The nature of the dependence of the magnitude of rate moves on the rates levels: a universal relationship

We look at the dependence of the magnitude of rate moves on the level of rates, and we find a universal relationship that holds across currencies and over a very extended period of time (almost 50 years). For the very low level of rates, we find a proportional behaviour; for rates of an intermediate level we find that the magnitude of moves becomes independent of the level. The linear dependence resumes, however, for very high rates. We find the results to be very robust across currencies, tenors and time periods. Even the data we have collected for the UK Consol yields going back to the XIX century conform closely to the same pattern. We discuss the importance of these findings for several theoretical and practical applications.