Final answer:
The statement is false. Portfolio variance accounts for the covariance between the stocks, not just the average of their individual variances. One assumptions for an F test of two variances is that the data must be normally distributed.
Step-by-step explanation:
The statement that the average of two stocks' individual variances always equals the variance of the portfolio combining those two stocks is false. In finance, the variance of a portfolio of stocks is not simply the average of the individual variances. Portfolio variance takes into account the covariance between the stocks. Covariance measures how two stocks move together. If two stocks are perfectly correlated, they move exactly in the same direction and the same proportion. However, if they have lower correlation, the variance of the portfolio can be less than the average of the individual variances due to diversification benefits.
One assumption that must be true to perform an F test of two variances is that the data must follow a normal distribution. This is required to ensure the validity of the test results. Another assumption is that the samples are independent of each other.
The central limit theorem states that, for a sufficiently large sample size, the sampling distribution of the mean will be approximately normally distributed, regardless of the distribution of the original data.