Cross- and auto-correlation effects arising from averaging: the case of US interest rates and equity duration

Most available monthly interest data series consist of monthly averages of daily observations. It is well known that this averaging introduces spurious autocorrelation in the first differences of the series. It is exactly this differenced series that one is interested in when estimating interest rate risk exposures, for example. This paper presents a method to filter this autocorrelation component from the averaged series. In addition, the potential effect of averaging on duration analysis is investigated, namely, when estimating the relationship between interest rates and financial market variables like equity or bond prices or exchange rates. In contrast to interest rates the latter price series are readily available in ultimo monthly form. It is found that combining monthly returns on market variables with changes in averaged interest rates leads to substantial biases in estimated correlations (R2), regression coefficients (durations) and their significance (t-statistics). These theoretical findings are confirmed by an empirical investigation of US interest rates and their relationship with US equities (S&P 500 Index).