What are random portfolios?
The idea of random portfolios is that they are a random sample of all of the portfolios that satisfy a given set of constraints. Suppose that our universe of assets is the stocks contained in the S&P 500. We might want to request 1000 long-only portfolios that have a value between one million dollars and 1.01 million dollars, no asset has a weight greater than 5%, and there are between 30 and 60 assets in the portfolio. So out of all the portfolios that might be constructed from those 500 assets, we are selecting portfolios that have a specific set of attributes. Notice that utility is not involved. Typically part of the point of using random portfolios is that we are ignoring utility when we select the portfolios. More on random portfolios can be found at Random Portfolios in Finance.
