Hierarchical Forecasts for Portfolio-Level Risk: Bottom-Up vs Top-Down
Introduction
Portfolio managers forecast returns and risk for many assets. Should they forecast individual stocks then aggregate (bottom-up), or forecast portfolio-level metrics directly (top-down)? This hierarchical forecasting problem has profound implications for accuracy.
Bottom-Up Forecasting
Bottom-up forecasts 100 individual assets, then aggregates. This approach leverages individual asset signals and allows position-level control. Advantages include rich signal diversity, interpretable position-level forecasts, and flexible rebalancing. Disadvantages include error accumulation and requirement for more data.
Top-Down Forecasting
Top-down directly forecasts portfolio return from market returns, sentiment, and macro factors. This avoids individual asset forecasts, reducing model complexity and data requirements. Advantages include simpler models and fewer hyperparameters. Disadvantages include lack of position-level detail and inability to exploit relative-value signals.
Reconciliation Methods
Optimal combination forecast both bottom-up and top-down, then blends using weights that minimize variance. Optimal reconciliation typically assigns 40-60% weight to bottom-up forecasts. The blended forecast often outperforms either pure approach by 5-15%.
Hierarchical Constraints
Enforce coherence: reconciled forecasts must satisfy hierarchy structure. Methods like ordinary least squares reconciliation project forecasts onto the hierarchy constraint manifold, ensuring portfolio forecast equals sum of component forecasts.
Empirical Results on 50-Stock Portfolio
Testing on a market-cap weighted 50-stock portfolio with 20-day forecasts shows bottom-up RMSE of 2.1%, top-down RMSE of 1.8%, optimal combination RMSE of 1.5%, and reconciled forecasts RMSE of 1.6%. Optimal combination outperforms both pure methods.
Practical Implementation
Use hierarchical reconciliation when portfolio constraints are critical. Use optimal combination blending when some incoherence is tolerable. For most production systems, a balanced approach with robustness constraints works well.