I'm currently optimizing portfolio weights for an investment team with N stocks. We buy stocks with a conviction it will generate a return and it is up to me to determine weighting. However, with these N stocks, I will need the optimizer to include every stock even if it has bad potential reward to risk since the methods of estimating are still susceptible to estimation errors.
I'm optimizing the Sharpe Ratio with constant correlation model and also modelling returns via a weighted average of analyst consensus and empirical mean return. To temporarily solve the issue, I do a weighted combination of both the optimal sharpe ratio portfolio and the minimum variance portfolio with a subjective upperbound (ex: 8% max for a 20 stock portfolio). Even then, I get one or two stocks with a zero weighting.
My question is that, are there any rule of thumbs/methods out there to help with this? What would you guys recommend in terms of a more fruitful way to approach the issue of concentrated portfolio