The variance of a portfolio of two investments will be equal to the sum of the variances of the two investments when the covariance between the investments is zero.

This statement is true. When the covariance between two investments is zero, it means that they have no correlation and do not move in tandem with each other. In such a scenario, the risk or variance of the portfolio can be calculated by adding the variances of each investment as they are assumed to be independent. However, if the investments have a positive covariance (meaning they move in the same direction) or a negative covariance (meaning they move in opposite directions), the variance of the portfolio will not be the simple sum of the variances of each investment, and instead, the formula for portfolio variance will need to be used.