Optimization of a Portfolio of Investment Projects: A Real Options Approach Using the Omega Measure

Javier Castro,Luiz Brandão,Edison Tito

doi:10.3390/jrfm14110530

Abstract

Investment decisions usually involve the assessment of more than one financial asset or investment project (real asset). The most appropriate way to analyze the viability of a real asset is not to study it in isolation but as part of a portfolio with correlations between the input variables of the projects. This study proposes an optimization methodology for a portfolio of investment projects with real options based on maximizing the Omega performance measure. The classic portfolio optimization methodology uses the Sharpe ratio as the objective function, which is a function of the mean-variance of the returns of the portfolio distribution. The advantage of using Omega as an objective function is that it takes into account all moments of the portfolio’s distribution of returns or net present values (NPVs), not restricting the analysis to its mean and variance. We present an example to illustrate the proposed methodology, using the Monte Carlo simulation as the main tool due to its high flexibility in modeling uncertainties. The results show that the best risk-return ratio is obtained by optimizing the Omega measure.

Highlights

In the financial literature, it is well known that investors seek to maximize the return on their investments while minimizing the associated risk as much as possible
Investors can identify all optimal portfolios by constructing an efficient frontier, which is the geometric locus with the best possible combination of assets in the portfolio, corresponding to the lowest level of risk for a given level of return
We propose a methodology to optimize a portfolio of investment projects by maximizing the Omega performance measure, considering the inclusion of real options in the projects

Summary

Introduction

It is well known that investors seek to maximize the return on their investments while minimizing the associated risk as much as possible. Markowitz (1952) developed the basis of the investment portfolio optimization theory, and he proposed the mean-variance model. According to his theory, investors can identify all optimal portfolios by constructing an efficient frontier, which is the geometric locus with the best possible combination of assets in the portfolio, corresponding to the lowest level of risk (standard deviation) for a given level of return. Markowitz’s (1952) theory is easy to apply and effective in determining the portfolio’s composition, it does not take into account the actual characteristics of the distribution, as it can be observed that the returns of most financial assets have non-Gaussian distributions

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