How it works
For two assets, portfolio volatility is σp = √(wA² × σA² + wB² × σB² + 2 × wA × wB × ρ × σA × σB), where wA and wB = 1 − wA are the weights, σA and σB the annual volatilities and ρ the correlation between the two return series. The simple weighted average wA × σA + wB × σB is the portfolio risk you would get if both assets moved in lockstep (ρ = 1). The diversification effect shows how far the portfolio volatility falls below that average.
With the default inputs, two assets with 20% volatility each, a 50/50 split and a correlation of 0 give about 14.14% portfolio volatility instead of 20%, roughly 29% less risk. With equal volatilities, a 50/50 split and a correlation of −1, the swings would cancel out completely in theory; at +1 there is no effect. The scatter plot shows simulated returns with the chosen correlation.
Correlation does not change the expected return of the mix, which stays the weighted average of the two expected returns. Correlations estimated from history are unstable and often rise in market stress, exactly when diversification would matter most. The calculator illustrates the math; it says nothing about which assets to combine.