Empirical Quantitative Portfolio Optimization, Risk Econometrics, and Probabilistic Market Modeling: An Analytics Evaluation of ISEQ Equities, Real Estate Assets, and Systematic Market Risk

This project executes an end-to-end quantitative financial analysis and econometric portfolio evaluation using market telemetry ingested from Bloomberg and Yahoo Finance. The empirical study investigates four major equities listed on the Irish Stock Exchange (ISEQ) representing distinct economic sectors—CRH plc (construction materials), Ryanair Holdings plc (aviation), Kingspan Group plc (building technology), and Bank of Ireland Group plc (financial services). Using historical monthly price data, individual asset performance was evaluated through descriptive statistical metrics, expected return vectors, and variance-covariance matrices. Bivariate correlation analysis ($\rho$) and mean-variance portfolio theory (MPT) were applied to construct two-stock portfolio allocations, empirically proving how non-perfect asset correlations mitigate overall portfolio risk while optimizing risk-adjusted returns across market cycles.Extending statistical mechanics to real estate asset valuation, the analysis applied fundamental probability rules (range, complement, addition, multiplication, conditional probability, and mutual exclusivity) to evaluate structural and pricing distributions within a Dublin housing market dataset. Discrete probability mass functions were fitted to bedroom count distributions, revealing a right-skewed concentration around 3–4 bedroom family properties, while outdoor amenities were modeled using binary Bernoulli distributions. Furthermore, house price distributions were evaluated against continuous Gaussian probability density functions to estimate tail probabilities and price threshold intervals, establishing benchmark probabilities for properties exceeding €230,000 versus sub-€220,000 valuations.Addressing theoretical financial frameworks, the project delivers a rigorous critical appraisal of the normal distribution assumption in Modern Portfolio Theory, Value at Risk (VaR), and derivatives pricing via the Black-Scholes model. The evaluation synthesizes empirical market anomalies—such as severe leptokurtosis (fat tails), negative skewness, and volatility clustering—that violate Gaussian assumptions during Black Swan market shocks. The critique highlights the failure of linear Gaussian models to capture severe drawdown events and explores advanced financial econometrics, including Student's t-distributions, heavy-tailed extreme value theory, and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) time-series modeling for dynamic volatility tracking.Finally, the project conducts an empirical asset pricing analysis evaluating single-stock price behavior relative to broad market benchmarks. Using daily historical market data, Apple Inc. was evaluated against the S&P 500 index baseline through ordinary least squares (OLS) linear regression. The analysis established descriptive location and dispersion metrics, evaluated market co-movement via Pearson correlation coefficients, and estimated systematic risk ($\beta$) to quantify the stock's sensitivity to macroeconomic index fluctuations. This multi-part analysis bridges theoretical corporate finance, quantitative portfolio construction, and applied econometrics for sophisticated investment decision-making.