Integrating statistical and fundamental risk models can unveil hidden risks, providing a new perspective that enhances short-term risk management. Discrepancies in forecasted risk between these approaches can offer critical insights and serve as early warnings signs for shifts in risk dynamics. By leveraging multiple methods to estimate risk, investors can converge on a more accurate risk evaluation, improving both short-term decision-making and overall portfolio resilience.

Multi-factor risk models

Robust risk analysis enables portfolio managers to determine if the level of risk undertaken aligns with expected returns and provides asset owners with a consistent framework for portfolio evaluation.

Multi-factor risk models, including both fundamental and statistical approaches, are instrumental in predicting portfolio volatility, identifying key sources of risk, and highlighting holdings that improve diversification. 

These models address the complexities associated with risk modelling based on the volatilities and correlations of individual assets, which may become unmanageable as the number of assets grows. Factor models

effectively reduce the dimensionality of the forecasting process and mitigate noise in asset-to-asset correlations by introducing common factors that capture asset relationships.

Moreover, these models enable the decomposition of risk into systematic (market risk) and idiosyncratic (stock-specific risk), identifying key factors driving portfolio dynamics. Systematic risk is the risk explained by the factors in the multi-factor risk model and is non-diversifiable, reflecting the commonalities among asset returns. Specific risk is quantified as residual variance unexplained by the model’s factors; it is diversifiable, idiosyncratic risk.

Multi-factor models also facilitate consistent risk analysis across portfolios, irrespective of the number of assets involved or the investment style.

Fundamental vs. statistical models

Traditional fundamental risk models have primarily served as the basis for equity risk management, being extensively utilised due to their compatibility with investment processes and stock selection methodologies. These models employ regression analysis and feature an intuitive and consistent framework comprising fixed factors (such as market, style, and industry factors) that are easily interpretable. These factors provide a rigorous econometric framework for understanding both return and risk.

However, these models might not fully capture the variety of risks investors face. When clusters of related assets within a portfolio or the broader market are influenced by novel and unforeseen factors not considered within the established set of fundamental factors, the effectiveness of the fundamental risk model in explaining market or portfolio behaviour diminishes.

Statistical models utilise a machine learning technique based on Principal Component Analysis (PCA), which does not rely on predefined factors but aims to maximise the model’s explanatory power. Unlike fundamental models that depend on predetermined structures, statistical models derive their explanatory factors directly from observed returns data.

These models adapt to changing market conditions more swiftly by identifying common return patterns among groups of assets on a daily basis. Although the number of statistical factors is fixed, the interpretation of each factor may vary daily, reflecting the current influences on the market or portfolio. Statistical factors are purely numerical and don’t inherently offer intuitive insights. However, their significance can be interpreted—though doing so requires a solid grasp of the portfolio strategy and a deeper analysis of the underlying holdings.

This adaptability allows statistical models to respond efficiently to short-term data fluctuations, potentially enhancing their accuracy over short forecast horizons. These models could play an important role in distinguishing between systematic and idiosyncratic risk, helping to identify transient systematic risks that might not be detected by fundamental models.

Case Study 1 – Managing active risk in a Large-Cap Momentum strategy

This case study examines a simulated US Large-Cap Momentum investment strategy, rebalanced monthly and constrained to a 3% tracking error (active risk) relative to the S&P 500, using a US fundamental short-horizon risk model. By construction, the strategy had large positive active exposures to the Medium-Term Momentum and Size style factors, which were the main contributors to both its active return and risk for the period under study (Jan. 2021 – Feb. 2024).

Over the 38-month period, the strategy outperformed the S&P 500 by 1,285 basis points (or 3.09% annualised). However, its realised tracking error was 3.86%, exceeding the 3% forecasted limit set by the fundamental model. This discrepancy highlights a gap between forecasted and actual risk.

When comparing the accuracy of the fundamental and statistical model forecasts against the 20-day forward volatility of the US Large-Cap Momentum strategy’s active return, the statistical model more effectively captured the higher risk levels of the strategy, even though it fell short of fully capturing the extreme peaks and troughs in realised volatility.

Although there were brief periods of alignment between the two models—such as early 2021 and from the third quarter in 2022 to October 2023—significant divergences were observed. The statistical-minus-fundamental spread remained significantly positive for most of the period, indicating that additional, unaccounted-for factors may have influenced the strategy’s returns and risk.

The findings suggest that relying solely on a fundamental risk model may not fully capture the strategy’s risk profile. Investors could enhance risk management by incorporating multiple risk perspectives and applying an additional risk constraint during strategy optimisation.

Specifically, applying total or active risk constraints based on both the statistical and fundamental models during portfolio rebalancing could help manage unexpected volatility, especially during short-term disruptions.

Figure 1. Large-Cap Momentum strategy: Realised vs. fundamental & statistical forecasted short-horizon active forecasts

Source: Axioma US 5.1 Fundamental and Statistical Short-Horizon Equity Factor Risk Models

Case Study 2 – Capturing transient themes such as ‘meme’

Once a positive spread between the statistical and fundamental risk forecasts is identified for a portfolio, a deeper analysis can be performed to evaluate the discrepancies at the factor and stock level.

Consider an equal weighted portfolio of 20 stocks that have attracted significant public attention: “pure” meme stocks (e.g., GME, AMC), newsworthy stocks (e.g., Tesla, Palantir), cryptocurrency-related stocks (e.g., MicroStrategy, Coinbase), and AI-focused stocks (e.g., Nvidia, Qualcomm)—referred to here as “Meme Portfolio.”¹

The statistical model not only accurately accounted for greater overall risk compared to its fundamental counterpart for this Meme Portfolio, but it also captured a higher level of systematic risk. This suggests that the statistical model identified more commonalities among these 20 stocks.

Further analysis identified that Factors 1, 2, and 4 collectively accounted for approximately 75% of the factor contribution to Meme Portfolio’s systematic risk. These factors comprise the majority of the factor risk in the market portfolio and thus are not the factors of interest.  

More interestingly, non-market statistical risk was concentrated in a relatively small set of factors. Specifically, five statistical factors (Factors 5, 14, 15, 17, and 19) accounted for an additional 20% of the total statistical systematic risk, potentially capturing an underlying theme.

Digging deeper at the stock level, the majority of the newly discovered systematic risk in the Meme Portfolio was concentrated in crypto-related companies, which in aggregate accounted for 60% to 80% of the risk spread between the two models in April 2025.

Using the statistical model in conjunction with the fundamental model, we were able to determine three key insights. Firstly, the statistical model forecast was more closely aligned with the realised risk of the portfolio, identifying additional risk. Secondly, the statistical model picked up more commonalities among the assets in the portfolio indicating higher systematic risk. Lastly, the majority of the additional risk was concentrated within a subset of assets.

Figure 2. Risk decomposition and non-market factor contributions

Source: Axioma US4 Statistical and Fundamental Short-Horizon Equity Factor Risk Models

Conclusion

By integrating statistical models with traditional fundamental risk models, investors can achieve a more comprehensive understanding of portfolio risks. Statistical models are particularly effective at capturing short-term and/or transient changes in risk. This capability is crucial for risk mitigation, especially in volatile environments where fundamental risk models may struggle to account for portfolio behaviour influenced by unforeseen, fleeting trends.

^{1 Analysis as of April 30, 2025.}

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