S-shaped utility, subprime crash and the black swan

I propose an S-shaped utility function of consumption which, combined with an heterogeneous agents and external habit setting, fits well the first order moments of the American financial and macroeconomic time series relevant for the equity premium puzzle in the second half of XX century. The average relative risk aversion of the agents remains in the 0-3 range. A "black swan"-kind phenomenon makes two of the 50 years considered (the two oil shocks) responsible for half the average of the stochastic discount factor, thus bringing the annual subjective discount factor to a very low level, around 0.5, which solves the risk-free puzzle. The shape of the relative risk aversion function of consumption suggests an explanation for the 2008 suprime crash akin to the breaking of waves on a beach in a lifecycle overlapping generations model.