ANALISIS MODEL INDEKS TUNGGAL UNTUK MEMBENTUK PORTOFOLIO OPTIMAL DALAM PENGAMBILAN KEPUTUSAN INVESTASI SAHAM (Studi Pada Saham Indeks LQ 45 di Bursa Efek Jakarta)

This study is a case study, titled "Application of Single Index Method for Forming the Optimal Portfolio Decision Investment Shares (Study on the LQ 45 Shares Listed on Stock Exchange Jakarta). "The purpose of this study was to determine the number of shares and proportion of funds that form the optimal portfolio, how risk and return portfolios, and whether the revised portfolio. The population used was as many as 90 listed companies included in LQ 45 index during August 2005-July 2006. Analysis using the index produce a single number of issuers that form the optimal portfolio period August 2005-January 2006 as many as 9 issuers with the proportion of funds are: SCMA (0.0032%), BBNI (0.0439%), LMAS (0.0306%), TKIM (0.3352%), MLPL (0.4890%), INCO (0.8840%), BMTR (2.5575%), TINS (1.3788%), NISP (94.2603%). While in the period February-July 2006 which established securities portfolio there are 6 issuers with an optimal proportion of funds are: NISP (34,691%), AALI (39.7217%), RMBA (11.9573%), HMSP (10.5739%), TSPC (0.17278%), EARTH (1.32779%). Portfolio risk of each period is 0.73365% for the period August 2005-January 2006. While the period February-July 2006 amounted to 0.031669%. Return expectations for optimal portfolio period August 2005-January 2006 amounted to 0.4343% smaller than expected portfolio return period February-July 2006 was 49.6243%. Portfolio revision occurred in this study because the period February-July 2006 the percentage increase in portfolio return is greater than increased risk of the portfolio compared with the period August 2005-January 2006

Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz

Using daily returns of the S&P 500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the extreme risk index (ERI). This method uses multivariate extreme value theory to minimize the probability of large portfolio losses. With more than 400 stocks to choose from, our study seems to be the first application of extreme value techniques in portfolio management on a large scale. The primary aim of our investigation is the potential of ERI in practice. The performance of this strategy is benchmarked against the minimum variance portfolio and the equally weighted portfolio. These fundamental strategies are important benchmarks for large-scale applications. Our comparison includes annualized portfolio returns, maximal drawdowns, transaction costs, portfolio concentration, and asset diversity in the portfolio. In addition to that we study the impact of an alternative tail index estimator. Our results show that the ERI strategy significantly outperforms both the minimum-variance portfolio and the equally weighted portfolio on assets with heavy tails.Comment: Manuscript accepted in the Journal of Empirical Financ

Complex Valued Risk Diversification

Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio construction method that incorporates the complex valued principal component analysis into the risk diversification portfolio construction. The proposed method is verified to outperform the conventional risk parity and risk diversification portfolio constructions

Leptokurtic Portfolio Theory

The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings due to non-Gaussian security returns are outlined. A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value. The theory is called Leptokurtic, because it minimises the effects from "fat tails" of returns. The leptokurtic portfolio theory provides an optimal portfolio for investors, who define their risk-aversion as unwillingness to experience sharp drawdowns in asset prices. Two types of risks in asset returns are defined: a fluctuation risk, that has Gaussian distribution, and a drawdown risk, that deals with distribution tails. These risks are quantitatively measured by defining the "noise kernel" -- an ellipsoidal cloud of points in the space of asset returns. The size of the ellipse is controlled with the threshold parameter: the larger the threshold parameter, the larger return are accepted for investors as normal fluctuations. The return vectors falling into the kernel are used for calculation of fluctuation risk. Analogously, the data points falling outside the kernel are used for the calculation of drawdown risks. As a result the portfolio optimisation problem becomes three-dimensional: in addition to the return, there are two types of risks involved. Optimal portfolio for drawdown-averse investors is the portfolio minimising variance outside the noise kernel. The theory has been tested with MSCI North America, Europe and Pacific total return stock indices.Comment: 10 pages, 2 figures, To be presented in NEXT-SigmaPh

A Benchmark Approach to Investing and Pricing

This paper introduces a general market modeling framework, the benchmark approach, which assumes the existence of the numeraire portfolio. This is the strictly positive portfolio that when used as benchmark makes all benchmarked nonnegative portfolios supermartingales, that is intuitively speaking downward trending or trendless. It can be shown to equal the Kelly portfolio which maximizes expected logarithmic utility. In several ways the Kelly or numeraire portfolio is the "best" performing portfolio and can not be out performed systematically by any other nonnegative portfolio. Its use in pricing as numeraire leads directly to the real world pricing formula, which employs the real world probability when calculating conditional expectations. In a large regular financial market, the Kelly portfolio is shown to be approximated by well diversified portfolios.Kelly portfolio; real world pricing; numeraire portfolio; strong arbitrage; diversification

On the microeconomic problems studied by portfolio theory

In the paper we consider economically motivated problems, which are treated with the help of methods of portfolio theory that goes back to the papers by H. Markowitz [1] and J. Tobin [2]. We show that the portfolio theory initially developed for risky securities (stocks) could be applied to other objects. In the present paper we consider several situations where such an application is reasonable and seems to be fruitful. Namely, we consider the problems of constructing the efficient portfolio of banking services and the portfolio of counteragents of a firm. © 2012 American Institute of Physics

Portfolio-aspects in real options management

Real options theory applies techniques known from finance theory to the valuation of capital investments. The present paper investigates further into this analogy, considering the case of a portfolio of real options. An implementation of real option models in practice will mostly be concerned with a portfolio of real options, so the analysis of portfolio aspects is of both academic and practical interest. Is a portfolio of real options special? In order to shed some light on this question, the present paper will outline the relevant features of a portfolio of real options. It will show that the analogy to financial options remains great if compound option models are applied. As a result, a portfolio of real options, and therefore the firm as such, generally is to be understood as one single compound, real option