of Funds portfolio manager is dealing with the short time series of comparable monthly fund performance reports. Detailed description of the simulation scheme can be found in Appendix \[sec:gbm\]. Every simulated (or, “realized”) portfolio scenario consists of 12 monthly returns for each asset. From these returns we calculated total realized return and realized volatility for each asset (which, obviously, differ from the their expected values $\mu$ and $\sigma$) and for the portfolio as a whole. We also calculated realized pairwise correlations between all assets according to the input uniform correlation $\rho$. Finally, we calculated individual assets and portfolio Sharpe ratios. For instance, with $\rho = 0.1$, $\mu = 0.075$, $\sigma = 0.15$ and the constant risk-free interest rate set at $r_0 = 0.015$, the expected Sharpe ratio for each asset in a portfolio is 0.4. The expected Sharpe ratio for the portfolio of $N$ assets is significantly larger due to the diversification and low correlation between the assets, e.g., for a 48-asset portfolio we would expect Sharpe ratio values from 0.5 (25th percentile) to 2.1 (75th percentile) with a mean around 1.4.

#### Constraint on the number of selected assets

In QUBOs, the standard way to deal with the cardinality 