A Tale of Four Tails: Inflation, the Policy Rate, Longer-Term Rates, and Stock Prices

We analyze empirical links between the perceived tail-risk of inflation, the policy rate, longer-term interest rates, and equity prices in the U.S. Their simultaneous changes enable us to distinguish between a systematic and \"exogenous\" response to monetary-policy news. And, those tail risks' co-movements are accounted for in quantifying the magnitude and persistence of their responses to key shocks. We find that: (i) in the medium-term, all four tail risks respond significantly and contemporaneously to domestic and foreign monetary-policy announcements, except for the equity tail risk to foreign policy; (ii) all four tail risks rarely change in response to other U.S. macroeconomic news; (iii) the directional pattern of their simultaneous reactions to policy announcements is often consistent with the systematic response to new information about the economic outlook rather than with the response to an exogenous shock; (iv) the few notable instances of the latter response are always in reaction to Fed announcements; and, (v) our impulse responses demonstrate that odds of extreme inflation outcomes and extreme policy-rate outcomes are tightly linked, and that both determine tail outcomes for longer-term interest rates but not for stock prices.