Content area
Financial market data is notoriously noisy and subject to constant change (Siegel, 2006; Bodie et al., 2013). As a consequence, information from even a decade or two ago may have limited value in forecasting present or future stock prices. However, non-probabilistic estimation methods, such as those based on maximum likelihood estimation (MLE), typically require extensive amount of data to produce stable parameter estimates (Montgomery & Peck, 1992), which is increasingly at odds with the demands of financial professionals who seek robust, predictive models that can perform reliably even with small or noisy data.
Historical events like stock market crashes and the collapse of Long-Term Capital Management (LTCM) were infamously unforeseen by non-probabilistic models (Taleb, 2008). Also, their inability to adapt to rapid changes or to quantify uncertainty in their predictions also limits their effectiveness (Jalaian et al., 2019). This is why probabilistic machine learning frameworks that incorporate uncertainty directly into their predictions in order to provide more informative outputs have emerged as a promising alternative to their non-probabilistic counterparts (Amit, 2022).
It is well recognized that most financial models contain inherent specification errors, making model fitting and estimation especially challenging. Non-probabilistic approaches often reduce outputs to single point estimates, thereby discarding valuable information regarding uncertainty. This limitation is particularly problematic in investment finance where markets are complex, dynamic, and influenced by numerous unpredictable factors, and therefore errors and estimation inaccuracies stemming from uncertainty and data noise are common. Additionally, these non-probabilistic methods frequently neglect prior domain knowledge such as expertise Brownstein et al. (2019) that could significantly improve model estimation accuracy as new data becomes available. So, while it is generally accepted that carefully constructed priors can enhance estimation accuracy, guidance on eliciting such priors is scarce in the published literature (Wesner & Pomeranz, 2021; Zondervan-Zwijnenburg et al., 2017)). This gap has led many financial professionals, especially those working in capital markets, to seek out estimation techniques that deliver stable results even in the face of small, noisy, or time-variant datasets.
This Praxis aims to evaluate the application of probabilistic machine learning methods, specifically probabilistic ensembles with uncertainty quantification through informative priors for improved financial model estimation. This Praxis employs the single factor market model (MM) as a case study (Sharp, 1963).
Empirical results indicate that the proposed method in this Praxis effectively manages small, noisy, or time-variant stock data to achieve performance improvements exceeding 10% over ordinary least squares (OLS) methods for the tested datasets. These findings suggest that probabilistic modeling approaches can offer substantial practical value for investment professionals that are operating within the capital markets.