Statman (1987)
Statman, Meir. "How Many Stocks Make a Diversified Portfolio?" Journal of Financial and Quantitative Analysis, 22, September 1987.
Argues that prior studies of diversification have underestimated the number of stocks needed to diversify portfolio, and discusses the theoretical implications of holding a randomly selected portfolio of 10 stocks, as opposed to 500. Cites data from Elton and Tamarkin [1977] indicating that the marginal cost of diversification does not exceed marginal utility until 100-200 stocks are held in the portfolio. Reviewing Ibbotson and Wall Street Journal data, the author estimates expected rates of return and standard deviation for 10-, 20-, 30-, 40-, 50-, and 100-stock portfolios. Finds that, after transaction costs are considered, the Vanguard Index Trust dominates a 35-stock portfolio for a borrowing investor and a 50-stock portfolio for a lending investor. The author notes that "the typical investor's stock portfolio contains only a small fraction of the available securities."
Link: https://www.jstor.org/stable/2330969
Here is a chart I made from Figure 9-3 of Statman's 1987 paper. As the number of assets in the portfolio increases, exposure to non-systematic risk declines, and ultimately we have a portfolio that is driven almost entirely by systematic risk. This logic should apply to an index of responsible stocks as much as to a conventional one. -lk