Final answer:
Perfectly positively correlated securities move in the same direction, and a correlation coefficient 'r' of 1 signifies a perfect positive correlation. To have a coefficient of determination of at least 0.50, the correlation coefficient must be around ±0.71.
Step-by-step explanation:
When we talk about two securities that are perfectly positively correlated, we are referring to a situation where the movement of one security is mirrored by the movement of the other. If one security's price increases, so does the price of the other, and if one decreases, the other follows suit. This correlation is measured by the correlation coefficient, denoted by 'r'.
The correlation coefficient ranges from -1 to 1. A value of 1 indicates a perfect positive correlation. In financial markets, a perfect positive correlation is rare, but it could happen when two securities are very similar or influenced by the same factors.
To achieve a coefficient of determination, also known as R-squared, of at least 0.50, which explains the proportion of variance in the dependent variable that is predictable from the independent variable, we would need a correlation coefficient (r) of roughly 0.71 or -0.71, rounded to two decimal places.
This means that there is a minimum of a 71% positive or negative correlation between the two variables.