Are hormone secretion variations the same for a pair of monozygotic twins?
Bartels et al. 2003 is a review that reports an estimate of the heritability of the cortisol level of 0.62. In comparison to most traits, it is a relatively high heritability.

So, in short, the answer is "no". Cortisol level variation is lower among twins than among unrelated individuals. If the definition of heritability is a little bit unclear to you, you should have a look at this post.

The reaction norm of cortisol level (and other stress response) with varying stress level also seems to be heritable (Ilsing and Hoelsboer 2006, Volckaert et al. 2012).