Final answer:
To create a risk-free portfolio using two stocks, the necessary correlation coefficient between the stocks should be −1.0, meaning they move in exactly opposite directions. this perfect negative correlation allows for the gains of one stock to offset the losses of the other, eliminating overall risk.
Step-by-step explanation:
To construct a risk-free portfolio using two stocks, an investor would ideally look for two stocks that when combined, create a portfolio with zero overall risk due to diversification. This can theoretically be attained when the stocks have a correlation coefficient of −1.0
When two stocks have a correlation coefficient of −1.0, it means they move in exactly opposite directions. If one stock goes up, the other goes down by a corresponding amount, and vice versa. This perfect negative correlation would allow the creation of a portfolio where the gains from one stock offset the losses from the other, leading to no overall risk in terms of price movement.The correlation coefficient is a statistical measure that reflects the degree to which two variables are related. A coefficient of 1 indicates a perfect positive correlation, while −1 represents a perfect negative correlation, and 0 indicates no correlation.In the context of the student's question, none of the other correlation coefficients provided (b) −0.5, (c) 0.0, or (d) 0.5 would allow for a perfectly risk-free portfolio. Only a coefficient of −1.0 indicates that the stocks move in a completely opposite manner, potentially cancelling out each other’s risks.