Portfolio optimization: Do risk metrics matter?

This paper compares the results of two formulations of the portfolio optimization problem, based on the same target return, but using different risk metrics: (i) the standard-deviation-of-returns, and (ii) the CVaR. The analysis reveals that both formulations yield portfolios that are markedly different in terms of their asset allocation percentages, yet remarkably similar in terms of their respective risk profiles. In short, given a specific risk-return target, numerous asset allocation combinations can satisfy such target. The findings, based on historical data covering a twenty-year period (which included two severe crises, subprime and COVID), prove robust across several tests (e.g., different time windows, different market segments). These results corroborate, albeit from a different perspective, the lack of stability that has been reported in relation to the conventional portfolio optimization framework, regardless of the risk metric employed. Additionally, and more importantly, they suggest the possibility of incorporating other constraints into the optimization formulation without compromising the risk-return balance.