Financial Portfolio Management using D-Wave’s Quantum Optimizer: The Case of Abu Dhabi Securities Exchange

Financial portfolio selection is the problem of optimal allocation of a fixed budget to a collection of assets (commodities, bonds, securities etc.) which produces random returns over time. The word optimal, however, can have different meanings. For instance, one could define optimal so that a solution to the portfolio problem maximizes expected or average value of the return. While this definition is intuitively appealing, it is also naive because the values of a random process can deviate from the expected value. A definition of optimal should therefore incorporate deviations from the expected value. In his 1952 paper [4], Harry Markowitz proposed just such a definition of optimal for the financial portfolio selection problem. Markowitz proposed that the problem has an optimal solution when an investor maximizes expected return and minimizes variance in the values of the return. In other words, an investor should look to maximize gain and minimize risk for a given financial portfolio. Markowitz’s portfolio selection theory also formalizes the wisdom of portfolio diversification, where instead of allocating the largest fractions of the budget to a select number of assets with largest expected return, an investor allocates his budget to many assets with the hope that the fortune of some of these assets will not be influenced by the misfortune of some others. Formally, consider a portfolio with n assets. Let ai be the percentage allocation of the total budget to asset i and let Ri denote the random variable representing the return from asset i. Further, let R denote the random variable for the return from the entire portfolio. Then