How can I quantify the marginal diversification benefit of adding a particular holding to a portfolio?
In this question, I asked about manually replicating a world-tracker ETF by buying its top N holdings directly. If you feel like your Boglehead is about to have a Boglestroke, please view that question for why I'd want to do such a silly thing! Anyway, I'd like to know what a reasonable minimal value of N is. In other words, how many of the top holdings of the ETF do I have to buy before buying the N+1'th holding is, in some measurable sense, "not worth it"?
I understand that diversification reduces the variance of expected returns, in the same way that rolling a million dice will basically guarantee a value-per-dice close to 3.5, while rolling a single die has the same expected value but a much bigger variance. Reducing variance is obviously super important for retirement funds.
In the context of investing $T in a portfolio, I could choose to replicate an S&P 500 tracker by buying its top N holdings, or its top N+1 holdings. How do I quantify the marginal diversification benefit of that extra holding? How do people model this? Are there publicly available tools for this?