The portfolio’s daily volatility taking into account correlations has been calculated using the formula:
a, b and c are the weights of the respective asset in the portfolio
X, Y, and Z are the assets in the portfolio
Variance (X) is the variance in X price/ rate returns, i.e. it is X’s volatility squared
Variance (Y) is the variance in Y price/ rate returns, i.e. it is Y’s volatility squared
Variance (Z) is the variance in Z price/ rate returns, i.e. it is Z’s volatility squared
is the correlation between X and Y
is the correlation between Y and Z
is the correlation between X and Z
(Note: This formula is for a portfolio that consists of three assets. However it can easily be extended to account for more assets).
If it is assumed that there is independence between the assets the correlation terms are set equal to zero in the equation above.
If it is assumed that the assets are perfectly correlated then the volatility of the portfolio is equal to the weighted average sum of the asset volatilities.