Lets say I have an alpha generating model that forecasts expected returns for SP500 stocks. I formulate a portfolio with 100 stocks having the highest expected return. What is the simplest way of reducing tracking error relative to the S&P500?
You ask about industry practice. In my experience, generally there are two phases: First an alpha model (which it seems you already have) proposes stocks likely to have above average returns, then a portfolio building model chooses from these stocks to form a portfolio with characteristcs similar (or not too distant) from the sp500 characteristics (in terms of sector composition, large cap/small cap and other variables considered relevant (in fact factor models are often used at this stage to compare the proposed portfolio to the sp500 portfolio and ensure they are no too far apart. For example the S&P500 may have a certain exposure to the oil price factor and you don't want your portfolio to have much more or much less exposure to this factor. Such models are commenrcially available BTW)).