Which of the following statements is true:I.

A high beta does not necessarily imply a high correlation with the market. The relationship

between beta and correlation can be expressed as 103.04.e2103.04.e2, where x is the market portfolio and y is the asset under consideration.

103.04.e

This means that a high market beta could be due to high volatility of the asset in question, and not because of a high correlation. Therefore statement I is not correct.Statement II is correct as correlation and covariance have the same sign. This is because correlation = covariance/product of standard deviations. Since standard deviation is always positive, correlation and covariance will have the same sign.A correlation of zero indicates the absence of a linear relationship between two variables - therefore statement III is correct.Statement IV is correct as well, because unless correlation is +1, diversification always reduces total portfolio risk.