Factor Risk Parity with Portfolio Weight Constraints

Handling risk factors in the context of a multi-asset risk parity portfolio allocation has created increased interest in recent literature. When allocating along risk factors through principal components, one major problem that persists is the potential existence of leverage or short positions for the optimal portfolio. It is possible, however, to avoid these positions if investors accept equal risk contributions for the first few risk factors, which explain most of the portfolio variation, and allow residual risk contributions to "float". Convex polytopes describe the entire set of solutions if the restrictions hold. A model to handle these kind of factor risk parity allocations with portfolio weight constraints is the subject of this paper. Focusing on equality in the first two risk contributions and requiring a sufficiently high explanation level for them is the main challenge. Different numerical allocation strategies for backtesting and performing the empirical analysis along two multi-asset data sets with different period lengths and a different number of assets are used