Applies to: @RISK, all versions

Simulated Correlations vs. Specified Correlations

For discrete distributions with few possible values, the simulated correlation can differ significantly from the specified correlation.

@RISK generates correlated uniform random numbers (U01) first, then maps them through each distribution’s inverse CDF.

For distributions like RiskBinomial(1,0.5), all U01 numbers below 0.5 map to 0, and above 0.5 map to 1.

This mapping loses much of the original correlation information: a U01 of 0.1 and 0.49 both become 0, so the rank-order correlation is reduced.

Essentially, with few discrete outcomes, there’s limited ability to preserve the desired correlation after mapping, which explains why the observed correlation is lower than requested.

 

Related Articles:

How @RISK Computes Rank-Order Correlation.

How @RISK Correlates Inputs