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Covariance measures how2 variables move together. Eg. consider2 securities A and B. How the return of A & B are moving together. That is what Covariance measures. Covariance is measured as Standard Deviation of A * Standard Deviation of B * Correlation Coefficient. It can be +ve or -ve.. It can take any value depending upon the relationship between variables.
Correlation is the measure of linear dependance between2 variables. It can vary from -1 to0 to +1. A correlation coefficient of -1 indicated perfect negative relationship i.e. if one variable increases the other variable decreases (Consider savings and expenses at constant income) and and a correlation coefficinet of +1 indicates perfect posive relationship, in other words, if one variabl increases the other variable also inreases (Consider income and savings at constant expenses)