opt to coarse-grain the individual funds Sharpe ratios and their mutual correlation values down to integer values by grouping intervals in buckets according to Table \[tab:tableBuckets\]. By using bucketed values we define a scorecard, which is loosely based on the past fund performances but can be easily adjusted by portfolio manager according to his/her personal views and any new information not yet reflected in the funds reports. Indeed, in real world scenarios, optimization needs to be performed with respect to the discretionary views about the future held by portfolio manager, not necessarily with respect to automatically fetched market data. Moreover, if we assume that funds report their NAV per share on a monthly basis and we have comparable funds data for the previous year, then we only have 12 NAV observations in our time series from which we want to construct a correlation matrix for $N$ assets ($N \gg 12$). It is likely that the resulting correlation matrix will not be positive definite due to the number of observations being much smaller than the number of assets, ruling out the traditional solvers of mean-variance portfolio optimization problems which require a positive definite correlation matrix.\

[@\*3c@]{} &\
Equally spaced buckets, & 