Showing this is wrong seems like a simple exercise:
Representative agent with log utility, or even power utility would work.
Aggregate endowment i.i.d. growth with one disaster state with a 40% drop, perhaps log-normal otherwise.
eg, ln(C_t)-ln(C_t-1) is a lognormal with probability 0.999 and drops by 40% with probability 0.01
The equilibrium has consumption proportional to wealth, so that in the 40% disaster state, and the stock market drops by 40%, and consumption also drops by 40%
The representative agent feels pretty bad when that happens, with his utility taking a big dive in the disaster state.
This is a homework exercise for a basic graduate macro or finance course.
I am not saying that I believe that the model captures reality, or that we should not try to worry about recessions, but saying that a big drop in wealth (and therefore a big drop in consumption by the permanent income hypothesis) is something that rational agents should not worry about is missing the point.
You could do this with a model with TFP shocks, capital accumulation, and production too. Simply replace exogenous consumption growth with the TFP shocks.
This, to me, argues that we spend time trying to understand TFP shocks, or exactly what could cause a 40% drop in consumption growth. It would have to be a pretty big ‘cost push shock’ to get this to work in a neo-Keynesian model, but so too with the TFP shock, etc.