Understand below is the most basic formula, but I don’t really get it. Could someone please help to eleborate/derive it? Many thanks.
The variance of a portfolio of two assets equals:
If ρ = +1, then:
σ²port = w1²σ1² + 2w1w2σ1σ2 + w2²σ2²
= (w1σ1 + w2σ2)²
σport = w1σ1 + w2σ2
So, with perfect, positive correlation, the standard deviation of the portfolio’s returns is the weighted average of the standard deviations of the constituent securities’ returns.
When ρ < 1, the standard deviation of the portfolio’s returns is less than the weighted average of the standard deviations of the constituent securities’ returns; that’s the diversification benefit.