VaR-Constrained Black-Litterman Allocation for Fund-of-Funds Portfolios

Summary

The document outlines a portfolio construction method for fund-of-funds portfolios targeting absolute returns. It combines Black-Litterman expected-return estimates, which blend market equilibrium returns with investors’ absolute or relative views according to their confidence, with a Value at Risk constraint. It also incorporates practical limits such as asset allocation bounds, diversification across regions and currencies, liquidity restrictions, and trading constraints. The intended effect is to reduce sensitivity to uncertain return estimates while controlling portfolio losses.

The article describes a probabilistic integer optimization problem and discusses deterministic equivalents or approximations that can make it tractable. It notes that VaR alone may allow concentrated allocations because it is not subadditive, motivating additional diversification constraints. Normal return assumptions can yield a direct VaR formulation, but the text recognizes that heavy tails weaken that assumption; when the return distribution is unknown, inequality-based approximations are proposed. It presents no empirical portfolio results, and approximation quality depends on distributional assumptions.

Key ideas

• Black-Litterman combines market-implied returns with absolute or relative investor views, weighted by confidence.
• The proposed fund-of-funds allocation applies a VaR loss constraint alongside asset, diversification, liquidity, and trading limits.
• Diversification limits address the possibility that VaR alone produces concentrated allocations.
• When return distributions are unknown or non-normal, inequality-based deterministic approximations can replace an exact probability constraint.
• The usefulness of these approximations depends on assumptions about portfolio return distributions.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.