The integration of cryptocurrencies into institutional portfolios necessitates the adoption of robust risk modeling frameworks. This study is a part of a series of subsequent works to fine-tune model risk analysis for cryptocurrencies. Through this first research work, we establish a foundational benchmark by applying the traditional industry-standard Geometric Brownian Motion (GBM) model. Popularly used for non-crypto financial assets, GBM assumes Lognormal return distributions for a multi-asset cryptocurrency portfolio (XRP, SOL, ADA). This work utilizes Maximum Likelihood Estimation and a correlated Monte Carlo Simulation incorporating the Cholesky decomposition of historical covariance. We present our stock portfolio model as a Minimum Variance Portfolio (MVP). We observe the model's structural shift within the heavy-tailed, non-Gaussian cryptocurrency environment. The results reveal limitations of the Lognormal assumption: the calculated Value-at-Risk at the 5% confidence level over the one-year horizon. For baselining our results, we also present a holistic comparative analysis with an equity portfolio (AAPL, TSLA, NVDA), demonstrating a significantly lower failure rate. This performance provides conclusive evidence that the GBM model is fundamentally the perfect benchmark for our subsequent works. Results from this novel work will be an indicator for the success criteria in our future model for crypto risk management, rigorously motivating the development and application of advanced models.

翻译：加密货币纳入机构投资组合需要采用稳健的风险建模框架。本研究是后续系列工作中微调加密货币模型风险分析的一部分。通过这项初步研究工作，我们应用传统行业标准几何布朗运动模型建立了基础基准。该模型在非加密金融资产中广泛使用，假设多资产加密货币投资组合具有对数正态收益分布。本研究采用最大似然估计法，并结合历史协方差矩阵的Cholesky分解进行相关蒙特卡洛模拟。我们将股票投资组合模型构建为最小方差投资组合。在重尾非高斯分布的加密货币环境中，我们观察到模型存在结构性偏移。结果揭示了对数正态假设的局限性：在一年期时间范围内5%置信水平下计算的风险价值。为建立结果基准，我们还对股票投资组合进行了整体对比分析，证明其失败率显著更低。这一表现为后续研究提供了决定性证据，表明几何布朗运动模型本质上是最理想的基准框架。本创新性研究的成果将为未来加密货币风险管理模型的成功标准提供指标，有力推动高级模型的开发与应用。