## Long-Short Minimum Risk Parity Optimization Using a Quantum or Digital Annealer

**By Gili Rosenberg & Maxwell Rounds**

In portfolio optimization, many weight allocation strategies result in long-only positions. We show how it is possible to formulate and solve an optimization problem that assigns a direction (long or short) to each weight allocation, such that the variance is minimized or maximized. This optimization problem can then be solved by many solvers, including D-Wave Systems’ quantum annealer, the Fujitsu Digital Annealer, and others. We present backtested results for three datasets solved using a tabu solver run on a CPU. Our results suggest that by utilizing intelligent shorting, this method is able to reduce the volatility of long-only strategies, leading to shorter maximum drawdowns and higher Sharpe ratios, albeit with a higher turnover. We also discuss possible extensions of this model such that it attempts to achieve market neutrality, sector neutrality, or takes into account a shorting aversion.