Can we generate data from two exponential distributions with correlation -1

Question

https://stats.stackexchange.com/questions/66775/attainable-correlations-for-exponential-random-variables

With reference to the above link I want to ask if it is impossible to generate two exponential distributions with correlation -1 ?

Answer 1

That is correct, it is impossible to generate two exponentials with a correlation of -1. Basically, this is because of the asymmetry around the mean.