risk reduction in PM

In Secret sauce(p183), “The higher the average correlation, the fewer stocks it takes to achieve a specified amount of risk reduction”. It looks right with formula: Sigma^2§ = Avg(Sigma^2) ( (1-rho)/n + rho). But this is counetr intuitive to me, the higher correlation should have higher overall risk. Then we need more stocks in the portfolio to reduce risk?

No. Assume the stocks have correlation 1. It doesn’t matter which stocks you choose, overall the risk will remain the same. There is nothing to gain by diversification. When the correlation is below 1 there is a benefit from diversification.

yes, it doesn’t help much to add stocks if these stocks are highly correlated. This makes sense to me.