The fractal dimension is the basic notion for describing structures that have a scaling symmetry. In finance, multi-fractality is one of the well known facts which characterized non-trivial properties of financial time series. The stock price (or index) fluctuations can be described in terms of long-range temporal correlations by a spectrum of the Holder exponents and a set of fractal dimensions. To forecast the market risk, assessing the stock price indices is the foundation. Multi-fractal has lots of advantages when explaining the volatility of the stock prices. The asset price returns are multi-period market depending on market scenarios which are the measure points. In this work, we use some tools of multi-fractal analysis to derive the worth growth rate of an investor’s portfolio for particular and general cases. For the particular case, we considered the situation when the mean interest rate of some stocks does not depend on other stocks in the market. That is, an investor has invested his money in a stock with a linear mean return. Under the general case, we considered a market comprising some units of assets in long position and a unit of the option in short position. Using Ito’s formula on the present value of the market, we derived the growth rate of investor’s portfolio. Our model equations, which are based on multiplicative processes, capture all the features of the returns. They are tested using data from Zenith Bank of Nigeria stock prices. From our graphs, the worth of investment grows as stock price increases and also decreases with stock price.
| Published in | American Journal of Applied Mathematics (Volume 13, Issue 6) |
| DOI | 10.11648/j.ajam.20251306.15 |
| Page(s) | 428-437 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Multi-fractal Spectrum Model, Worth Growth Rate, Investor’s Portfolio, Zenith Bank of Nigeria, Stock Prices
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APA Style
Adindu-Dick, J. I. (2025). Derivation of Worth Growth Rate of an Investor’s Portfolio Under Multi-fractal Analysis. American Journal of Applied Mathematics, 13(6), 428-437. https://doi.org/10.11648/j.ajam.20251306.15
ACS Style
Adindu-Dick, J. I. Derivation of Worth Growth Rate of an Investor’s Portfolio Under Multi-fractal Analysis. Am. J. Appl. Math. 2025, 13(6), 428-437. doi: 10.11648/j.ajam.20251306.15
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Download@article{10.11648/j.ajam.20251306.15,
author = {Joy Ijeoma Adindu-Dick},
title = {Derivation of Worth Growth Rate of an Investor’s Portfolio Under Multi-fractal Analysis},
journal = {American Journal of Applied Mathematics},
volume = {13},
number = {6},
pages = {428-437},
doi = {10.11648/j.ajam.20251306.15},
url = {https://doi.org/10.11648/j.ajam.20251306.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251306.15},
abstract = {The fractal dimension is the basic notion for describing structures that have a scaling symmetry. In finance, multi-fractality is one of the well known facts which characterized non-trivial properties of financial time series. The stock price (or index) fluctuations can be described in terms of long-range temporal correlations by a spectrum of the Holder exponents and a set of fractal dimensions. To forecast the market risk, assessing the stock price indices is the foundation. Multi-fractal has lots of advantages when explaining the volatility of the stock prices. The asset price returns are multi-period market depending on market scenarios which are the measure points. In this work, we use some tools of multi-fractal analysis to derive the worth growth rate of an investor’s portfolio for particular and general cases. For the particular case, we considered the situation when the mean interest rate of some stocks does not depend on other stocks in the market. That is, an investor has invested his money in a stock with a linear mean return. Under the general case, we considered a market comprising some units of assets in long position and a unit of the option in short position. Using Ito’s formula on the present value of the market, we derived the growth rate of investor’s portfolio. Our model equations, which are based on multiplicative processes, capture all the features of the returns. They are tested using data from Zenith Bank of Nigeria stock prices. From our graphs, the worth of investment grows as stock price increases and also decreases with stock price.},
year = {2025}
}
TY - JOUR T1 - Derivation of Worth Growth Rate of an Investor’s Portfolio Under Multi-fractal Analysis AU - Joy Ijeoma Adindu-Dick Y1 - 2025/12/17 PY - 2025 N1 - https://doi.org/10.11648/j.ajam.20251306.15 DO - 10.11648/j.ajam.20251306.15 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 428 EP - 437 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20251306.15 AB - The fractal dimension is the basic notion for describing structures that have a scaling symmetry. In finance, multi-fractality is one of the well known facts which characterized non-trivial properties of financial time series. The stock price (or index) fluctuations can be described in terms of long-range temporal correlations by a spectrum of the Holder exponents and a set of fractal dimensions. To forecast the market risk, assessing the stock price indices is the foundation. Multi-fractal has lots of advantages when explaining the volatility of the stock prices. The asset price returns are multi-period market depending on market scenarios which are the measure points. In this work, we use some tools of multi-fractal analysis to derive the worth growth rate of an investor’s portfolio for particular and general cases. For the particular case, we considered the situation when the mean interest rate of some stocks does not depend on other stocks in the market. That is, an investor has invested his money in a stock with a linear mean return. Under the general case, we considered a market comprising some units of assets in long position and a unit of the option in short position. Using Ito’s formula on the present value of the market, we derived the growth rate of investor’s portfolio. Our model equations, which are based on multiplicative processes, capture all the features of the returns. They are tested using data from Zenith Bank of Nigeria stock prices. From our graphs, the worth of investment grows as stock price increases and also decreases with stock price. VL - 13 IS - 6 ER -
Department of Mathematics, Imo State University, Owerri, Nigeria
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