is defined as where is the i th order statistic (rate of returns), à ¢Ã¢â‚¬ ¹Ã‚ ¯ . à ¢Ã¢â‚¬ ¹Ã‚ ¯ / is the sample mean, are the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal, and V is the covariance matrix of those order statistics. Note that the values of are provided in Shapiro-Wilk (1965) table based on the order i. The Shapiro-Wilk tests the null hypothesis of normality: H0: The population is normally distributed. H1: The population is not normally distributed.    If the p-value is less than the significant level (i.e. 1%, 5%, or 10%), then the null hypothesis of normal distribution is rejected. Thus, there is statistical evidence that the sample return distribution does not came from a normally distributed population. On the other hand, if the p-value is greater than the chosen alpha level, then the null hypothesis that the return distribution came from a normally distributed population cannot be rejected. 4.2 Solving for the multi-objective portfolio problem Following Lai (1991) and Chunhachinda et. al. (1997), the multi-objective portfolio selection with higher momentscan be examined based on the following assumptions: Investors are risk-averse individuals who maximize the expected utility of their end-ofperiod wealth. There are n + 1 assets and the (n + 1)th asset is the risk-free asset. All assets are marketable, perfectly divisible, and have limited liability. The borrowing and lending rates are equal to the rate of return r on the risk-free asset. The capital market is perfect, there are no taxes and transaction costs. Unlimited short sales of all assets with full use of the proceeds are allowed. The mean, variance, skewness, and kurtosis of the rate of return on asset are assumed to exist for all risky assets for 1,2, à ¢Ã¢â€š ¬Ã‚ ¦ . Then, I define the variables in the analysis as = ,, à ¢Ã¢â€š ¬Ã‚ ¦ , be the transpose of portfolio component , where is the percentage of wealth invested in the th risky asset, = ,, à ¢Ã¢â€š ¬Ã‚ ¦ , be the transpose of whose mean denoted by , = the rate of return on the th risky asset, = the rate of return on the risk-free asset, = a (n x 1) vector of expected excess rates of return, = the expectation operator, = the (n x 1) vector of ones, = the variance-covariance (n x n) matrix of , = the skewness-coskewness (n x n2) matrix of ,= the kurtosis-cokurtosis (n x n3) matrix of . Then, the mean, the variance, the skewness, and the kurtosis of the portfolio returns can be defined as:[7] , , à ¢Ã…  -,[8] Kurtosis = = à ¢Ã…  - à ¢Ã…  - . Note that because of certain symmetries, only ((n+1)*n)/2 elements of the skewnesscoskewness matrix and ((n+2)*(n+1)*n)/6 elements of the kurtosis-cokurtosis matrix must be computed. The components of the variance-covariance matrix, the skewness-coskewness matrix, and the kurtosis-cokurtosis matrix can be computed as follows: à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ. Therefore, the optimal solution is to select a portfolio component . The portfolio selection can be determined by solving the following multiple objectives, which are maximizing the expected return and the skewness while minimizing the variance and the kurtosis: , , à ¢Ã…  -, = à ¢Ã…  - à ¢Ã…  - . subject to 1. Since the percentage invested in each asset is the main concern of the portfolio decision, Lai (1991) suggests that the portfolio choice can be rescaled and restricted on the unit variance space (i.e. | 1 ). Under the condition of unit variance, the portfolio selection problem with skewness and kurtosis (P1) can be formulated as follows: , à ¢Ã…  -, (P1) = à ¢Ã…  - à ¢Ã…  - , subject to 1 , 1 . Usually, the solution of the problem (P1) does not satisfy three objectives (, , ) simultaneously. As a result, the above multi-objective problem (P1) involves a two-step procedure. First, a set of non-dominated solutions independent of investors preferences is developed. Then, the next step can be accomplished by incorporating investors preferences for objectives into the construction of a polynomial goal programming (PGP). Consequently, portfolio selection by satisfying the multiple objectives that is the solution of PGP can be achieved. In PGP the objective function ( ) does not contain a portfolio component , it contains deviational variables ( , , ) which represent deviations between goals and what can be achieved, given a set of constrains. Therefore, the objective function ( ) is minimization of the deviation variables ( , , ) to determine the portfolio component . Moreover, if the goals are at the same priority level, the deviations from the goals ( , , ) are non-negative variables. Given an investors preferences among mean, skewness, and kurtosis ( , , ), a PGP model can be expressed as: . subject to à ¢Ã‹â€ - , à ¢Ã…  -à ¢Ã‹â€ - , (P2) à ¢Ã…  - à ¢Ã…  - = à ¢Ã‹â€ - , 1 , 1 , ,, 0 . where à ¢Ã‹â€ - = the extreme value of objective when they are optimized individually, then à ¢Ã‹â€ - |1 , à ¢Ã‹â€ - |1 , and à ¢Ã‹â€ - |1 , = the non-negative variables which represent the deviation of and à ¢Ã‹â€ -, = the non-negative parameters representing the investors subjective degree of preferences between objectives, The combinations of represent different preferences of the mean, the skewness, and the kurtosis of a portfolio return. For example, the higher , the more important the mean (skewness or kurtosis) of the portfolio return is to the investor. Thus, the efficient portfolios are the solutions of problem (P2) for various combinations of preferences . The expected results provided in this section refer to two parts of methodology, the normality test and the international portfolio optimization in four-moment framework. 5.1 The expected results of the normality test Many researches examine the international stock indices and found that most of the stock return distributions exhibit skewness and their excess kurtosis are far from zero. For instance, in the work of Chunhachinda et. al. (1997), the Shapiro-Wilk statistics indicate 5 markets and 11 markets reject the null hypothesis of normal distribution at ten percent significant level, for weekly and monthly data, respectively. Prakash et. al. (2003) use the Jarque-Bera test to trial the normality of each international stock index, their results indicate that for 17 markets for weekly returns and 10 markets for monthly returns reject the null hypothesis of normal distribution five percent significant level. Therefore, I expected that the Shapiro-Wilk tests in the proposed study will be significant and reject the null hypothesis of normality. In other words, the return distributions of international stock markets during the period under study are expected to be non-normal. 5.2 The expected results of the multi-objective portfolio selection 5.2.1 The changes in the allocation of optimal portfolios Chunhachinda et. al. (1997) and Prakash et. al. (2003) both indicated that the incorporation of skewness into the portfolio selection problem causes a major change in the allocation of the optimal portfolio. However, their definitions of a major change are different. Chunhachinda et. al. (1997) found that there is a modification in the allocation when they compare between the mean-variance and the mean-variance-skewness efficient portfolios. However, both types of portfolios are dominated by the investment components of only four markets[9]. On the other hand, Prakash (2003) results show that the structural weights of the mean-variance and the mean-variance-skewness optimal portfolios are dominated by different markets. Therefore, I expected that when I compare between of the mean-variance efficient portfolios, the three-moment efficient portfolios, and the mean-variance efficient portfolios, the percentage invested in each asset will be different in magnitude and ranking. 5.2.2 The trade-off between expected return and skewness Most of the studies of international portfolio selection with higher moments (e.g. Chunhachinda et. al., 1997; Prakash et. al., 2003; Jondeau and Rockinger, 2003 and 2006) reported that the mean-variance efficient portfolios have the higher expected return while the three-moment efficient portfolios have greater skewness. Thus, they indicated that after incorporation of skewness into portfolio selection problem, the investor will trade the expected return of the portfolio for the skewness. More recently, Davies et. al. (2005) applied PGP to determine the set of the four-moment efficient funds of hedge funds and found not only the trade-off between the mean and the skewness, but also the trade-off between the variance and the kurtosis. Thus, I expected to discover the trade-off between the expected return and the skewness and the trade-off between the variance and the kurtosis. In addition, I will also investigate other relationships between the moments of return distribution and report them in both numerical and graphical ways. 5.2.3 The less diversification compared to the mean-variance model. To investigate whether the incorporation of higher moments than the second (i.e. skewness and kurtosis) can help explain the home bias puzzle, I will examine the hypothesis: H0: ZMV à ¢Ã¢â‚¬ °Ã‚ ¤ ZMVSK. H1: ZMV > ZMVSK. where ZMV and ZMVSK are the number of nonzero weights of the mean-variance efficient portfolios and the four-moment efficient portfolios, respectively. If the number of nonzero weights of the mean-variance efficient portfolios (ZMV) is greater than the number of nonzero weights of the four-moment efficient portfolios (ZMVSK), then I will rejected the null hypothesis. This implies that the incorporation of the higher moments into the portfolio decision can help explain the home bias puzzle. However, the results from the literature are mixed. On one hand, several researchers (e.g. Prakash et. al., 2003; Briec et. al., 2007; Guidolin and Timmermann, 2008) provided the evidence that the incorporation of skewness into the portfolio selection causes the less diversification in the efficient portfolio. On the other hand, the results of some studies (e.g. Chunhachinda et. al., 1997; Jondeau and Rockinger, 2003 and 2006) found that when compare with the mean-variance efficient portfolios, the diversification of the higher-moment efficient portfolios seem to be same or even became more diversify. I expected the results to show that the four-moment efficient portfolio is less diversified than the mean-variance one. In other words, the incorporation of the skewness and the kurtosis into the international portfolio selection can help explain the home bias. [1] Jurczenko, E. and Maillet, B. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. xxii. [2] Semi-variance is a measure of the dispersion of all observations that fall below the average or target value of a data set. [3] The first set consists of four stocks and the second set consists of four equity indices, two commodities, and a risk-free asset. 6 Jurczenko, E. Maillet, B., and Merlin, P. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. 52. [4] Guidolin and Timmermann (2008) analyze the portfolio selection problem by using the dual approach. [5] Chunhachinda et. al. (1997) and Prakash et. al. (2003) studied the portfolio selection across national stock markets by using two data sets, weekly and monthly data. [6] Guidolin and Timmermann (2008) reported that these markets represent roughly 97% of the world equity market capitalization. [7] I use the derivations of skewness and kurtosis as provided in the textbook Multi-Moment Asset Allocation and Pricing Models of Jurczenko and Maillet (2006) to transform the expectation operators into the matrix terms. [8] Let A be an (nÃÆ'-p) matrix and B an (mÃÆ'-q) matrix. The (mnÃÆ'-pq) matrix Aà ¢Ã…  -B is called the of matrix A and matrix B: [9] The four markets are Hong Kong, Netherlands, Singapore, and Switzerland. These markets have high rankings of the coefficient of variation under the sample period.

Evidence from International Stock Markets

Evidence from International Stock Markets Portfolio Selection with Four Moments: Evidence from International Stock Markets Despite the international diversification suggested by several researchers (e.g. Grulbel, 1968; Levy and Sarnat, 1970; Solnik, 1974) and the increased integration of capital markets, the home bias has not decreased (Thomas et. al., 2004 and Coeurdacier and Rey, 2013) and there is no complete explanation of this puzzle. Furthermore, there are the fastgrowing concerns of investor for extreme risks[1] and the investors preference toward odd moments (e.g. mean and skewness) and an aversion toward even moments (e.g. variance and kurtosis) considered by numerous studies (e.g. Levy, 1969; Arditti, 1967 and 1971; Jurczenko and Maillet, 2006). According to these reasons, this paper propose to investigate whether the incorporation of investor preferences in the higher moments into the international asset allocation problem can help explain the home bias puzzle. The study will allow investor preferences to depend not only the first two moments (i.e. mean and variance) but also on the higher moments, such as skewness and kurtosis, by using the polynomial goal programming (PGP) approach and then generate the three-dimensional efficient frontier. The main objective of the proposed study is to investigate whether the incorporation of skewness and kurtosis into the international stock portfolio selection causes these issues: The changes in the construction of optimal portfolios, the patterns of relationships between moments, and the less diversification compared to the mean-variance model. Since several researchers (e.g. Grulbel, 1968; Levy and Sarnat, 1970; Solnik, 1974) suggest that investment in a portfolio of equities across foreign markets provide great diversification opportunities, then investors should rebalance there portfolio away from domestic toward foreign equities. However, US investors continue to hold equity portfolios that are largely dominated by domestic assets. Thomas et. al. (2004) reported that by the end of 2003 US investors held only 14 percent of their equity portfolios in foreign stocks. Furthermore, Coeurdacier and Rey (2013) also reported that in 2007, US investors hold more than 80 percent of domestic equities. Many explanations have been recommended in the literature to explain this home bias puzzle include direct barriers such as capital controls and transaction costs (e.g. Stulz, 1981; Black, 1990; Chaieb and Errunza, 2007), and indirect barriers such as information costs and higher estimation uncertainty for foreign than domestic equities (e.g. Brennan and Cao, 1997; Guidolin, 2005; Ahearne et. al., 2004). Nevertheless, several studies (e.g. Karolyi and Stulz, 1996; Lewis, 1999) suggests that these explanations are weakened since the direct costs to international investment have come down significantly overtime and the financial globalization by electronic trading increases exchanges of information and decreases uncertainty across markets. Since the modern portfolio theory of Markowitz (1952) indicates how risk-averse investors can construct optimal portfolios based upon mean-variance trade-off, there are numerous studies on portfolio selection in the framework of the first two moments of the return distributions. However, as many researchers (e.g., Kendall and Hill, 1953; Mandelbrot, 1963a and 1963b; Fama, 1965) discovered that the presence of significant skewness and excess kurtosis in asset return distributions, there is a great concern that highermoments than the variance should be accounted in portfolio selection. The motivation for the generalization to higher moments arises from the theoretical work of Levy (1969) provided the cubic utility function depending on the first three moments. Later, the empirical works of Arditti (1967 and 1971) documented the investors preference for positive skewness and aversion negative skewness in return distributions of individual stocks and mutual funds, respectively. Even Markowitz (1959) himself also supports this aspect by suggesting that a mean-semi-variance trade-off [2], which gives priority to avoiding downside risk, would be superior to the original mean-variance approach. While the importance of the first three moments was recognized, there were some arguments on the incorporation of higher moments than the third into the analysis. First, Arditti (1967) suggested that most of the information about any probability distribution is contained in its first three moments. Later, Levy (1969) argued that even the higher moments are approximately functions of the first moments, but not that they are small in magnitude. Several authors (Levy, 1969; Samuelson, 1970; Rubinstein, 1973) also recommend that in general the higher moments than the variance cannot be neglected, except when at least one of the following conditions must be true: All the higher moments beyond the first are zero. The derivatives of utility function are zero for the higher moments beyond the second. The distributions of asset returns are normal or the utility functions are quadratic. However, ample evidence (e.g., Kendall and Hill, 1953; Mandelbrot, 1963a and 1963b; Fama, 1965) presented not only the higher moments beyond the first and their derivatives of the utility function are not zero, but also the asset returns are not normally distributed. Furthermore, several researchers (Tobin, 1958; Pratt, 1964; Samuelson, 1970; Levy and Sarnat, 1972) indicate that the assumption of quadratic utility function is appropriate only when return distributions are compact. Therefore, the higher moments of return distributions, such as skewness, are relevant to the investors decision on portfolio selection and cannot be ignored. In the field of portfolio theory with higher moments, Samuelson (1970) was the first author who recommends the importance of higher moments than the second for portfolio analysis. He shows that when the investment decision restrict to the finite time horizon, the use of mean-variance analysis becomes insufficient and the higher moments than the variance become more relevant in portfolio selection. Therefore, he developed three-moment model based on the cubic utility function which expressed by Levy (1969)3. Following Samuelson (1970), number of studies (e.g. Jean, 1971, 1972 and 1973; Ingersoll, 1975; and Schweser, 1978) explained the importance of skewness in security returns, derived the risk premium as functions of the first three moments, and generated the three-dimensional efficient frontier with a risk-free asset. Later, Diacogiannis (1994) proposed the multi-moment portfolio optimization programme by minimizing variance at any given level of expected return and skewness. Consequently, Athayde and Flores (1997) developed portfolio theory taking the higher moments than the variance into consideration in a utility maximizing context. The expressions in this paper greatly simplified the numerical solutions of the multi-moment portfolio optimal asset allocation problems4. 23 Levy (1969) defines the cubic utility function as U(x) which has the form: U(x) = ax + bx + cx , where x is a random variable and a,b,c are coefficients. This function is concave in a certain range but convex in another. Jurczenko, E. and Maillet, B. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. xxii. Different approaches have been developed to incorporate the individual preferences for higher-order moments into portfolio optimization. These approaches can be divided into two main groups, the primal and dual approaches. The dual approach starts from a specification of the higher-moment utility function by using the Taylors series expansion to link between the utility function and the moments of the return distribution. Then, the dual approaches will determine the optimal portfolio via its parameters reflecting preferences for the moments of asset return distribution. Harvey et. al. (2004) uses this approach to construct the set of the three-moment efficient frontier by using two sets of returns[3]. The results show that as the investors preference in skewness increases, there are sudden change points in the expected utility that lead to dramatically modifications in the allocation of the optimal portfolio. Jondeau and Rockinger (2003 and 2006) and Guidolin and Timmermann (2008) extend the dual approach in portfolio selection from three- to four-moment framework. A shortcoming of this dual approach is that the Taylor series expansion may converge to the expected utility under restrictive conditions. That is for some utility functions (e.g. the exponential function), the expansion converges for all possible levels of return, whereas for some types of utility function (e.g. the logarithm-power function), the convergence of Taylor series expansion to the expected utility is ensured only over a restricted range6. Furthermore, since Taylor series expansion have an infinite number of terms, then using a finite number of terms creates the truncation error. To circumvent these problems, the primal approach parameters that used to weight the moment deviations are not relate precisely to the utility function. Tayi and Leonard (1988) introduced the Polynomial Goal Programming (PGP), which is a primal approach to solve the goal in portfolio optimization by trade-off between competing and conflicting objectives. Later, Lai (1991) is the first researcher who proposed this method to solve the multiple objectives determining the set of the mean-variance-skewness efficient portfolios. He illustrated the three-moment portfolio selection with three objectives, which are maximizing both the expected return and the skewness, and minimizing the variance of asset returns. Follows Lai (1991) who uses a sample of five stocks and a risk-free asset, Chunhachinda et. al. (1997) and Prakash et. al. (2003) examines three-moment portfolio selection by using international stock indices. Regarding the under-diversification, many studies (e.g. Simkowitz and Beedles, 1978; Mitton and Vorkink, 2004; and Briec et. al., 2007) suggested that incorporation of the higher moments in the investors objective functions can explain portfolio under-diversification. Home bias puzzle is one of the under-diversification. It is a tendency to invest in a large proportion in domestic securities, even there are potential gains from diversification of investment portfolios across national markets. Guidolin and Timmermann (2008)[4] indicate that home bias in US can be explained by incorporate the higher moments (i.e. skewness and kurtosis) with distinct bull and bear regimes in the investors objective functions. Several researchers use the primal and the dual approaches to examine the  international portfolio selection. Jondeau and Rockinger (2003 and 2006) and Guidolin and Timmermann (2008) applied the dual approaches using a higher-order Taylor expansion of the utility function. They provide the empirical evidence that under large departure from normality of the return distribution, the higher-moment optimization is more efficient than the mean-variance framework. Chunhachinda et. al. (1997) and Prakash (2003) applied the Polynomial Goal Programming (PGP), which is a primal approach, to determine the optimal portfolios of international stock indices. Their results indicated that the incorporation of skewness into the portfolio selection problem causes a major change in the allocation of the optimal portfolio and the trade-off between expected return and skewness of the efficient portfolio. Appendix 1 presents methodology and data of the previous papers that study international portfolio selection with higher moments. In the proposed study, I will extend PGP approach to the mean-variance-skewnesskurtosis framework and investigate the international asset allocation problem that whether the incorporation of investor preferences in the higher moments of stock return distributions returns can help explain the home bias puzzle. Since previous research (e.g. Levy, 1972; Singleton and Wingerder, 1986) points out that the estimated values of the moments of the asset return distribution sensitive to the choices of an investment horizon, I will examine daily, weekly, and monthly data sets in the study[5]. The sample data will consist of daily, weekly, and monthly rates of return of five international indices for all available data from January 1975 to December 2016. These five indices cover the stock markets in the main geographical areas, namely the United States, the United Kingdom, Japan, the Pacific region (excluding Japan), and Europe (excluding United Kingdom)[6]. Moreover, the study also use three-month US Treasury bill rates as the existence of the risk-free asset in order that the investor is not restricted to invest only in risky assets. The data source of these indices is the Morgan Stanley Capital International Index (MSCI) who reports these international price indices as converted into US dollar at the spot foreign exchange rate. The MSCI stock price indices and T-bill rates are available in Datastream. The methodology proposed in the study consists of two parts. First, the rate of return distribution of each international index will be tested for normality by using the Shapiro-Wilk test. Then, the PGP approach will be utilized to determine the optimal portfolio in the fourmoment framework. 4.1 Testing for normality of return distribution At the beginning of the empirical work, I will test the normality of return distributions of international stock indices and the US T-bill rates. This test provides the foundation for examine the portfolio selection problem in the mean-variance-skewness-kurtosis framework. Although several methods are developed, there is an ample evidence that the ShapiroWilk is the best choice for evaluating normality of data under various specifications of the probability distribution. Shapiro et. al. (1968) provide an empirical sampling study of the sensitivities of nine normality-testing procedures and concluded that among those procedures, the Shapiro-Wilk statistic is a generally superior measure of non-normality. More recently, Razali and Wah (2011) compared the power of four statistical tests of normality via Monte Carlo simulation of sample data generated from various alternation distributions. Their results support that Shapiro-Wilk test is the most powerful normality test for all types of the distributions and sample sizes. The Shapiro-Wilk statistic is defined as where is the i th order statistic (rate of returns), à ¢Ã¢â‚¬ ¹Ã‚ ¯ . à ¢Ã¢â‚¬ ¹Ã‚ ¯ / is the sample mean, are the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal, and V is the covariance matrix of those order statistics. Note that the values of are provided in Shapiro-Wilk (1965) table based on the order i. The Shapiro-Wilk tests the null hypothesis of normality: H0: The population is normally distributed. H1: The population is not normally distributed.    If the p-value is less than the significant level (i.e. 1%, 5%, or 10%), then the null hypothesis of normal distribution is rejected. Thus, there is statistical evidence that the sample return distribution does not came from a normally distributed population. On the other hand, if the p-value is greater than the chosen alpha level, then the null hypothesis that the return distribution came from a normally distributed population cannot be rejected. 4.2 Solving for the multi-objective portfolio problem Following Lai (1991) and Chunhachinda et. al. (1997), the multi-objective portfolio selection with higher momentscan be examined based on the following assumptions: Investors are risk-averse individuals who maximize the expected utility of their end-ofperiod wealth. There are n + 1 assets and the (n + 1)th asset is the risk-free asset. All assets are marketable, perfectly divisible, and have limited liability. The borrowing and lending rates are equal to the rate of return r on the risk-free asset. The capital market is perfect, there are no taxes and transaction costs. Unlimited short sales of all assets with full use of the proceeds are allowed. The mean, variance, skewness, and kurtosis of the rate of return on asset are assumed to exist for all risky assets for 1,2, à ¢Ã¢â€š ¬Ã‚ ¦ . Then, I define the variables in the analysis as = ,, à ¢Ã¢â€š ¬Ã‚ ¦ , be the transpose of portfolio component , where is the percentage of wealth invested in the th risky asset, = ,, à ¢Ã¢â€š ¬Ã‚ ¦ , be the transpose of whose mean denoted by , = the rate of return on the th risky asset, = the rate of return on the risk-free asset, = a (n x 1) vector of expected excess rates of return, = the expectation operator, = the (n x 1) vector of ones, = the variance-covariance (n x n) matrix of , = the skewness-coskewness (n x n2) matrix of ,= the kurtosis-cokurtosis (n x n3) matrix of . Then, the mean, the variance, the skewness, and the kurtosis of the portfolio returns can be defined as:[7] , , à ¢Ã…  -,[8] Kurtosis = = à ¢Ã…  - à ¢Ã…  - . Note that because of certain symmetries, only ((n+1)*n)/2 elements of the skewnesscoskewness matrix and ((n+2)*(n+1)*n)/6 elements of the kurtosis-cokurtosis matrix must be computed. The components of the variance-covariance matrix, the skewness-coskewness matrix, and the kurtosis-cokurtosis matrix can be computed as follows: à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ. Therefore, the optimal solution is to select a portfolio component . The portfolio selection can be determined by solving the following multiple objectives, which are maximizing the expected return and the skewness while minimizing the variance and the kurtosis: , , à ¢Ã…  -, = à ¢Ã…  - à ¢Ã…  - . subject to 1. Since the percentage invested in each asset is the main concern of the portfolio decision, Lai (1991) suggests that the portfolio choice can be rescaled and restricted on the unit variance space (i.e. | 1 ). Under the condition of unit variance, the portfolio selection problem with skewness and kurtosis (P1) can be formulated as follows: , à ¢Ã…  -, (P1) = à ¢Ã…  - à ¢Ã…  - , subject to 1 , 1 . Usually, the solution of the problem (P1) does not satisfy three objectives (, , ) simultaneously. As a result, the above multi-objective problem (P1) involves a two-step procedure. First, a set of non-dominated solutions independent of investors preferences is developed. Then, the next step can be accomplished by incorporating investors preferences for objectives into the construction of a polynomial goal programming (PGP). Consequently, portfolio selection by satisfying the multiple objectives that is the solution of PGP can be achieved. In PGP the objective function ( ) does not contain a portfolio component , it contains deviational variables ( , , ) which represent deviations between goals and what can be achieved, given a set of constrains. Therefore, the objective function ( ) is minimization of the deviation variables ( , , ) to determine the portfolio component . Moreover, if the goals are at the same priority level, the deviations from the goals ( , , ) are non-negative variables. Given an investors preferences among mean, skewness, and kurtosis ( , , ), a PGP model can be expressed as: . subject to à ¢Ã‹â€ - , à ¢Ã…  -à ¢Ã‹â€ - , (P2) à ¢Ã…  - à ¢Ã…  - = à ¢Ã‹â€ - , 1 , 1 , ,, 0 . where à ¢Ã‹â€ - = the extreme value of objective when they are optimized individually, then à ¢Ã‹â€ - |1 , à ¢Ã‹â€ - |1 , and à ¢Ã‹â€ - |1 , = the non-negative variables which represent the deviation of and à ¢Ã‹â€ -, = the non-negative parameters representing the investors subjective degree of preferences between objectives, The combinations of represent different preferences of the mean, the skewness, and the kurtosis of a portfolio return. For example, the higher , the more important the mean (skewness or kurtosis) of the portfolio return is to the investor. Thus, the efficient portfolios are the solutions of problem (P2) for various combinations of preferences . The expected results provided in this section refer to two parts of methodology, the normality test and the international portfolio optimization in four-moment framework. 5.1 The expected results of the normality test Many researches examine the international stock indices and found that most of the stock return distributions exhibit skewness and their excess kurtosis are far from zero. For instance, in the work of Chunhachinda et. al. (1997), the Shapiro-Wilk statistics indicate 5 markets and 11 markets reject the null hypothesis of normal distribution at ten percent significant level, for weekly and monthly data, respectively. Prakash et. al. (2003) use the Jarque-Bera test to trial the normality of each international stock index, their results indicate that for 17 markets for weekly returns and 10 markets for monthly returns reject the null hypothesis of normal distribution five percent significant level. Therefore, I expected that the Shapiro-Wilk tests in the proposed study will be significant and reject the null hypothesis of normality. In other words, the return distributions of international stock markets during the period under study are expected to be non-normal. 5.2 The expected results of the multi-objective portfolio selection 5.2.1 The changes in the allocation of optimal portfolios Chunhachinda et. al. (1997) and Prakash et. al. (2003) both indicated that the incorporation of skewness into the portfolio selection problem causes a major change in the allocation of the optimal portfolio. However, their definitions of a major change are different. Chunhachinda et. al. (1997) found that there is a modification in the allocation when they compare between the mean-variance and the mean-variance-skewness efficient portfolios. However, both types of portfolios are dominated by the investment components of only four markets[9]. On the other hand, Prakash (2003) results show that the structural weights of the mean-variance and the mean-variance-skewness optimal portfolios are dominated by different markets. Therefore, I expected that when I compare between of the mean-variance efficient portfolios, the three-moment efficient portfolios, and the mean-variance efficient portfolios, the percentage invested in each asset will be different in magnitude and ranking. 5.2.2 The trade-off between expected return and skewness Most of the studies of international portfolio selection with higher moments (e.g. Chunhachinda et. al., 1997; Prakash et. al., 2003; Jondeau and Rockinger, 2003 and 2006) reported that the mean-variance efficient portfolios have the higher expected return while the three-moment efficient portfolios have greater skewness. Thus, they indicated that after incorporation of skewness into portfolio selection problem, the investor will trade the expected return of the portfolio for the skewness. More recently, Davies et. al. (2005) applied PGP to determine the set of the four-moment efficient funds of hedge funds and found not only the trade-off between the mean and the skewness, but also the trade-off between the variance and the kurtosis. Thus, I expected to discover the trade-off between the expected return and the skewness and the trade-off between the variance and the kurtosis. In addition, I will also investigate other relationships between the moments of return distribution and report them in both numerical and graphical ways. 5.2.3 The less diversification compared to the mean-variance model. To investigate whether the incorporation of higher moments than the second (i.e. skewness and kurtosis) can help explain the home bias puzzle, I will examine the hypothesis: H0: ZMV à ¢Ã¢â‚¬ °Ã‚ ¤ ZMVSK. H1: ZMV > ZMVSK. where ZMV and ZMVSK are the number of nonzero weights of the mean-variance efficient portfolios and the four-moment efficient portfolios, respectively. If the number of nonzero weights of the mean-variance efficient portfolios (ZMV) is greater than the number of nonzero weights of the four-moment efficient portfolios (ZMVSK), then I will rejected the null hypothesis. This implies that the incorporation of the higher moments into the portfolio decision can help explain the home bias puzzle. However, the results from the literature are mixed. On one hand, several researchers (e.g. Prakash et. al., 2003; Briec et. al., 2007; Guidolin and Timmermann, 2008) provided the evidence that the incorporation of skewness into the portfolio selection causes the less diversification in the efficient portfolio. On the other hand, the results of some studies (e.g. Chunhachinda et. al., 1997; Jondeau and Rockinger, 2003 and 2006) found that when compare with the mean-variance efficient portfolios, the diversification of the higher-moment efficient portfolios seem to be same or even became more diversify. I expected the results to show that the four-moment efficient portfolio is less diversified than the mean-variance one. In other words, the incorporation of the skewness and the kurtosis into the international portfolio selection can help explain the home bias. [1] Jurczenko, E. and Maillet, B. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. xxii. [2] Semi-variance is a measure of the dispersion of all observations that fall below the average or target value of a data set. [3] The first set consists of four stocks and the second set consists of four equity indices, two commodities, and a risk-free asset. 6 Jurczenko, E. Maillet, B., and Merlin, P. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. 52. [4] Guidolin and Timmermann (2008) analyze the portfolio selection problem by using the dual approach. [5] Chunhachinda et. al. (1997) and Prakash et. al. (2003) studied the portfolio selection across national stock markets by using two data sets, weekly and monthly data. [6] Guidolin and Timmermann (2008) reported that these markets represent roughly 97% of the world equity market capitalization. [7] I use the derivations of skewness and kurtosis as provided in the textbook Multi-Moment Asset Allocation and Pricing Models of Jurczenko and Maillet (2006) to transform the expectation operators into the matrix terms. [8] Let A be an (nÃÆ'-p) matrix and B an (mÃÆ'-q) matrix. The (mnÃÆ'-pq) matrix Aà ¢Ã…  -B is called the of matrix A and matrix B: [9] The four markets are Hong Kong, Netherlands, Singapore, and Switzerland. These markets have high rankings of the coefficient of variation under the sample period.

Evidence from International Stock Markets

Evidence from International Stock Markets Portfolio Selection with Four Moments: Evidence from International Stock Markets Despite the international diversification suggested by several researchers (e.g. Grulbel, 1968; Levy and Sarnat, 1970; Solnik, 1974) and the increased integration of capital markets, the home bias has not decreased (Thomas et. al., 2004 and Coeurdacier and Rey, 2013) and there is no complete explanation of this puzzle. Furthermore, there are the fastgrowing concerns of investor for extreme risks[1] and the investors preference toward odd moments (e.g. mean and skewness) and an aversion toward even moments (e.g. variance and kurtosis) considered by numerous studies (e.g. Levy, 1969; Arditti, 1967 and 1971; Jurczenko and Maillet, 2006). According to these reasons, this paper propose to investigate whether the incorporation of investor preferences in the higher moments into the international asset allocation problem can help explain the home bias puzzle. The study will allow investor preferences to depend not only the first two moments (i.e. mean and variance) but also on the higher moments, such as skewness and kurtosis, by using the polynomial goal programming (PGP) approach and then generate the three-dimensional efficient frontier. The main objective of the proposed study is to investigate whether the incorporation of skewness and kurtosis into the international stock portfolio selection causes these issues: The changes in the construction of optimal portfolios, the patterns of relationships between moments, and the less diversification compared to the mean-variance model. Since several researchers (e.g. Grulbel, 1968; Levy and Sarnat, 1970; Solnik, 1974) suggest that investment in a portfolio of equities across foreign markets provide great diversification opportunities, then investors should rebalance there portfolio away from domestic toward foreign equities. However, US investors continue to hold equity portfolios that are largely dominated by domestic assets. Thomas et. al. (2004) reported that by the end of 2003 US investors held only 14 percent of their equity portfolios in foreign stocks. Furthermore, Coeurdacier and Rey (2013) also reported that in 2007, US investors hold more than 80 percent of domestic equities. Many explanations have been recommended in the literature to explain this home bias puzzle include direct barriers such as capital controls and transaction costs (e.g. Stulz, 1981; Black, 1990; Chaieb and Errunza, 2007), and indirect barriers such as information costs and higher estimation uncertainty for foreign than domestic equities (e.g. Brennan and Cao, 1997; Guidolin, 2005; Ahearne et. al., 2004). Nevertheless, several studies (e.g. Karolyi and Stulz, 1996; Lewis, 1999) suggests that these explanations are weakened since the direct costs to international investment have come down significantly overtime and the financial globalization by electronic trading increases exchanges of information and decreases uncertainty across markets. Since the modern portfolio theory of Markowitz (1952) indicates how risk-averse investors can construct optimal portfolios based upon mean-variance trade-off, there are numerous studies on portfolio selection in the framework of the first two moments of the return distributions. However, as many researchers (e.g., Kendall and Hill, 1953; Mandelbrot, 1963a and 1963b; Fama, 1965) discovered that the presence of significant skewness and excess kurtosis in asset return distributions, there is a great concern that highermoments than the variance should be accounted in portfolio selection. The motivation for the generalization to higher moments arises from the theoretical work of Levy (1969) provided the cubic utility function depending on the first three moments. Later, the empirical works of Arditti (1967 and 1971) documented the investors preference for positive skewness and aversion negative skewness in return distributions of individual stocks and mutual funds, respectively. Even Markowitz (1959) himself also supports this aspect by suggesting that a mean-semi-variance trade-off [2], which gives priority to avoiding downside risk, would be superior to the original mean-variance approach. While the importance of the first three moments was recognized, there were some arguments on the incorporation of higher moments than the third into the analysis. First, Arditti (1967) suggested that most of the information about any probability distribution is contained in its first three moments. Later, Levy (1969) argued that even the higher moments are approximately functions of the first moments, but not that they are small in magnitude. Several authors (Levy, 1969; Samuelson, 1970; Rubinstein, 1973) also recommend that in general the higher moments than the variance cannot be neglected, except when at least one of the following conditions must be true: All the higher moments beyond the first are zero. The derivatives of utility function are zero for the higher moments beyond the second. The distributions of asset returns are normal or the utility functions are quadratic. However, ample evidence (e.g., Kendall and Hill, 1953; Mandelbrot, 1963a and 1963b; Fama, 1965) presented not only the higher moments beyond the first and their derivatives of the utility function are not zero, but also the asset returns are not normally distributed. Furthermore, several researchers (Tobin, 1958; Pratt, 1964; Samuelson, 1970; Levy and Sarnat, 1972) indicate that the assumption of quadratic utility function is appropriate only when return distributions are compact. Therefore, the higher moments of return distributions, such as skewness, are relevant to the investors decision on portfolio selection and cannot be ignored. In the field of portfolio theory with higher moments, Samuelson (1970) was the first author who recommends the importance of higher moments than the second for portfolio analysis. He shows that when the investment decision restrict to the finite time horizon, the use of mean-variance analysis becomes insufficient and the higher moments than the variance become more relevant in portfolio selection. Therefore, he developed three-moment model based on the cubic utility function which expressed by Levy (1969)3. Following Samuelson (1970), number of studies (e.g. Jean, 1971, 1972 and 1973; Ingersoll, 1975; and Schweser, 1978) explained the importance of skewness in security returns, derived the risk premium as functions of the first three moments, and generated the three-dimensional efficient frontier with a risk-free asset. Later, Diacogiannis (1994) proposed the multi-moment portfolio optimization programme by minimizing variance at any given level of expected return and skewness. Consequently, Athayde and Flores (1997) developed portfolio theory taking the higher moments than the variance into consideration in a utility maximizing context. The expressions in this paper greatly simplified the numerical solutions of the multi-moment portfolio optimal asset allocation problems4. 23 Levy (1969) defines the cubic utility function as U(x) which has the form: U(x) = ax + bx + cx , where x is a random variable and a,b,c are coefficients. This function is concave in a certain range but convex in another. Jurczenko, E. and Maillet, B. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. xxii. Different approaches have been developed to incorporate the individual preferences for higher-order moments into portfolio optimization. These approaches can be divided into two main groups, the primal and dual approaches. The dual approach starts from a specification of the higher-moment utility function by using the Taylors series expansion to link between the utility function and the moments of the return distribution. Then, the dual approaches will determine the optimal portfolio via its parameters reflecting preferences for the moments of asset return distribution. Harvey et. al. (2004) uses this approach to construct the set of the three-moment efficient frontier by using two sets of returns[3]. The results show that as the investors preference in skewness increases, there are sudden change points in the expected utility that lead to dramatically modifications in the allocation of the optimal portfolio. Jondeau and Rockinger (2003 and 2006) and Guidolin and Timmermann (2008) extend the dual approach in portfolio selection from three- to four-moment framework. A shortcoming of this dual approach is that the Taylor series expansion may converge to the expected utility under restrictive conditions. That is for some utility functions (e.g. the exponential function), the expansion converges for all possible levels of return, whereas for some types of utility function (e.g. the logarithm-power function), the convergence of Taylor series expansion to the expected utility is ensured only over a restricted range6. Furthermore, since Taylor series expansion have an infinite number of terms, then using a finite number of terms creates the truncation error. To circumvent these problems, the primal approach parameters that used to weight the moment deviations are not relate precisely to the utility function. Tayi and Leonard (1988) introduced the Polynomial Goal Programming (PGP), which is a primal approach to solve the goal in portfolio optimization by trade-off between competing and conflicting objectives. Later, Lai (1991) is the first researcher who proposed this method to solve the multiple objectives determining the set of the mean-variance-skewness efficient portfolios. He illustrated the three-moment portfolio selection with three objectives, which are maximizing both the expected return and the skewness, and minimizing the variance of asset returns. Follows Lai (1991) who uses a sample of five stocks and a risk-free asset, Chunhachinda et. al. (1997) and Prakash et. al. (2003) examines three-moment portfolio selection by using international stock indices. Regarding the under-diversification, many studies (e.g. Simkowitz and Beedles, 1978; Mitton and Vorkink, 2004; and Briec et. al., 2007) suggested that incorporation of the higher moments in the investors objective functions can explain portfolio under-diversification. Home bias puzzle is one of the under-diversification. It is a tendency to invest in a large proportion in domestic securities, even there are potential gains from diversification of investment portfolios across national markets. Guidolin and Timmermann (2008)[4] indicate that home bias in US can be explained by incorporate the higher moments (i.e. skewness and kurtosis) with distinct bull and bear regimes in the investors objective functions. Several researchers use the primal and the dual approaches to examine the  international portfolio selection. Jondeau and Rockinger (2003 and 2006) and Guidolin and Timmermann (2008) applied the dual approaches using a higher-order Taylor expansion of the utility function. They provide the empirical evidence that under large departure from normality of the return distribution, the higher-moment optimization is more efficient than the mean-variance framework. Chunhachinda et. al. (1997) and Prakash (2003) applied the Polynomial Goal Programming (PGP), which is a primal approach, to determine the optimal portfolios of international stock indices. Their results indicated that the incorporation of skewness into the portfolio selection problem causes a major change in the allocation of the optimal portfolio and the trade-off between expected return and skewness of the efficient portfolio. Appendix 1 presents methodology and data of the previous papers that study international portfolio selection with higher moments. In the proposed study, I will extend PGP approach to the mean-variance-skewnesskurtosis framework and investigate the international asset allocation problem that whether the incorporation of investor preferences in the higher moments of stock return distributions returns can help explain the home bias puzzle. Since previous research (e.g. Levy, 1972; Singleton and Wingerder, 1986) points out that the estimated values of the moments of the asset return distribution sensitive to the choices of an investment horizon, I will examine daily, weekly, and monthly data sets in the study[5]. The sample data will consist of daily, weekly, and monthly rates of return of five international indices for all available data from January 1975 to December 2016. These five indices cover the stock markets in the main geographical areas, namely the United States, the United Kingdom, Japan, the Pacific region (excluding Japan), and Europe (excluding United Kingdom)[6]. Moreover, the study also use three-month US Treasury bill rates as the existence of the risk-free asset in order that the investor is not restricted to invest only in risky assets. The data source of these indices is the Morgan Stanley Capital International Index (MSCI) who reports these international price indices as converted into US dollar at the spot foreign exchange rate. The MSCI stock price indices and T-bill rates are available in Datastream. The methodology proposed in the study consists of two parts. First, the rate of return distribution of each international index will be tested for normality by using the Shapiro-Wilk test. Then, the PGP approach will be utilized to determine the optimal portfolio in the fourmoment framework. 4.1 Testing for normality of return distribution At the beginning of the empirical work, I will test the normality of return distributions of international stock indices and the US T-bill rates. This test provides the foundation for examine the portfolio selection problem in the mean-variance-skewness-kurtosis framework. Although several methods are developed, there is an ample evidence that the ShapiroWilk is the best choice for evaluating normality of data under various specifications of the probability distribution. Shapiro et. al. (1968) provide an empirical sampling study of the sensitivities of nine normality-testing procedures and concluded that among those procedures, the Shapiro-Wilk statistic is a generally superior measure of non-normality. More recently, Razali and Wah (2011) compared the power of four statistical tests of normality via Monte Carlo simulation of sample data generated from various alternation distributions. Their results support that Shapiro-Wilk test is the most powerful normality test for all types of the distributions and sample sizes. The Shapiro-Wilk statistic is defined as where is the i th order statistic (rate of returns), à ¢Ã¢â‚¬ ¹Ã‚ ¯ . à ¢Ã¢â‚¬ ¹Ã‚ ¯ / is the sample mean, are the expected values of the order statistics of independent and identically distributed random variables sampled from the standard normal, and V is the covariance matrix of those order statistics. Note that the values of are provided in Shapiro-Wilk (1965) table based on the order i. The Shapiro-Wilk tests the null hypothesis of normality: H0: The population is normally distributed. H1: The population is not normally distributed.    If the p-value is less than the significant level (i.e. 1%, 5%, or 10%), then the null hypothesis of normal distribution is rejected. Thus, there is statistical evidence that the sample return distribution does not came from a normally distributed population. On the other hand, if the p-value is greater than the chosen alpha level, then the null hypothesis that the return distribution came from a normally distributed population cannot be rejected. 4.2 Solving for the multi-objective portfolio problem Following Lai (1991) and Chunhachinda et. al. (1997), the multi-objective portfolio selection with higher momentscan be examined based on the following assumptions: Investors are risk-averse individuals who maximize the expected utility of their end-ofperiod wealth. There are n + 1 assets and the (n + 1)th asset is the risk-free asset. All assets are marketable, perfectly divisible, and have limited liability. The borrowing and lending rates are equal to the rate of return r on the risk-free asset. The capital market is perfect, there are no taxes and transaction costs. Unlimited short sales of all assets with full use of the proceeds are allowed. The mean, variance, skewness, and kurtosis of the rate of return on asset are assumed to exist for all risky assets for 1,2, à ¢Ã¢â€š ¬Ã‚ ¦ . Then, I define the variables in the analysis as = ,, à ¢Ã¢â€š ¬Ã‚ ¦ , be the transpose of portfolio component , where is the percentage of wealth invested in the th risky asset, = ,, à ¢Ã¢â€š ¬Ã‚ ¦ , be the transpose of whose mean denoted by , = the rate of return on the th risky asset, = the rate of return on the risk-free asset, = a (n x 1) vector of expected excess rates of return, = the expectation operator, = the (n x 1) vector of ones, = the variance-covariance (n x n) matrix of , = the skewness-coskewness (n x n2) matrix of ,= the kurtosis-cokurtosis (n x n3) matrix of . Then, the mean, the variance, the skewness, and the kurtosis of the portfolio returns can be defined as:[7] , , à ¢Ã…  -,[8] Kurtosis = = à ¢Ã…  - à ¢Ã…  - . Note that because of certain symmetries, only ((n+1)*n)/2 elements of the skewnesscoskewness matrix and ((n+2)*(n+1)*n)/6 elements of the kurtosis-cokurtosis matrix must be computed. The components of the variance-covariance matrix, the skewness-coskewness matrix, and the kurtosis-cokurtosis matrix can be computed as follows: à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ, à ¢Ã‹â€ Ã¢â‚¬Ëœ. Therefore, the optimal solution is to select a portfolio component . The portfolio selection can be determined by solving the following multiple objectives, which are maximizing the expected return and the skewness while minimizing the variance and the kurtosis: , , à ¢Ã…  -, = à ¢Ã…  - à ¢Ã…  - . subject to 1. Since the percentage invested in each asset is the main concern of the portfolio decision, Lai (1991) suggests that the portfolio choice can be rescaled and restricted on the unit variance space (i.e. | 1 ). Under the condition of unit variance, the portfolio selection problem with skewness and kurtosis (P1) can be formulated as follows: , à ¢Ã…  -, (P1) = à ¢Ã…  - à ¢Ã…  - , subject to 1 , 1 . Usually, the solution of the problem (P1) does not satisfy three objectives (, , ) simultaneously. As a result, the above multi-objective problem (P1) involves a two-step procedure. First, a set of non-dominated solutions independent of investors preferences is developed. Then, the next step can be accomplished by incorporating investors preferences for objectives into the construction of a polynomial goal programming (PGP). Consequently, portfolio selection by satisfying the multiple objectives that is the solution of PGP can be achieved. In PGP the objective function ( ) does not contain a portfolio component , it contains deviational variables ( , , ) which represent deviations between goals and what can be achieved, given a set of constrains. Therefore, the objective function ( ) is minimization of the deviation variables ( , , ) to determine the portfolio component . Moreover, if the goals are at the same priority level, the deviations from the goals ( , , ) are non-negative variables. Given an investors preferences among mean, skewness, and kurtosis ( , , ), a PGP model can be expressed as: . subject to à ¢Ã‹â€ - , à ¢Ã…  -à ¢Ã‹â€ - , (P2) à ¢Ã…  - à ¢Ã…  - = à ¢Ã‹â€ - , 1 , 1 , ,, 0 . where à ¢Ã‹â€ - = the extreme value of objective when they are optimized individually, then à ¢Ã‹â€ - |1 , à ¢Ã‹â€ - |1 , and à ¢Ã‹â€ - |1 , = the non-negative variables which represent the deviation of and à ¢Ã‹â€ -, = the non-negative parameters representing the investors subjective degree of preferences between objectives, The combinations of represent different preferences of the mean, the skewness, and the kurtosis of a portfolio return. For example, the higher , the more important the mean (skewness or kurtosis) of the portfolio return is to the investor. Thus, the efficient portfolios are the solutions of problem (P2) for various combinations of preferences . The expected results provided in this section refer to two parts of methodology, the normality test and the international portfolio optimization in four-moment framework. 5.1 The expected results of the normality test Many researches examine the international stock indices and found that most of the stock return distributions exhibit skewness and their excess kurtosis are far from zero. For instance, in the work of Chunhachinda et. al. (1997), the Shapiro-Wilk statistics indicate 5 markets and 11 markets reject the null hypothesis of normal distribution at ten percent significant level, for weekly and monthly data, respectively. Prakash et. al. (2003) use the Jarque-Bera test to trial the normality of each international stock index, their results indicate that for 17 markets for weekly returns and 10 markets for monthly returns reject the null hypothesis of normal distribution five percent significant level. Therefore, I expected that the Shapiro-Wilk tests in the proposed study will be significant and reject the null hypothesis of normality. In other words, the return distributions of international stock markets during the period under study are expected to be non-normal. 5.2 The expected results of the multi-objective portfolio selection 5.2.1 The changes in the allocation of optimal portfolios Chunhachinda et. al. (1997) and Prakash et. al. (2003) both indicated that the incorporation of skewness into the portfolio selection problem causes a major change in the allocation of the optimal portfolio. However, their definitions of a major change are different. Chunhachinda et. al. (1997) found that there is a modification in the allocation when they compare between the mean-variance and the mean-variance-skewness efficient portfolios. However, both types of portfolios are dominated by the investment components of only four markets[9]. On the other hand, Prakash (2003) results show that the structural weights of the mean-variance and the mean-variance-skewness optimal portfolios are dominated by different markets. Therefore, I expected that when I compare between of the mean-variance efficient portfolios, the three-moment efficient portfolios, and the mean-variance efficient portfolios, the percentage invested in each asset will be different in magnitude and ranking. 5.2.2 The trade-off between expected return and skewness Most of the studies of international portfolio selection with higher moments (e.g. Chunhachinda et. al., 1997; Prakash et. al., 2003; Jondeau and Rockinger, 2003 and 2006) reported that the mean-variance efficient portfolios have the higher expected return while the three-moment efficient portfolios have greater skewness. Thus, they indicated that after incorporation of skewness into portfolio selection problem, the investor will trade the expected return of the portfolio for the skewness. More recently, Davies et. al. (2005) applied PGP to determine the set of the four-moment efficient funds of hedge funds and found not only the trade-off between the mean and the skewness, but also the trade-off between the variance and the kurtosis. Thus, I expected to discover the trade-off between the expected return and the skewness and the trade-off between the variance and the kurtosis. In addition, I will also investigate other relationships between the moments of return distribution and report them in both numerical and graphical ways. 5.2.3 The less diversification compared to the mean-variance model. To investigate whether the incorporation of higher moments than the second (i.e. skewness and kurtosis) can help explain the home bias puzzle, I will examine the hypothesis: H0: ZMV à ¢Ã¢â‚¬ °Ã‚ ¤ ZMVSK. H1: ZMV > ZMVSK. where ZMV and ZMVSK are the number of nonzero weights of the mean-variance efficient portfolios and the four-moment efficient portfolios, respectively. If the number of nonzero weights of the mean-variance efficient portfolios (ZMV) is greater than the number of nonzero weights of the four-moment efficient portfolios (ZMVSK), then I will rejected the null hypothesis. This implies that the incorporation of the higher moments into the portfolio decision can help explain the home bias puzzle. However, the results from the literature are mixed. On one hand, several researchers (e.g. Prakash et. al., 2003; Briec et. al., 2007; Guidolin and Timmermann, 2008) provided the evidence that the incorporation of skewness into the portfolio selection causes the less diversification in the efficient portfolio. On the other hand, the results of some studies (e.g. Chunhachinda et. al., 1997; Jondeau and Rockinger, 2003 and 2006) found that when compare with the mean-variance efficient portfolios, the diversification of the higher-moment efficient portfolios seem to be same or even became more diversify. I expected the results to show that the four-moment efficient portfolio is less diversified than the mean-variance one. In other words, the incorporation of the skewness and the kurtosis into the international portfolio selection can help explain the home bias. [1] Jurczenko, E. and Maillet, B. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. xxii. [2] Semi-variance is a measure of the dispersion of all observations that fall below the average or target value of a data set. [3] The first set consists of four stocks and the second set consists of four equity indices, two commodities, and a risk-free asset. 6 Jurczenko, E. Maillet, B., and Merlin, P. (2006) Multi-Moment Asset Allocation and Pricing Models, Wiley Finance, p. 52. [4] Guidolin and Timmermann (2008) analyze the portfolio selection problem by using the dual approach. [5] Chunhachinda et. al. (1997) and Prakash et. al. (2003) studied the portfolio selection across national stock markets by using two data sets, weekly and monthly data. [6] Guidolin and Timmermann (2008) reported that these markets represent roughly 97% of the world equity market capitalization. [7] I use the derivations of skewness and kurtosis as provided in the textbook Multi-Moment Asset Allocation and Pricing Models of Jurczenko and Maillet (2006) to transform the expectation operators into the matrix terms. [8] Let A be an (nÃÆ'-p) matrix and B an (mÃÆ'-q) matrix. The (mnÃÆ'-pq) matrix Aà ¢Ã…  -B is called the of matrix A and matrix B: [9] The four markets are Hong Kong, Netherlands, Singapore, and Switzerland. These markets have high rankings of the coefficient of variation under the sample period.

Saturday, January 18, 2020

Nitric Acid

Nitric acid is a highly reactive oxidizing agent used in making fertilizers, explosives, and rocket fuels, and in a wide variety of industrial metallurgical processes. It is also a component of acid rain. Its chemical formula is HNO3 and it has been known as â€Å"aqua fortis†, which means strong water, to alchemists. It is a transparent, colorless to yellowish, fuming corrosive liquid. Nitric acid is a strong acid and therefore it completely dissociates in water. It has a gravity of 1. 41 and the concentration of the hydronium ions(1) yields a pH of 0. . Its boiling point is 122C and its melting point is -42C. It was first mentioned by Pseuso-Geber, a European alchemist born in the 13th century. Described by Albert the Great in the 13th century and named by Ramon Lull, who prepared it and called it â€Å"eau forte† (aqua fortis). There were people saying that it was discovered by Joseph-Louis Gay-Lussac or Johann Rudolf, but nobody knows who really did discover that. A s it is a intoxicating, oxidizing acid, it reacts most with metals, but does not react with pure gold.However, noble metals could be oxidized and dissolved by nitric acid which leads to colour changes of gold-alloy surface. So nitric acid is used in jewelry shops to spot low-gold alloys (< 14 carats(2)) and to asses the gold purity. Nitric acid also reacts powerfully with most of the organic material, which may also explode. It reacts with non-metallic elements except for nitrogen, oxygen, noble gases, silicon and halogens. It oxides them to their highest oxidation states(3) as acids with the formation of nitrogen dioxide for concentrated acid and nitric oxide for dilute acid.Chromium (Cr), iron (Fe) and aluminium (Al) dissolve in dilute nitric acid, which the concentrated acid forms a metal oxide layer that protects the metal from further oxidation, and it is called passivation. Nitric acid can be made in laboratory or industrially. In laboratory, nitric acid can be made from coppe r(II) nitrate or by reacting approximately equal masses of a nitrate salt with 96% sulfuric acid (H2SO4), and distilling this mixture at nitric acid's boiling point of 83  °C until only a white crystalline mass, a metal sulfate, remains. Then, the red fuming itric acid obtained may be converted to the white nitric acid, which the equation is H2SO4 + NO? 3 > HSO? 4(s) + HNO3(g). In view of the fact that it is a really violent and strong acid, people make this acid for many different uses. It can be used in various forms as the oxidizer in liquid-fueled rockets. The forms include red fuming nitric acid and white fuming nitric acid. Red fuming nitric acid, known as RFNA, is a oxidizer used as a rocket propellant, which can be stored very long. It consists mainly of nitric acid, but also contains 13% of dinitrogen tetroxide(4) and 3% of water.It breaks down to a certain degree to form nitrogen dioxide. The white fuming nitric acid, known as WFNA, does not contain free dinitrogen tetro xide. It consists of pure nitric acid with 2% of water and less than 0. 5% of dissolved nitrogen dioxide. If the forms are mixed with sulfuric acid, it forms with the HF inhibitor. Nitric acid can also be used in some woodwork. In a low concentration (10% of nitric acid in water), it is sometimes used to artificially make pines and maple look older. It produces a grey-gold, old looking wood colour on wood.By looking at the usage of nitric acid, we can see that, this kind of acid has a great impact to the society and the global economy. As it is not quite expensive, and you can make it in laboratories, there were many incidents where people throw glasses containers holding nitric acid on crowed streets. Many people got hurt, the nitric acid burnt through their clothes and burn them. Concentrated nitric acid makes human skin yellow, because of a reaction with keratin(5). The keratin is the key structural material making up the outer layer of the human skin, and it is also a structural component of hair and nails.It will turn orange when neutralized. However, this acid has many usages and also helps us a lot. It helps the astronauts to fly to space where nitric acid is used in rocket fuels. It also helps us decorate our places with artificial old wood furniture. This acid creates more job opportunities in the job market as the companies need people to work for it. Nitric acid is extremely hazardous and corrosive, and mostly, a poison. Inhaling will cause you breathing problems and lead to pneumonia and pulmonary edema, which may be fatal.Other symptoms may include choking, coughing, irritation of both nose and throat, and also respiratory tract. Ingesting it can cause sudden burn or pain in the mouth, throat, esophagus, and gastrointestinal tract. It can also cause skin burns if there is any skin contact. Concentrated solutions can cause deep ulcers and stain skin a yellow or yellow-brown colour. If it gets into the eye, it is even worse, as it is corrosive, the vapors are irritating and will cause damage to the eyes including burns and permanent eye damage.Long-term exposure to concentrated vapors may cause erosion of teeth and lung damage. Long-term exposures seldom occur due to the corrosive properties of the acid. People with pre-existing skin disorders, eye disease, or cardiopulmonary diseases must be susceptible to the effects of this substance. There are rules to follow when using the nitric acid. If people don’t follow it, it will be very dangerous to use it. Acid rain is a form of precipitation which contains a high level of sulfuric and nitric acids.It has a pH of approximately 5. 5-5. 6. It is produced when sulfur dioxide and various nitrogen oxides combine together with atmospheric moisture. Acid rain can contaminate drinking water, damage the plants and aquatic life. It also erode buildings and monuments. If the plants are damaged, people won’t be abled to see the green things again and will also affect our eye-si ght. And we won’t have vegetables to eat after acid rain because acid may cause many harmful effects to our body. If we still eat the vegetables, then we be sick.The government had made an effort to reduce the amount of sulfur dioxide released, but it can be produced naturally by volcanic eruptions. Nitrogen oxide can be produced by lightning strikes. Acid rain had became a political issue in 1980s, where Canada claimed that pollutants from the US were contaminating the forests and waters, so power plants were asked to reduce the amount of sulfur dioxide released. Although there are harmful effects of nitric acid, people still keep on producing nitric acid. They only reduced producing them, still shows that there are still benefits of this acid! Nitric Acid Copper + Nitric Acid Copper is a reddish-brown metal, widely used in plumbing and electrical wiring; it is perhaps most familiar to people in the United States in the form of the penny. (Although since 1983, pennies are actually made of zinc surrounded by a paper-thin copper foil to give them the traditional appearance of pennies. ) Copper is oxidized by concentrated nitric acid, HNO3, to produce Cu2+ ions; the nitric acid is reduced to nitrogen dioxide, a poisonous brown gas with an irritating odor: Cu(s) + 4HNO3(aq) ——> Cu(NO3)2(aq) + 2NO2(g) + 2H2O(l)When the copper is first oxidized, the solution is very concentrated, and the Cu2+ product is initially coordinated to nitrate ions from the nitric acid, giving the solution first a green, and then a greenish-brownish color. When the solution is diluted with water, water molecules displace the nitrate ions in the coordinate sites around the copper ions, causing the solution to change to a blue color. In dilute nitric aci d, the reaction produces nitric oxide, NO, instead: 3Cu(s) + 8HNO3(aq) ——> 3Cu(NO3)2(aq) + 2NO(g) + 4H2O(l)In the following demonstration, a balled-up piece of thin copper wire is added to about 100 mL of concentrated nitric acid; once the copper is added the evolution of nitrogen dioxide occurs quickly. Once all of the copper has reacted, the solution is diluted with distilled water, changing the solution from a dark brown to a pale blue color. This demonstration can be done with copper in the form of shot, pellets, thicker wire, or bars, but is a great deal slower than with copper wire. Video Clip: REAL, 7. 02 MB [pic] |[pic] | |[pic] |[pic] | |[pic] |[pic] | |[pic] |[pic] | |[pic] |[pic] |[pic] |[pic] | |[pic] |[pic] | |[pic] |[pic] | |[pic] |[pic] |A Historical Sidelight: Ira Remsen on Copper and Nitric Acid Ira Remsen (1846-1927) founded the chemistry department at Johns Hopkins University, and founded one of the first centers for chemical research in the United S tates; saccharin was discovered in his research lab in 1879. Like many chemists, he had a vivid â€Å"learning experience,† which led to a heightened interest in laboratory work: While reading a textbook of chemistry I came upon the statement, â€Å"nitric acid acts upon copper. † I was getting tired of reading such absurd stuff and I was determined to see what this meant.Copper was more or less familiar to me, for copper cents were then in use. I had seen a bottle marked nitric acid on a table in the doctor's office where I was then â€Å"doing time. † I did not know its peculiarities, but the spirit of adventure was upon me. Having nitric acid and copper, I had only to learn what the words â€Å"act upon† meant. The statement â€Å"nitric acid acts upon copper† would be something more than mere words. All was still. In the interest of knowledge I was even willing to sacrifice one of the few copper cents then in my possession.I put one of them on the table, opened the bottle marked nitric acid, poured some of the liquid on the copper and prepared to make an observation. But what was this wonderful thing which I beheld? The cent was already changed and it was no small change either. A green-blue liquid foamed and fumed over the cent and over the table. The air in the neighborhood of the performance became colored dark red. A great colored cloud arose. This was disagreeable and suffocating. How should I stop this? I tried to get rid of the objectionable mess by picking it up and throwing it out of the window.I learned another fact. Nitric acid not only acts upon copper, but it acts upon fingers. The pain led to another unpremeditated experiment. I drew my fingers across my trousers and another fact was discovered. Nitric acid acts upon trousers. Taking everything into consideration, that was the most impressive experiment and relatively probably the most costly experiment I have ever performed. . . . It was a revelation to me. It resulted in a desire on my part to learn more about that remarkable kind of action.Plainly, the only way to learn about it was to see its results, to experiment, to work in a laboratory. from F. H. Getman, â€Å"The Life of Ira Remsen†; Journal of Chemical Education: Easton, Pennsylvania, 1940; pp 9-10; quoted in Richard W. Ramette, â€Å"Exocharmic Reactions† in Bassam Z. Shakhashiri, Chemical Demonstrations: A Handbook for Teachers of Chemistry, Volume 1. Madison: The University of Wisconsin Press, 1983, p. xiv: !!! Hazards !!! Nitric acid is extremely corrosive. Handle with care. The nitrogen dioxide produced in this reaction is poisonous. This reaction must be done in a fume hood!

Friday, January 10, 2020

Health for All Children

Is health for all children an achievable goal? The world’s children have rights to health which are enshrined in international law. The United Nations Convention on the Rights of the Child Articles 6 and 24 pertain to the rights of children to life, survival and development, enjoyment of the highest attainable standards of health and facilities for the treatment of illness and the rehabilitation of health (Block 4, p. 94).However, every year throughout the world vast numbers of children suffer ill health and die. Nearly 11 million children still die each year before their fifth birthday, often from readily preventable causes. An estimated 150 million children are malnourished (UNICEF 2001) (Block 4, p. 94. ) What follows is an exploration of the causes and treatments of ill health looking at the major challenges of poverty, inequality, culture and gender, and the social and political dimensions of such matters.The effectiveness or otherwise of international health intervention programmes is analysed and a measure of the progress made so far and the possibility of health for the world’s children becoming a realistic goal is discussed. Health is a culturally constructed concept, a collection of ideas and beliefs gathered from our experiences of living within a family, community and wider society. It is recognised by health professionals, theorists and researchers that being healthy means different things to different people.When considering matters of health it needs to be understood that health and disease are complex terms that are more than just a matter of genetics. Health is influenced by personal, cultural, social, economic and political circumstances. The definition of the term health as used by the World Health Organisation (WHO) since 1948 is as follows: ‘a state of complete physical, mental, and social well-being and not merely the absence of disease or infirmity’. (WHO, 2009). The WHO definition promotes an holistic view of h ealth that has been criticised for being idealistic and difficult to put into practice.What is important about this definition is that it is a positive interpretation that implies that health for all is something that can be achieved. Certainly this definition has aided thinking around health as more than simply the absence of infirmity and emphasises a social dimension. Globalisation, economics, adverse living conditions, the lack of availability of primary health care, differing social practices and cultural notions of health are all factors that impact on the health of people.These factors present both challenges and opportunities for the world regarding the possibility of achieving health for all children. Medical advancements in the latter half of the twentieth century has seen most notably the development of antibiotics, vitamins, vaccinations for serious infectious diseases such as Measles, Mumps, Rubella and Chicken Pox, to name but a few, along with a vaccination that eradi cated Small Pox.One advantage of globalisation is the increasing awareness of the plight of children in developing countries which has marshalled medical intervention and has resulted in a drastic decrease in child and young people’s mortality rates. However, despite advancements in medical technology, the availability of health treatments has not guaranteed the eradication of some preventable and curable illnesses (for example, Diarrhoea).Diarrhoea can be treated very effectively with a low cost intervention. Oral Rehydration Salts (ORS) prevent dehydration which is the cause of deaths amongst children with diarrhoea. However, in studies of the Huli people in Papua New Guinea it was noted that although at first the mortality rate from diarrhoea fell as a result of the ORS intervention programme, the improvements were not sustained and the Huli people became dissatisfied with the treatment.The Huli people desired a treatment that would address the symptoms of diarrhoea: dry u p the runny stools of the sick children. Administering ORS fluids didn’t make sense and clashed with their understanding of the illness. Furthermore, the need to dissolve the ORS medication in water necessitates a clean water supply, something so basic but something that isn’t always available in communities in the South. The ‘Miracle cure’ or ‘Magic bullet’ for diarrhoea, ORS, is an example of how selective, vertical interventions may save lives.But it is also a prime example of how a purely medical approach to health does little to improve the quality of lives when other causes of illness such as poor sanitation and lack of clean water are not addressed. (Block 4, p. 125). A Western biomedical approach to the treatment of ill health has its limitations. Technological cures in the form of drugs, although vitally important, will on their own do little but not enough to make health an attainable goal for the world’s children.The concept of human rights and rights for children has gained increased recognition across the world. The status of children has been raised and children’s interests placed on political agenda’s throughout many states. ‘As of November 2009, 194 countries ratified, accepted, or acceded to the UNCRC (some with stated reservations or interpretations) including every member of the United Nations except Somalia and the United States. Somalia has announced that it would shortly do so’ (Wikipedia, 2010).Yet there remains concern about the real levels of commitment to concepts of children’s rights and concern about the lack of accountability to make nations uphold right’s for children. Through media coverage of world catastrophes, such as famines and droughts and through campaigns delivered by humanitarian and charitable organisations an ethical and moral debate is taking place about the need to address global health that has pricked the moral conscience. What is now required is effective systems that can help realise children’s rights and mobilise efforts to make health for all an achievable goal.The economic power of some nations and global corporations, and structural adjustment programmes (SAP’s) have created imbalances of power and forces that have worked against health goals with the effect of widening economic disparities between rich and poor across and within nations. SAP’s have been imposed to ensure debt repayment and economic restructuring. But some poor countries have had to reduce spending on things like health, education and development, while debt repayment and other economic policies have been made the priority.For many basic health care has become a service that can only be accessed if an individual has money to purchase it. Free health care has become less about a human right and more of a commodity to be bought. A further challenge to health for children in relation to economics is that within coun tries where there is political instability and conflict nations priorities become one of national security, funding arms and defense programmes and as a result there is decreased funding for basic care and education. At present an attitude prevails that nations should ‘look after heir own’. There does exists a humanitarian approach to supporting poorer countries at times of emergency but there are no effective systems that legally oblige nations to work together to ensure that basic living conditions, health care and the right’s of children are upheld. A change of attitude within and across nations and governments regarding whose responsibility it is to intervene and the importance of intervening to produce more egalitarian societies would go a long way to making health for all children an achievable goal.Global medical advancements, the development in the concept of rights for children internationally and world economic systems have been investigated to demonstr ate how they have resulted in both opportunities and challenges to improving health for all children. Yet it is also necessary to look closer at the more personal experiences encountered by children and families and focus on the social and cultural factors that impact on health.Securing health for all children requires more than having medical expertise and drugs on hand to prevent and/or treat medical ailments. Several examples of differing cultural understandings around illness can be offered that illustrates this idea. The Bozo tribe of Mali believe that red urine in adolescent boys, a condition caused by a parasitic infection, is normal and indicates sexual maturity; as such it is celebrated as a sign of males reaching manhood. Within the Bozo tribal people the symptoms are not viewed as a sign of illness and the condition goes untreated.In Nigeria 76% of women perceive diarrhoea as a symptom of teething and as such a normal part of growth and development and not something which requires treatment (Block 4, p. 103). In both these examples the cultural and social dimensions of ill health contrast with Western biomedical approaches to children’s health. When culturally interpreted ideas of health conflict with medical systems where there is a focus purely on the biological causation of illness, the acceptance of a diagnosis and treatment of a condition can be problematic.Some challenges in achieving health for all children is managing and resolving the clash of differing world views regarding health, that is, people’s perceptions of health together with their level of understanding and acceptance of scientific notions of health, and how to increase community participation in health programmes. UNICEF states that ‘chronic poverty remains the greatest obstacle to fulfilling the rights of children’. In the UNICEF book, ‘We are the Children’, it is cited that half of humanity is desperately impoverished and half of the 1. billion people forced to live on less than $1 per day are children. (Block 4, p. 108). UNICEF and the World Bank have defined absolute poverty (less than $1 per day per person) as being the minimum amount that purchases the goods and services deemed necessary for basic survival. (Block 4, p. 49). This definition is most appropriate for those living in the poorest countries of the South, however, poverty affects many children living within the richest countries of the world also.Relative rather than absolute poverty, that is, the inequality and deprivation experienced relative to those better off living in the same society, can impact on health causing emotional stress, humiliation and social exclusion. Andrea Ashworth writing about her experiences of growing up in Manchester in the 1970’s described the multiple effects of poverty that she experienced; living in a flea infested home, eating a less than nutritious diet, the shame of not being able to afford certain basic items of food, the stress that poverty had on her mother and how it manifested symptoms of depression that impacted on the whole family. Reading B, Ashworth). Studies by the Child Poverty Action Group in the United Kingdom concludes that children growing up in poverty are more likely to be born prematurely, suffer chronic illnesses in later life, die from accidents, live in poor quality homes, have fewer employment opportunities, get in trouble with the police and be at greater risk of alcohol or drug misuse. Poverty impacts on both the physical and mental health of children and their overall quality of life. (Block 4, p. 57).In order to make improvements in the health of the world’s children it is necessary therefore not simply to make health care freely available to all but to confront and tackle wider issues of social justice, inequality and poverty. Cuba is an example of a country with limited material resources that has created a more egalitarian society by providing food, emp loyment, education and health care for all. They now have infant mortality rates on a par with some of the world’s wealthiest countries.Similarly, in Bangladesh as a result of a national commitment to invest in basic social services, the under fives mortality rate has decreased substantially. (Block 4, p. 109). This is strong evidence of the ability to make health for all an achievable goal if there is government commitment to tackling social justice and inequality. A further dimension of inequality is the discrimination in matters of health based on gender, birth order and social status at a local level.In cases of malnutrition in Mali, Dettwyler identified that access or entitlement to resources is shaped ‘by the social relations prevailing between and within families within communities’ (Block 4, p. 119). Dettwyler provides an example of discrimination against children that begins with discrimination against the mother. Aminata, since she was fostered by the f amily, was considered to be of low status. When she became pregnant with twins her status was further lowered along with her entitlement to food and freedoms.She had to accept a life of drudgery and hard work providing for others in the family which took precedence over caring for her own children who were suffering from malnutrition despite food being in plentiful supply. Aminata’s quality of life only improved when one of her children died, the other was sent away and Aminata married into a new family. Her social standing increased along with her quality of life. Aminata gave birth to three more children, two of whom survived and were reported to be only mildly malnourished. Reading C). Beliefs about female inferiority within many parts of the world impacts on rates of malnutrition and mortality amongst girls compared to boys. Studies have shown in India and China that girls are less likely to be breast fed for as long boys, are less likely to be given extra food and more l ikely to be abandoned. These social attitudes and practices towards girls can be changed through development policy on the education of females.Through education the chances of health and survival of children can be improved (Block 4, p. 116) It has been argued that to achieve health for all children multiple factors need to be addressed. Free basic primary health care needs to be available to all, yet this on its own will do a little but not enough to sustain health and survival. Sustainability requires adequate housing, sanitation, clean water and an environment free from pollutants. Education, skills training and employment enable people to contribute to society.They are determinants of health in that they raise self-esteem, feelings of worth and have the ability to empower, organise and rally people together to make changes to advance wealth and health. The health of the world’s children cannot be left in the hands of humanitarian and charitable organisations. Unscrupulou s governments and some economic policies are malign forces that impede progress. The ethical and moral questions regarding international intervention and the level of responsibility that different nations should or can have towards the peoples of other nations are difficult to answer.However, the goal of health for all, as complicated or impossible it may at first seem, has seen progress which should not be underestimated. Within sixty years the WHO has been set up, the UNCRC has been established, international policies have been devised that have bound nations to working together, unprecedented medical knowledge has been gained, lessons regarding what has worked and hasn’t worked have been learnt, cultural understandings have been developed and ethical and moral debates keep the issue of poverty and health in the minds of all.The world is entering a crucial phase where the scope to tackle world poverty and health of children is beginning to be realised. The know-how, experti se and resources exist to achieve health for all children. Perhaps the greatest challenge to success is establishing worldwide commitment to the endeavour.Word count 2,505 References Open University (2007) U212, Changing Childhoods, Local and Global, Block 4, Achieving Health for Children, Milton Keynes, The Open University Open University (2007), Changing Childhoods, Local and Global, Block 4, Achieving Health for all Children, Reading C, ‘Cases of Malnutrition in Mali’, Milton Keynes, The Open University. Open University (2007), Changing Childhoods, Local and Global, Block 4, Children, Poverty and Social Inequality, Reading B, ‘Once in a House on Fire’, Milton Keynes, The Open University. Wikipedia 2010 http://en. wikipedia. org/wiki/UNCRC [accessed 5 September 2010] World Health Organisation 2003 http://en. wikipedia. org/wiki/UNCRC [accessed 5 September 2010]