A univariate distribution describes the distribution of a single random variable.
A multivariate distribution describes the distribution of a combination of two or more random variables. It is meaningful only when the behavior of each random variable in the group is dependent on the behavior of the other variables in some way. So, it is extremely important in the distribution of returns of a portfolio consisting of more than one stock.
We need mean and variance of the combination of random variables to draw a multivariate distribution. To calculate the variance of a combination of random variables (such as returns on stocks), we need a pairwise correlation between the variables.
A multivariate distribution for the returns on n stocks is defined by the following three parameters:
- The mean returns on the individual securities (total n distinct means)
- The variance of return of each security (total n distinct variances)
- The distinct pairwise return correlations between the securities (total 0.5n(n-2) distinct correlations)
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