Cardinality Constrained Portfolio Optimisation

Abstract

The traditional quadratic programming approach to portfolio optimisation is difficult to implement when there are cardinality constraints. Recent approaches to resolving this have used heuristic algorithms to search for points on the cardinality constrained frontier. However, these can be computationally expensive when the practitioner does not know a priori exactly how many assets they may desire in a portfolio, or what level of return/risk they wish to be exposed to without recourse to analysing the actual trade-off frontier. This study introduces a parallel solution to this problem. By extending techniques developed in the multi-objective evolutionary optimisation domain, a set of portfolios representing estimates of all possible cardinality constrained frontiers can be found in a single search process, for a range of portfolio sizes and constraints. Empirical results are provided on emerging markets and US asset data, and compared to unconstrained frontiers found by quadratic programming.

Evolutionary multi-objective portfolio optimization in practical context

“…Alternatively, additional objective functions have been incorporated to enhance the original model. To handle the cardinality constraints, Fieldsend et al [8] considered the cardinal as an additional objective to be optimized. This approach allows the direct extraction of the 2-dimensional cardinality constrained frontier for any particular cardinality.…”

“…The significance of the efficient portfolio is that any combination of it and the risk-free asset, attainable by either lending or borrowing at the rate of R f , will allow the individual to operate at any point on the capital market line, above the efficient frontier, resulting in higher return for any given amount of risk than any optimal portfolio on F F . Mathematically, the efficient portfolio is the point on the efficient frontier that can maximize the objective function (8).…”

Efficient Cardinality/Mean-Variance Portfolios

“…Although there are exact algorithms for the solution of MIQPs (see [5,6,7,25]), many researchers and portfolio managers prefer to use heuristics approaches (see [3,9,11,15,17,26]). Some of these heuristics vary among evolutionary algorithms, tabu search, and simulated annealing (see [15,26]).…”

“…Some of these heuristics vary among evolutionary algorithms, tabu search, and simulated annealing (see [15,26]). Promotion of sparsity is also used in the field of signal and imaging processing, where a new technique called compressed sensing has been intensively studied in the recent years.…”

Regression Error Characteristic Optimisation of Non-Linear Models

“…This approach is then augmented with the simultaneous optimisation of model complexity, with a similar framework to that introduced in [13]. The highlighting of regions of the REC curve on which we can confidently out-perform the maximum a posteriori (MAP) trained model is also introduced, through bootstrapping the optimised REC curve.…”