Abstract
In this paper we reviewed some numerical algorithms, implemented in R language which solve the Risk Budgeting (RB) allocation problem. We demonstrated that the well known Sequential Quadratic Programming (SQP) whose objective function is not strictly convex, fails to converge for high dimensional baskets. On the contrary, the new explored algorithms tackle this issue by transforming the objective function into a strictly convex one. Amongst them, the ”Spinu Algorithm” proves to be the most robust and fastest algorithm, both for large equity and small multi-asset portfolios. Surprisingly, the promising Cyclical Coordinate Descent (CCD) algorithm proposed by Griveau et.al. (2013) which suits well for risk budgeting on a large basket of equity stocks, lacks robustness when performed on a multi-asset universe. Our results confirm that the ”Spinu Algorithm” is the most robust framework to implement risk-budgeting portfolios for any type of investment universe.
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