Multivariate Distribution

RiskAMP Concepts

A multivariate distribution is a joint distribution including two or more individual distributions with defined cross-correlation.

RiskAMP provides a set of functions to create and sample from multivariate distributions. In a single multivariate distribution, the component distributions can be of different types.

This page will describe the basics of setting up a mutivariate distribution in Excel. There’s a longer article with more examples on our main website.

A multivariate distribution has two parts: a correlation matrix and a set of distribution functions, in a range.

Range of values

Each of the individual distribution functions making up the multivariate distribution should be next to each other, in a single column or row. The first parameter of all of the Multivariate.x functions points to this range of values. (That means each function will point to a range including itself. In this case that’s not a circular reference).

Correlation matrix

The correlation matrix is a two-dimensional array describing the cross-correlation among the individual distributions. This matrix must be symmetric and positive-definite. You can provide just the lower-triangular matrix. The second parameter of all of the Multivariate.x functions points to this correlation matrix.

If you see a #VALUE error when entering a multivariate function, it’s likely the correlation matrix is not correct. There’s a tool on the RiskAMP toolbar to validate the correlation matrix.

Distribution parameters

After the first two parameters, each of the multivariate functions takes different parameters, depending on the distribution.

Example

In this example, the correlation matrix is in B2:D4. The range of values is in B7:B9. If you click on any of the cells in B7:D9, you’ll see that the first two parameters of the function refer to the range of values and the correlation matrix.

Validating correlation

To check the cross-correlation in your multivariate distribution, use the function SimulationCorrelationMatrix. This function takes a range of cells and returns correlation observed during the simulation.