A change in the correlation between two stocks has no impact on the shape of investment opportunity set.
a. True
b. False
The correct answer and explanation is:
The correct answer is: b. False
The correlation between two stocks significantly affects the shape of the investment opportunity set. The investment opportunity set is a graphical representation of all possible portfolios that can be created by combining two assets, showing the risk (standard deviation) and return for each combination. The correlation between the assets directly influences the diversification benefits, which in turn shapes the opportunity set.
When the correlation between two stocks is positive, the opportunity set will be relatively steep, meaning the risk increases as the proportion of the higher-risk asset increases. This is because when the prices of the two stocks move in the same direction, diversification provides limited risk reduction.
In contrast, when the correlation is negative, diversification benefits increase because the stocks tend to move in opposite directions. This results in a flatter, more spread-out investment opportunity set, as investors can reduce overall risk by holding a mix of the two stocks.
If the correlation between the two assets changes, it alters how their returns move in relation to one another. A change in correlation affects the overall risk and return trade-off, shifting the portfolio frontier (the boundary of the investment opportunity set) either outward or inward, depending on whether the correlation increases or decreases. For example, when the correlation decreases, investors can create portfolios with lower risk for the same return, expanding the opportunity set. Conversely, when the correlation increases, the set becomes more compact, reflecting higher risk for a given return.
Therefore, the correlation between two stocks plays a crucial role in determining the optimal mix of assets and the shape of the investment opportunity set, impacting how an investor constructs a diversified portfolio.