How efficient is naive portfolio diversification? an educational note

Standard textbooks of Investment/Financial Management teach that although portfolio diversification can help reduce investment risk without sacrificing the expected rate of return, the benefit of diversification is exhausted with a portfolio size of 10–15. Since by then, most of the diversifiable risk is eliminated, leaving only the portion of systematic risk. How valid is this “common” knowledge? What is the exact value of “most” in the above statement? This paper examines the issue on naive (equal weight) diversification and analytically shows that for an infinite population of stocks, a portfolio size of 20 is required to eliminate 95% of the diversifiable risk on average. However, an addition of 80 stocks (i.e., a size of 100) is required to eliminate an extra 4% (i.e., 99% total) of diversifiable risk. This result depends neither on the investment horizons, sampling periods nor the markets involved.