Question

Choose the correct code for the following statements being correct or incorrect.

Statement I : When the two securities returns are perfectly positively correlated, the risk of their portfolio is just a weighted average of the individual risks of the securities. In such case, diversification does not provide risk reduction but only risk averaging.

Statement II : Total risk of a portfolio of two risk securities can be completely eliminated when their returns are perfectly negatively correlated and their proportionate holdings in the portfolio are inversely related to the relative individual risks of the securities. 

1. Both the statement I and II are correct.
2. Both the statement I and II are incorrect.
3. Statement I is correct, but II is incorrect.
4. Statement II is correct, but I is incorrect.

Answer 1

Correct Answer - Option 1 : Both the statement I and II are correct.

Statement I: When the two securities returns are perfectly positively correlated, the risk of their portfolio is just a weighted average of the individual risks of the securities. In such a case, diversification does not provide risk reduction but only risk averaging.

Explanation:

1. A perfectly positive correlation means that 100% of the time, the variables in question move together by the exact same percentage and direction. 
2. When security returns are perfectly positively correlated, the correlation coefficient between the two securities will be +1.
3. The returns of the two securities will move up or down together, then the portfolio happens to be undiversified which does not provide risk reduction but only risk averaging. Thus, the statement I is correct.

Statement II: Total risk of a portfolio of two risk securities can be completely eliminated when their returns are perfectly negatively correlated and their proportionate holdings in the portfolio are inversely related to the relative individual risks of the securities. 

Explanation: 

1. Other things equal, the smaller the correlation between two assets, the smaller will be the risk of a portfolio of long positions in the two assets. 
2. When security returns are perfectly negatively correlated, the correlation coefficient between the two securities will be -1.
3. The two returns will always move in exactly opposite directions making the portfolio diversified which helps to eliminate risk. Thus, statement II is correct.

Thus, option 1 is the correct answer.