This paper finds the first evidence of time variation in the relationship between inflation expectations and the price of cryptocurrency futures. Daily data on the futures markets of Bitcoin – starting in December 2017 – and Ethereum – available since February 2021 – reveal responses to inflation expectations that are consistently positive across both measures in a full sample encompassing 2022. These results hold for a sample that precedes the Luna crash in May 13, 2022. However, the response turns negative in the period between the failures of the Luna and FTX crypto exchanges. We find cryptocurrency futures provide an effective hedge against inflation expectations and may provide a hedge against idiosyncratic market risk if the ensuing uncertainty is embraced by traders leading them to search-for-yield behavior. Risk that is more systemic – and not properly digested by financial markets – may lead futures contract holders to exit their positions ahead of expiration, leading to a bid down of futures prices and an erosion of their hedging ability. This may have contributed to the turbulence in cryptocurrencies experienced during the latter part of 2022.

This paper derives the user cost of monetary assets and credit card services with interest rate risk under the assumption of intertemporal non-separability. Barnett and Su (2016) derived theory permitting inclusion of credit card transaction services into Divisia monetary aggregates. The risk adjustment in their theory is based on consumption capital asset pricing model (CCAPM) under intertemporal separability. The equity premium puzzle focusses on downward bias in the CCAPM risk adjustment to common stock returns. Despite the high risk of credit card interest rates, the risk adjustment under the CCAPM assumption of intertemporal separability might nevertheless be similarly small. While the known downward bias of CCAPM risk adjustments are of little concern with Divisia monetary aggregates containing only low risk monetary assets, that downward bias cannot be ignored, once high risk credit card services are included. We believe that extending to intertemporal non-separability could provide a non-negligible risk adjustment, as has been emphasized by Barnett and Wu (2015). In this paper, we extend the credit-card-augmented Divisia monetary quantity aggregates to the case of risk aversion and intertemporal non-separability in consumption. Our results are for the “representative consumer” aggregated over all consumers. While credit-card interest-rate risk may be low for some consumers, the volatility of credit card interest rates for the representative consumer is high, as reflected by the high volatility of the Federal Reserve’s data on credit card interest rates aggregated over consumers. One method of introducing intertemporal non-separability is to assume habit formation. We explore that possibility.