Benchmark-Adjusted Stochastic Valuation of Real Estate Assets: Evidence from Ghana

This study develops a benchmark-relative application of geometric Brownian motion (GBM) for evaluating the capital-value performance of real estate under uncertainty. It introduces a valuation-regime taxonomy that distinguishes the growth conditions for benchmark-adjusted mean, median, and modal property values and links them to benchmark underperformance and downside risk over alternative holding horizons. Using a compiled annual median residential property-price series for Accra and Tema (2016–2026), the Ghanaian application illustrates how nominal property appreciation can coexist with deteriorating benchmark-relative performance when appreciation is insufficient relative to the selected investment benchmark. The analysis further demonstrates that expected and median benchmark-adjusted values may exhibit opposing growth patterns, while the probability of benchmark underperformance depends on the interaction among appreciation, benchmark return, volatility, and investment horizon. Rental-yield sensitivity further shows that relatively small positive net yields can alter the classification. The proposed approach provides a probabilistic assessment of benchmark-relative capital-value performance, complementing conventional nominal growth projections.