Mathematical Optimisation Techniques for Enterprise Finance: Maximising Returns and Minimising Risk
This study demonstrates that applying mathematical optimisation to daily stock data from five Indian companies reveals a trade-off where unconstrained return maximisation leads to excessive concentration and high volatility, whereas diversified strategies like minimum-risk or equally weighted portfolios offer more stable returns and better risk-adjusted performance for enterprise finance.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Every business that manages money faces a fundamental, unyielding tension: the desire to grow wealth versus the need to protect it. In the world of enterprise finance, this is not a matter of guessing or intuition, but of navigating a landscape where higher potential rewards are inextricably linked to higher chances of loss. To manage this, financial leaders rely on a concept known as the risk-return trade-off. Simply put, an investment that promises a large gain usually carries a significant chance of falling in value, while a safe investment often offers only modest growth. The challenge for any organization is to find the precise mix of assets that delivers the best possible return for the amount of risk they are willing to accept. This is where mathematical optimisation enters the picture, offering a systematic way to calculate the ideal distribution of funds across different investments, rather than relying on gut feeling.
A team of researchers from universities in Ghana set out to test how these mathematical tools perform in the real world of enterprise finance. They focused on five major companies listed on the National Stock Exchange of India, tracking their daily stock prices over a decade, from 2015 to 2025. The companies represented different industries, including automobiles, banking, technology, pharmaceuticals, and steel, providing a diverse set of data to work with. The researchers did not just look at how much money each company made; they measured how much those earnings fluctuated day to day and how the performance of one company moved in relation to the others. By analyzing these patterns, they built three distinct investment strategies to see which approach offered the most value for an enterprise.
The first strategy was the simplest: an equally weighted portfolio. In this approach, the business would split its money evenly, putting the same amount into each of the five companies. The second strategy aimed to find the absolute safest path, a minimum-risk portfolio designed to keep the value of the investment as stable as possible, even if that meant accepting lower profits. The third strategy was the opposite, a maximum-return portfolio that sought to squeeze out every possible dollar of profit, regardless of how wild the ride might be. The researchers used computer models to calculate the exact percentage of money to allocate to each stock for the second and third strategies, letting the mathematics decide the best mix based on the historical data.
The results revealed a stark contrast between these approaches. The strategy that chased the highest possible profit ended up putting all the money into just one company, Tata Steel. While this approach generated a massive annual return of 32.89 percent, it came with a price: the value of the investment swung wildly, with an annual volatility of 48.72 percent. This extreme concentration meant that if Tata Steel faced trouble, the entire investment would suffer. The study found that this kind of "all-in" approach, while mathematically optimal for pure profit, creates a level of risk that is often too high for a stable business.
In contrast, the minimum-risk strategy produced a very different picture. By carefully spreading the money across the five companies, with the largest share going to the technology firm Infosys, the portfolio achieved an annual return of 16.91 percent. More importantly, the value of this portfolio was much steadier, with a volatility of only 18.55 percent. This demonstrated that by diversifying—spreading investments across different companies that do not move in perfect lockstep—the business could significantly reduce the chance of a sharp drop in value. The equally weighted approach, which simply split the money five ways without complex calculations, landed somewhere in the middle, delivering a 19.87 percent return with a volatility of 20.80 percent.
The study concludes that while mathematical models are powerful tools for making investment decisions, they must be used with caution. The research suggests that blindly following a model that seeks only to maximize returns can lead to dangerous over-concentration in a single asset. Instead, the most practical approach for an enterprise is to use these models to find a balanced allocation that respects the need for stability. The findings indicate that a diversified portfolio, which accepts a slightly lower return in exchange for much lower risk, is often the smarter choice for long-term financial health. By combining mathematical precision with sensible rules about how much money to put into any single investment, businesses can navigate the uncertainty of the market with greater confidence and clarity.
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