If all the assets of a portfolio have a correlation of 1, i.e., perfect correlation, the portfolio volatility (standard deviation) will be equal to the weighted sum of the individual asset volatilities. Hence the portfolio variance will be equal to the square of the total weighted sum of the individual asset volatilities.

If all the assets have a correlation of 0, i.e., perfectly uncorrelated, the portfolio variance is the sum of the individual asset weights squared times the individual asset variance (and volatility is the square root of this sum). If correlation is less than zero, i.e., the assets are inversely correlated, the portfolio variance and hence volatility will be less than if the correlation is 0.