Black-Litterman and Implied Market Returns

The first step in the Black-Litterman method is to find the "implied market returns" (the prior). Usually this is calculated as: $$\Pi = \lambda \Sigma w$$, where $$\Pi$$ is the vector of returns "implied by the market", $$w$$ is the vector of market weights (each element = security market cap / total market cap), $$\Sigma$$ is the covariance matrix, $$\lambda$$ is the market risk aversion (a constant).

I would like to use Black-Litterman to optimise a portfolio of individual stocks (something like 20 securities). My question is on the calculation of $$\Pi$$. Which universe should I use to calculate the vector $$\Pi$$?

1. should I use only the stocks in my portfolio
2. should I use all the stocks in the "market"? I could use all the stocks in the "market" but usually if I take an index (like FTSE World or S&P500) some security in the portfolio might not be present in the index. This might be an issue.

Thanks

The first thing I would say is that your formula for $$\Pi$$ is missing the risk free rate, but I guess you assumed it zero.

Second, as prior, one should build a benchmark. If you do not have one yourself, the benchmark will be the market neutral, so based on the stocks you picked you may select MSCI and from it take the composition of your stocks. That will give you the w.

As I said depends on the stocks, if you have only stocks from developed country you can select MSCI developed, otherwise MSCI all country.

Once your PI is built you can then set your views and confidence so that if you have no views or if your confidence is very low, the returns of Black-Litterman will converge towards the market neutral.