Standard Deviation of a Two-Stock Portfolio Least Likely

Explanation

In a two-stock portfolio, the standard deviation measures the volatility or risk associated with the portfolio's returns. Let's analyze each answer choice:

A. "The standard deviation of a two-stock portfolio must be less than or equal to the weighted-average standard deviation."

This statement is true. The weighted-average standard deviation of a portfolio is calculated by taking into account the individual standard deviations of the stocks and their respective weights in the portfolio. The standard deviation of a portfolio is a measure of the portfolio's total risk, which includes both the individual stock risks and the correlation between the stocks. Mathematically, the weighted-average standard deviation represents the upper bound for the standard deviation of the portfolio. Therefore, it must be greater than or equal to the standard deviation of the portfolio.

B. "The standard deviation of a two-stock portfolio can be reduced by increasing the relative weight of the stock with lower standard deviation."

This statement is true. The standard deviation of a portfolio is influenced by the weights assigned to each stock. By increasing the weight of a stock with a lower standard deviation (i.e., lower risk), the overall risk of the portfolio decreases. This is because the lower-risk stock contributes a larger portion to the portfolio's returns, resulting in a reduction in overall volatility.

C. "The standard deviation will be the lowest when the correlation between the two stocks equals zero."

This statement is incorrect. The correlation between two stocks measures the degree to which their returns move together. A correlation of zero implies that the two stocks have no linear relationship in their returns. However, it does not guarantee that the portfolio's standard deviation will be the lowest. The lowest standard deviation of a two-stock portfolio occurs when the correlation between the stocks is -1, indicating perfect negative correlation. In this case, the returns of the two stocks move in opposite directions, which helps to offset each other's risk, resulting in the lowest overall volatility for the portfolio.

To summarize, the correct answer is C. The standard deviation of a two-stock portfolio will not be the lowest when the correlation between the two stocks equals zero; instead, it will be the lowest when the correlation is -1, representing perfect negative correlation.