Super-exponential growth expectations and the global financial crisis

We construct risk-neutral return probability distributions from S&P 500 options data over the decade 2003 to 2013, separable into pre-crisis, crisis and post-crisis regimes. The pre-crisis period is characterized by increasing realized and, especially, option-implied returns. This translates into transient unsustainable price growth that may be identified as a bubble. We evaluate a "real-minus-implied risk premium", defined as the difference between real and option-implied returns, which reveals a doubling of the risk-aversion of investors, from 8% in the pre-crisis to 16% in the post-crisis period. Granger causality tests demonstrate that changes of option-implied returns lead the changes of Treasury bill yields with a lag of a few days in the pre-crisis period, while the reverse is true with a lag of 50 to 200 days in the post-crisis period. This suggests a transition from an abnormal regime preceding the crisis to a "new normal" post-crisis