The valuation performance of mathematically-optimised equity-based composite multiples

Purpose – This paper aims to examine the valuation precision of composite models in each of six key industries in South Africa. The objective is to ascertain whether equity-based composite multiples models produce more accurate equity valuations than optimal equity-based single-factor multiples models. Design/methodology/approach – This study applied principal component regression and various mathematical optimisation methods to test the valuation precision of equity-based composite multiplesmodels vis-à-vis equity-based single-factor multiples models. Findings – The findings confirmed that equity-based composite multiples models consistently produced valuations that were substantially more accurate than those of single-factor multiples models for the periodbetween 2001 and 2010. The research results indicated that composite models produced up to 67 per cent more accurate valuations than single-factor multiples models for the period between 2001 and 2010 which represents a substantial gain in valuation precision. Research implications – The evidence therefore suggests that equity-based composite modelling may offer substantial gains in valuation precision over single-factor multiples modelling. Practical implications – In light of the fact that analysts’ reports typically contain various different multiples it seems prudent to consider the inclusion of composite models as a more accurate alternative. Originality/value – This study adds to the existing body of knowledge on the multiples-based approach to equity valuations by presenting composite modelling as a more accurate alternative to the conventionalsingle-factor multiples-based modelling approach.Propósito – Este documento intenta examinar la precisión de la valoración de los modelos compuestos en cada una de las seis industrias clave en Sudáfrica. El objetivo es determinar si los modelos de múltiplos compuestos basados en la equidad producen valoraciones de capital más precisas que los modelos de múltiplos de factor único óptimos basados en la equidad. Diseño/metodología/enfoque – Este estudio aplicó la regresión de componentes principales y varios métodos de optimización matemática para probar la precisión de la valoración de los múltiplos compuestos basados en capital frente a modelos múltiples de factor único basados en acciones. Hallazgos – Los hallazgos confirmaron que los modelos de múltiplos compuestos basados en la equidad produjeron sistemáticamente valoraciones que fueron sustancialmente más precisas que las de los modelos de múltiplos de un solo factor para el período entre 2001 y 2010. Los resultados de la investigación indicaron que los modelos compuestos produjeron hasta un 67 por ciento de valoraciones más precisas que los modelos de múltiplos de factor único para el período entre 2001 y 2010 lo que representa una ganancia sustancial en la precisión de la valoración. Implicancias de la investigación – La evidencia por lo tanto sugiere que el modelado compuesto basado en la equidad puede ofrecer ganancias sustanciales en la precisión de la valoración sobre el modelado de múltiplos de un solo factor. Implicancias prácticas – A la luz de que los informes de los analistas suelen contener varios múltiplos diferentes parece prudente considerar la inclusión de modelos compuestos como una alternativa más precisa. Originalidad/valor – Este estudio se suma al conocimiento existente sobre el enfoque basado en múltiplos para las valoraciones de capital al presentar el modelado compuesto como una alternativa más precisa al enfoque convencional de modelado de factor único basado en múltiplos

BiplotGUI: Interactive Biplots in R

Biplots simultaneously provide information on both the samples and the variables of a data matrix in two- or three-dimensional representations. The BiplotGUI package provides a graphical user interface for the construction of, interaction with, and manipulation of biplots in R. The samples are represented as points, with coordinates determined either by the choice of biplot, principal coordinate analysis or multidimensional scaling. Various transformations and dissimilarity metrics are available. Information on the original variables is incorporated by linear or non-linear calibrated axes. Goodness-of-fit measures are provided. Additional descriptors can be superimposed, including convex hulls, alpha-bags, point densities and classification regions. Amongst the interactive features are dynamic variable value prediction, zooming and point and axis drag-and-drop. Output can easily be exported to the R workspace for further manipulation. Three-dimensional biplots are incorporated via the rgl package. The user requires almost no knowledge of R syntax.

Precious metals as safe haven assets in the South African market

Abstract: The role of precious metals as hedges and safe havens has been extensively studied across various markets. However, no precious metals other than gold have been considered in a South African setting. This study extends previous literature by making use of the methodology established by Baur and Lucey (2010) to determine which of the four precious metals provides the most viable hedge and safe haven in relation to the domestic stock and bond markets for South African investors? The results suggest that all four precious metals have significant hedging properties in relation to domestic bond market but not the stock market. It was also determined that while all four metals contain safe haven properties, gold is the only precious metal to act as a significant safe haven against both South African stocks and bonds

Visualising Incomplete Data with Subset Multiple Correspondence Analysis

Determining the cause of missing values is a challenge, but an important task in order to select correct analysis techniques for missing data. This paper presents a new approach to identify the missing data mechanism (MDM) by applying cluster analysis to biplots of data having missing observations. Subset multiple correspondence analysis (sMCA) enables an isolated analysis of a chosen subset while preserving the scaffolding of the original data set. Multivariate categorical data sets are frequently represented in a coded dummy matrix, referred to as an indicator matrix. Additional category levels can be created for the indicator matrix to account for the unobserved information which has the advantage of not forfeiting any observed information. The extended indicator matrix easily partitions a data set into observed and unobserved subsets. sMCA biplots are used for the visual exploration of the subsets. Configurations of the incomplete subsets enable the recognition of non-response patterns which could aid in the identification of a particular MDM. The missing at random (MAR) MDM refers to missing responses that are dependent on the observed information and is expected to be identified by patterns and groupings occurring in the incomplete sMCA biplot. The missing completely at random (MCAR) MDMstates that all observations have the same probability of not being captured which could be identified by a random cloud of points in the incomplete sMCA biplot. The partitioning around mediods (pam) clustering technique is used to establish the number of available clusters in an incomplete sMCA biplot. A simulation study confirmed that there is a difference in the number of sufficient clusters that can by identified from MAR and MCAR simulated data sets. A real data set is also explored and the MDM is identified using the results of the simulation study as guidelines

The valuation performance of mathematically-optimised equity-based composite multiples

Purpose – This paper aims to examine the valuation precision of composite models in each of six key industries in South Africa. The objective is to ascertain whether equity-based composite multiples models produce more accurate equity valuations than optimal equity-based single-factor multiples models. Design/methodology/approach – This study applied principal component regression and various mathematical optimisation methods to test the valuation precision of equity-based composite multiplesmodels vis-à-vis equity-based single-factor multiples models. Findings – The findings confirmed that equity-based composite multiples models consistently produced valuations that were substantially more accurate than those of single-factor multiples models for the periodbetween 2001 and 2010. The research results indicated that composite models produced up to 67 per cent more accurate valuations than single-factor multiples models for the period between 2001 and 2010 which represents a substantial gain in valuation precision. Research implications – The evidence therefore suggests that equity-based composite modelling may offer substantial gains in valuation precision over single-factor multiples modelling. Practical implications – In light of the fact that analysts’ reports typically contain various different multiples it seems prudent to consider the inclusion of composite models as a more accurate alternative. Originality/value – This study adds to the existing body of knowledge on the multiples-based approach to equity valuations by presenting composite modelling as a more accurate alternative to the conventionalsingle-factor multiples-based modelling approach.Propósito – Este documento intenta examinar la precisión de la valoración de los modelos compuestos en cada una de las seis industrias clave en Sudáfrica. El objetivo es determinar si los modelos de múltiplos compuestos basados en la equidad producen valoraciones de capital más precisas que los modelos de múltiplos de factor único óptimos basados en la equidad. Diseño/metodología/enfoque – Este estudio aplicó la regresión de componentes principales y varios métodos de optimización matemática para probar la precisión de la valoración de los múltiplos compuestos basados en capital frente a modelos múltiples de factor único basados en acciones. Hallazgos – Los hallazgos confirmaron que los modelos de múltiplos compuestos basados en la equidad produjeron sistemáticamente valoraciones que fueron sustancialmente más precisas que las de los modelos de múltiplos de un solo factor para el período entre 2001 y 2010. Los resultados de la investigación indicaron que los modelos compuestos produjeron hasta un 67 por ciento de valoraciones más precisas que los modelos de múltiplos de factor único para el período entre 2001 y 2010 lo que representa una ganancia sustancial en la precisión de la valoración. Implicancias de la investigación – La evidencia por lo tanto sugiere que el modelado compuesto basado en la equidad puede ofrecer ganancias sustanciales en la precisión de la valoración sobre el modelado de múltiplos de un solo factor. Implicancias prácticas – A la luz de que los informes de los analistas suelen contener varios múltiplos diferentes parece prudente considerar la inclusión de modelos compuestos como una alternativa más precisa. Originalidad/valor – Este estudio se suma al conocimiento existente sobre el enfoque basado en múltiplos para las valoraciones de capital al presentar el modelado compuesto como una alternativa más precisa al enfoque convencional de modelado de factor único basado en múltiplos

Properties of individual differences scaling and its interpretation

Indscal models consider symmetric matrices \[ B_k = XW_k X^' \] for \[ k = 1,..., K \] where \[ X:n \times R \] is a compromise matrix termed the group-average and $W_k$ is a diagonal matrix of weights given by the $\textit{k}th$ individual to the $R$, specified in advance, columns of $X$; non-negative weights are preferred and usually $R < n$. We propose a new two-phase alternating least squares (ALS) algorithm, which emphasizes the two main components (group average and weighting parameters) of the Indscal model and specifically helps with the interpretation of the model. Furthermore, it has thrown new light on the properties of the converged solution, that would be satisfied by any algorithm that minimizes the basic Indscal criterion: min\[ \sum_{k=1}^{K} || B_k - XW_k {X^'} ||^2 where the minimization is over $X$ and the $W_k$. The new algorithm has also proved to be a useful tool in unravelling the algebraic understanding of the role played by parameter constraints and their interpretation in variants of the Indscal model. The proposed analysis focusses on Indscal but the approach may be of more widespread interest, especially in the field of multidimensional data analysis. A major issue is that simultaneous least-squares estimates of the parameters may be found without imposing constraints. However, group average and individual weighting parameters may not be estimated uniquely, without imposing some subjective constraint that could encourage misleading interpretations. We encourage the use of linear constraints \[ \sum_{k=1}^{K} 1'W_k = 1', as it enables a comparison of the weights obtained (i) within group $k$ and (ii) between the same item drawn from two or more groups. However, it is easy to exchange one system of constraints to another in a post- or pre-analysis. The new two-phase ALS algorithm (i) computes for fixed \[ X:n \times R \] the weights $W_k$ subject to \[ \sum_{k=1}^{K} 1'W_k = 1', and then (ii) keeping $W_k$ fixed, it updates $X$. At convergence, the estimates of \[ X:n \times R \] and the $W_k$ will apply to all algorithms that minimize the Indscal criterion. Furthermore, we show that only at convergence an analysis-of-variance property holds on the demarcation region between over- and under-fitting. When the analysis-of-variance is valid, its validity extends over the whole matrix domain, over trace operations, and to individual matrix elements. The optimization process is unusual in that optima and local optima occur on the edges of what seem to be closely related to Heywood cases in Factor analysis

Flexible graphical assessment of experimental designs in R: The vdg package

textabstractThe R package vdg provides a flexible interface for producing various graphical summaries of the prediction variance associated with specific linear model specifications and experimental designs. These methods include variance dispersion graphs, fraction of design space plots and quantile plots which can assist in choosing between a catalogue of candidate experimental designs. Instead of restrictive optimization methods used in traditional software to explore design regions, vdg utilizes sampling methods to introduce more flexibility. The package takes advantage of R’s modern graphical abilities via ggplot2 (Wickham 2009), adds facilities for using a variety of distance methods, allows for more flexible model specifications and incorporates quantile regressions to help with model comparison