International Portfolio Formation, Skewness & the Role of Gold (2006)
This paper investigates the role of higher moments in portfolio selection and outlines the potential role of gold in equity portfolios.
The paper firstly discusses that ignoring higher moments in portfolio selection only holds under very restrictive assumptions such as no utility placed on the higher moments, the normally distributed asset returns and the quadratic utility function, which however are challengeable. In the real world, asset returns are usually not normally distributed and investors are assumed to have a preference for positive over negative skewness.
By applying Polynomial Goal Programming, the mean-variance optimal portfolios and mean-skewness-variance optimal portfolios are constructed using weekly, monthly and quarterly data.
Examining the FTSE indices, gold plays a small (2% – 6%) but consistent role,
Examining the ‘national’ indices, the importance of gold emerges again and when it’s selected it is with a high weight, especially in the MVS quarter horizon a weight of 25% is suggested.
This paper applies Lai (1991)’s model – Polynomial Goal Programming.
The rationale underlying the model is that when we consider the relative set of weights allocated to various assets when higher moments are relevant, the problem can be simplified if the optimizations are rescaled on the unit variance space. Polynomial goal programming breaks the overall problem into soluble elements and then iteratively finding solutions that preserve as closely as possible the individual solutions.
For portfolio selection, three elements considered are:
1) Selection of weights that form a mean-variance (MV) optimal portfolio with unit variance
2) Weights that form a skewness-variance optimal portfolio with unit variance
3) Selection of weights that form a mean-skewness-variance (MSV) optimal portfolio
A number of different indices (FTSE-US, FTSE-Japan, FTSE-UK, FTSE-Germany, FTSE-Canada, FTSE-Swiss, FTSE-Hongkong, FTSE-Italy, FTSE-Australia and national indices NYSE, NASDAQ, TOPIX, FTSE-A, DAX30, TSX, SMI, HangSeng, COMIT) are examined over weekly, monthly and quarterly basis.
The markets chosen account on average for in excess of 87% of world market value over August 1988 to September 2003.
Lucey, Brian M, Edel Tully and Volerio Poti, 2006, International Portfolio Formation, Skewness and the Role of Gold, Frontiers in Finance and Economics 3, 49-68
This paper examines the optimal allocation of assets in well diversified equity based portfolio where the investor is concerned not only with mean and variance but also with the skewness of the returns. Beginning with an analysis of the rationale for concerning with skewness, the paper then discusses previous attempts to model multi-objective portfolio problems. The second part of the paper outlines the attractive nature of the gold asset in equity portfolios. The paper then integrates the two elements, showing the changes in portfolio composition that arise when not only skewness but gold are concerned.