Geometric Brownian Motion Calculation

teenagepirate:

SirTradesaLot:

If you have a view, Black Litterman. If not, an equilibrium model. Google it and you will find a ton of results. Start off by defining your 'market portfolio' and go from there. I don't think it's a simple question to answer at all.

Black Litterman is an asset allocation model that takes expected return as an input...

It is an allocation model that does not require you to have a view on the returns on each of the assets, but importantly allows you to come up with one. Basically, you start with a risk free rate and a risky asset that you define a risk premium for (usually S&P 500). You take a market weight portfolio across asset classes and then solve for the expected return taking into account the covarianve across the different assets. This allows you to derive reasonable return assumptions for a stable MVO. This is just an equilibrium model at this point. You could use it for asset classes or for individual securities (long or short), you just need to modify what you define as the market portfolio.

The Black Litterman framework allows the user to input things like "I think x asset will outperform y asset by 2% per year with 65% confidence" or any other input you would like (absolute or relative performance). Based on that input, it will recalibrate the other expected returns so that they 'make sense' in the context of that view. For instance, if my only view is that I believe FB will underperform the market by 5% per year with a 75% confidence, the model will overweight and underweight each component that has higher or lower correlation to FB.

The point is your portfolio weights and expected returns are linked (you buy more of things you think will appreciate). The market portfolio is a known thing, so you are better off starting off with that and deriving expected returns and then taking those expected returns to construct your portfolio.