Contents
How is correlation a scaled version of covariance?
Correlation is a scaled version of covariance; note that the two parameters always have the same sign (positive, negative, or 0). Note also that correlation is dimensionless, since the numerator and denominator have the same physical units, namely the product of the units of X and Y.
What does covariance mean when the mean is 0?
Note also that if one of the variables has mean 0, then the covariance is simply the expected product. Trivially, covariance is a symmetric operation. cov(X, Y) = cov(Y, X). As the name suggests, covariance generalizes variance.
What are the upper and lower limits of covariance?
The upper and lower limits for the covariance depend on the variances of the variables involved. These variances, in turn, can vary with the scaling of the variables. Even a change in the units of measurement can change the covariance.
How does covariance and correlation impact portfolio risk?
Interpretation: The correlation between the returns of the two companies is very strong (almost +1) and the returns move linearly in the same direction. How does Correlation Impact Portfolio Risk? +1 = returns are perfectly positively correlated. 0 = returns of two assets are not correlated.
How to calculate the covariance of X and Y?
The covariance of (X, Y) is defined by cov(X, Y) = E([X − E(X)][Y − E(Y)]) and, assuming the variances are positive, the correlation of (X, Y) is defined by cor(X, Y) = cov(X, Y) sd(X)sd(Y) If cov(X, Y) > 0 then X and Y are positively correlated. If cov(X, Y) < 0 then X and Y are negatively correlated. If…
How to find the correlation coefficient of a variable?
The correlation coefficient, denoted by $\\rho_{XY}$ or $\\rho(X,Y)$, is obtained by normalizing the covariance. In particular, we define the correlation coefficient of two random variables $X$ and $Y$ as the covariance of the standardized versions of $X$ and $Y$.
How is the variance of a correlated variable determined?
Since the two variables are correlated, we use Equation 4.7.2 instead of Equation 4.7.1 for uncorrelated (independent) variables. Hence, the variance of the sum is which is equal to 31, 488. The variance of the difference is also determined by Equation 4.7.2: which is equal to 10, 512.