1QBit

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.

WHITE PAPER

In credit scoring and classification, feature selection is used to reduce the number of variables input to a classifier. This can be done with a quadratic unconstrained binary optimization (QUBO) model, which attempts to select features that are both independent and influential. Quadratic optimization scales exponentially with the number of features, but a QUBO implementation on a quantum annealer has the potential to be faster than classical solvers. Tests were done using the German Credit Data from UC Irvine, and the results compared with those reported in the literature. In comparison with recursive feature elimination (RFE), a technique found in many software packages, QUBO Feature Selection yielded a smaller feature subset with no loss of accuracy. This opens up the possibility of using quantum annealers to programatically reduce the size of very large feature sets, especially as the size and availability of these devices increases.

An expanded version of this white paper has been published in: High-Performance Computing in Finance: Problems, Methods, and Solutions (2018)

WHITE PAPER

We present a quantum-inspired approach to portfolio optimization that is based on an optimization problem that can be solved using a quantum annealer. The proposed algorithm utilizes a hierarchical clustering tree that is based on the covariance matrix of the asset returns. We use real market data to benchmark our approach against other common portfolio optimization methods and demonstrate its strong performance in terms of a variety of risk measures and lower susceptibility to inaccuracies in the input data.

WHITE PAPER

Swap trades that are cleared through a clearing house may be netted against each other. By doing this, the clearing house reduces its risk exposure, and the counterparties regain the use of capital that was previously tied up in margin accounts. The simplest form of netting is to cancel trades that offset each other exactly. However, it is also possible to net trades, or chains of trades, that sum to a very small residual. The ability to find new nettable combinations can lead to new capital efficiencies. The 1QBit swap netting solution makes use of a quantum annealer to identify such combinations and presents them as a netting proposal. The candidate swaps are chosen based on an incompatibility function, which incorporates differences in economic terms in a flexible way.

WHITE PAPER

We present two formulations for finding optimal arbitrage opportunities as a quadratic unconstrained binary optimization problem, which can be solved using a quantum annealer. The formulations are based on finding the most profitable cycle in a graph in which the nodes are the assets and the edge weights are the conversion rates. The edge-based formulation is simpler, whereas the node-based formulation allows for the identification of specific optimal arbitrage strategies, while possibly requiring fewer variables. In addition, an alternative form is presented which allows the arbitrage opportunities that best balance profit and risk to be found, based on the trader’s risk aversion. We discuss considerations for usage in practice. In particular, we suggest an application to illiquid assets and present an illustrative example.

WHITE PAPER