The covariance of returns of Stock $1$ with Stock $2$ is $150.$ The covariance of Stock $3$ with Stock $4$ is $200.$ The covariance of Stock $5$ with Stock $6$ is $-100.$ Which of the following statements is $($are$)$ definitely true?

I. The correlation coefficient between Stock $1$ and Stock $2$ is greater than the correlation coefficient between stock $5$ and $6.$

II$.$ Stock $1$ and Stock $2$ have a lower correlation coefficient than Stock $3$ and Stock $4.$

III. Stock $5$ and Stock $6$ have a lower correlation coefficient than Stock $3$ and Stock $4.$

IV$.$ The correlation coefficient between Stock $1$ and Stock $2$ is positive