Sayed, Amani Idris A
(2023)
Modeling The Modified Internal Rate
Of Return (Mirr) For Long-Term
Investment Strategy By The
Assumption Of Gamma Distribution.
PhD thesis, Universiti Sains Malaysia.
Abstract
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.
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