Expected Inflation Rate and Equity Returns: New Perspectives from Market Efficiency with Weekly Data and the Option’s RHO

Abstract

We examine the Fisher hypothesis with weekly equity returns and latently obtained simulated expected weekly inflation rates for five sectors in USA, Japan, UK, Canada and South Africa between Jan. 1975 and May 2009 and for several sub-periods, including that for the global financial crisis. Three main interdependent innovations define this paper. First, market efficiency, combined with noisy rational expectations equilibrium, posits an insignificant relation in data with a frequency that matches the frequency of the inflation announcements. Our evidence from estimations with monthly data supports this prediction. Second, new ideas, based on the option role of levered equity, indicate a dynamic, non-linear, and not one-for-one Fisher relation for equity returns and expected inflation rates. In particular, this interpretation emphasizes for the first time the effect of the changes in the aggregate amount of outstanding corporate debt on the Fisher hypothesis and also exposes the economic forces, other than the alluded market efficiency, that lead to insignificance. Third, a novel simulation-based approach with weekly data, when the inflation announcements occur monthly, examines empirically these option-theoretic arguments. We (i) introduce the Brownian Bridge to construct a reliable and simulated path of weekly inflation rates, (ii) extract its expected / unexpected inflation rate paths via the Kalman filter, and (iii) perform an estimation. This procedure is repeated 10,000 for each sector, country, and (sub-) sample period, leading to more than 1,250,000 estimations and rich distributions for the estimates. Our work stays clear of the concern for the power of the test, which is inherent in the long-horizon data of previous literature. Further, this approach captures the rich information in short-horizon return data. We find evidence in support of the option-theoretic arguments and offer an explanation for the dynamic changes in the signs and magnitudes of the coefficient estimates over time.