Mathematical Analysis of Stock Market Trends for Investment Decisions

Abstract

This study, titled "Mathematical Analysis of Stock Market Trends for Investment Decisions," evaluates the quantitative factor weightings, predictive mean squared error (MSE), riskadjusted alpha generation, and financial feasibility of mathematical modeling in equity trading. Stock markets exhibit non-linear price trajectories, stochastic volatility, and regime shifts. A five-year project lifecycle (2021-2025) of a mathematical algorithmic trading platform is evaluated using standard capital budgeting parameters: Net Present Value (NPV), Internal Rate of Return (IRR), Payback Period (PBP), and Benefit-Cost Ratio (BCR). Quantitative analysis reveals that trend-following moving average factors represent 40% of the factor model weightings. Deploying a Deep Wavelet Neural Network reduces trend prediction MSE to 0.005 compared to 0.048 under traditional linear regression models. Higher predictive precision increases trading signal win rates from 58.2% to 84.6%, expanding portfolio Sharpe ratios to 2.85 and annualized portfolio returns to 38.5% alongside NIFTY 50 benchmarks reaching 25,200 by 2025. Large-cap equities contribute 38% of total risk-adjusted alpha. The financial model yields a positive NPV of 284.5 Crores and an IRR of 38.6%, far exceeding the 10% discount hurdle rate. The study concludes that investing in mathematical trend modeling is highly viable, enabling portfolio managers and institutional investors to achieve superior risk-adjusted returns.