The correct answer is: A. perfectly positively correlated with each other.
If two securities are perfectly positively correlated, then they will move in the same direction. This means that if one security goes up, the other security will also go up, and if one security goes down, the other security will also go down. This means that owning two perfectly positively correlated securities does not reduce risk, because the risk of one security is simply doubled.
Option B is incorrect because if two securities are perfectly independent of each other, then they will not move in the same direction. This means that if one security goes up, the other security could go up, down, or stay the same. This means that owning two perfectly independent securities does reduce risk, because the risk of one security is not correlated with the risk of the other security.
Option C is incorrect because if two securities are perfectly negatively correlated, then they will move in opposite directions. This means that if one security goes up, the other security will go down, and if one security goes down, the other security will go up. This means that owning two perfectly negatively correlated securities does reduce risk, because the risk of one security is offset by the risk of the other security.
Option D is incorrect because the category of a security does not affect its correlation with other securities. For example, two blue chip stocks could be perfectly positively correlated, perfectly independent, or perfectly negatively correlated.