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 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