Explanation
All the statements given are true, except that standard deviations cannot be averaged to get the portfolio standard deviation unless the assets are perfectly positively correlated. Therefore Choice 'd' is the false statement, and the correct answer.
For a portfolio of uncorrelated assets, ie correlations being equal to zero, variances can be added together to get portfolio variance. Also, regardless of correlations, portfolio returns are always the weighted average of asset returns, and just averages will do in this case as the portfolio is said to be equally weighted across the assets. A correlation of zero produces a risk level less than that possible with positive correlations.