How do you calculate the Volatility of a Stock/ETF Portfolio?

You can calculate the volatility of a Stock/ETF portfolio using a Covariance matrix. First you must calculate a Covariance matrix from the underlying portfolio. 

Covariance matrix calculated from a Stock/ETF portfolio below. 

Using the Covariance matrix you use matrix algebra to calculate the Variance of the portfolio. Portfolio volatility calculated using the covariances of each security will be lower than just using a weighted average of the variance/volatility. The diagonal in the matrix above are the calculated variances for each position and the other cells are the covariances. Once you have the Variance calculated you take the SQRT (Square Root) of the Variance to get the Volatility. Once you have the Volatility you can then also calculate the Portfolio Sharpe Ratio, Modigliani (M-squared) ratio, and Conditional Sharpe ratio. 

Cheers.