Modeling The Modified Internal Rate Of Return (Mirr) For Long-Term Investment Strategy By The Assumption Of Gamma Distribution

• Main Author: Sayed, Amani Idris A
• Format: Thesis
• Language: English
• Published: 2023
• Subjects: QA1 Mathematics (General)
• Online Access: http://eprints.usm.my/60164/1/AMANI%20IDRIS%20A%20SAYED%20-%20TESIS%20cut.pdf; http://eprints.usm.my/60164/

This research aims to develop a model for the Modified Internal Rate of Return (MIRR) in long-term investment strategies using the gamma distribution. The MIRR offers a solution to the problem of multiple Internal Rate of Return (IRR) values encountered when using traditional models like Net Present Value (NPV) and IRR. The study explores the use of the gamma distribution, which provides greater flexibility compared to the normal and exponential distributions commonly used in finance. To model the MIRR over an extended investment period, various financial parameters, including stock price, reinvested dividends, stock splits, bonus issues, and treasury share dividends, are taken into account. The estimation of the shape and scale parameters of the gamma distribution is relatively straightforward using the method of moments. However, simultaneously estimating all three parameters (shape, scale, and growth) through the maximum-likelihood function is computationally complex. Alternative approaches such as the Simulated Annealing (SA) algorithm, which maximizes the log-likelihood function, and Bayesian MCMC estimation are considered. The study analyzes data from 62 publicly listed Malaysian property businesses spanning the period from 2008 to 2019. Different investment durations ranging from one to eight years are considered. The findings demonstrate that the gamma distribution provides a good fit for modeling the transformed MIRR over a long-term investment period. By utilizing the proposed methods, the research successfully estimates the parameters of the gamma distribution and validates its suitability for capturing the distribution of returns on financial assets. The gamma distribution emerges as a suitable choice for modeling the MIRR in long-term investment strategies. It offers greater flexibility compared to the commonly used normal distribution.