Speaker: Dr Godfrey Charles-Cadogan, Lecturer in Finance, University of Leicester
Time: Wednesday, 30 October 2019, 13:00-15:00
Venue: S314 (Paul Webley Wing, Senate House)

Abstract
We introduce a novel single factor singular integral representation theorem for the equity premium, which accommodates rare disasters, and consistently produces statistically significant implied risk aversion (IRA) index estimates in line with  economic theory and risk elicitation experiments, i.e. IRA index <<1. The estimated equity premium (ERP) is more than 10-times larger than that for CAPM over the sample period. In most of the literature, the IRA index required to explain the ERP is either calibrated or estimated with values in the range [2, 100] often with low power. Our model seems to be the first to produce strong statistically significant estimates for the IRA index for equity premia (and Fama-French hedge factors) according to theory and experiments, i.e., (0.41, p<0.001).  The distribution of intertemporal substitution of consumption (IMRS) in our sample of US monthly data over the last 20-years is bimodal with median value 3.37. It peaks with high volatility during market bubbles but falls precipitously and remains flat after rare disasters as risk averse agents hold more cash. So, consumption is very sensitive to interest rates. The distribution of IRA index is right skewed with clustering in the tail around IRA index =1 for rare disasters as predicted by Arrow's theory. Our model is distinguished from Wachter's (2013) jump diffusion approach where a single factor--time varying probability of rare disasters--drives results, and Delikouras and Kostakis (2018) disappointment aversion where a single factor--the indicator function when consumption growth is less than its endogenous certainty equivalent--motivates results. Unlike those models, there is no calibration in our model. The single factor in our model is based on a loss aversion index for intolerance to decline in consumption, and it is formulated from the entire distribution of consumption growth. It is a sufficient statistic for habit formation and it explodes during rare disasters. In fact, it supports a mixture random variable that matches observed consumption growth. Estimated time varying IRA index tracks the CBOE VIX over time, identifies background risk, and facilitates forecast for states of the economy.

Keywords:  loss aversion, risk aversion, consumption, mixture distribution, asset pricing, pricing kernel, rare disasters

JEL Classification: C16, D81, G12

The seminars are sponsored by grants from DFID and ESRC [ESRC Ref: ES/N013344/2], ESRC and NSFC [ESRC Ref: ES/P005241/1] and AXA Research Fund