In reply to John Lawo.

Thanks for writing. The variance of the estimates depends on several factors. Some you can control and some you can't:
1. The sample size. The parameter estimates in large samples tend to be closer than the estimates in small samples. Said differently, the standard error of an estimate decreases when the sample size increases.
2. The number of Monter Carlo simulations. For some statistical tests and procedures, you can get good estimates by using a moderate number of simulations. For example, you can probably use 1,000 MC simulations to get good estimates for a univariate mean whereas you might need 100,000 to get good estimates for kurtosis. That is because the variance of the mean estimator is much smaller than the variance of the kurtosis estimator.

So there is not a simple solution to your problem. Some statistics require many MC simulations, others do not.