Effect of intervalling and skewness on portfolio selection in developed and developing markets

Abstract

Based on several research studies and in particular the theoretical study of Prakash et al. (1997), it is known that the variance as well as the skewness of the probability distribution of rates of return increases if the investors’ investment interval increases. In the present study, using the portfolio selection procedure developed by Lai (1991) under the presence of skewness and subsequently used by Chunhachinda et al. (1997) and Prakash et al. (2003), we find that the selection of investment interval (e.g. daily, weekly versus monthly) significantly changes not only the optimal allocation of weights, but also the number of markets selected in the portfolio.

Notes

¹ See Harris et al. (2004, p. 195).

² See Josey et al. (2001). To avoid any confusion with phrases like ‘invest horizon’, ‘holding period rate of return’, etc., we have adopted the phrase ‘investment interval’ throughout this article.

³ This brief discussion on the effect of intervalling on variance and skewness of the rates of return probability distribution is largely taken from Prakash et al. (1997).

⁴ Dividends are ignored. Whether they are deterministic or random they can be considered a part of P_{j− 1} or , respectively.

⁵ Whether we examine the probability distribution of or one plus the rate of return (wealth ratio) the result remains the same.

⁶ Some of the skewness measures are negative. Here, we provide the count for absolute skewness only. If, however, we do not ignore the negative signs, then the weekly skewness is two, rather than one, instances is greater than its monthly counterparts.

⁷ To convert the SD of the annualized weekly return to the weekly return, divide the obtained SD by the square root of 52. Similarly, the monthly SD can be obtained by dividing the SD of the annualized monthly return by the square root of 12.

⁸ There will not be any difference in the measure of skewness whether it is obtained ‘holding period’ or nominally annualized returns.

⁹ See Prakash et al. (2003) for exact definitions of a and b.

¹⁰ Other combination values of a and b are provided because in this programming problem one can increase the preferences for a parameter at will. However, theoretically speaking, this article is concerned mainly with the comparison of mean-variance versus mean-variance-skewness preferences.

¹¹ We are indebted to an anonymous referee for pointing this findings out. The explanations have been provided about these seemingly ‘implausible’ findings.