US dollar exchange rate elasticity of gold returns at different federal fund rate zones

We examine the relationship between gold prices and the U.S. dollar exchange rate, arguing that their interactions are state-dependent and asymmetric under different market conditions. State dependency hinges on different short-term interest rate zones. To prove this point, we determine three distinct levels or zones of the effective federal funds rate using SETAR(2,p) tests. Subsequently, we perform conditional least square estimations of log changes in gold prices as a function of log changes in the nominal broad U.S. dollar exchange rate index for each of the obtained zones. Their relationship is consistently inverse, suggesting that gold and the U.S. dollar are risk-hedging substitutes for normal market periods. This also implies that gold is a safe-haven asset against the U.S. dollar exchange rate risk against a broad range of currencies. The substitution is weaker in the low-interest rate zone, more robust in the intermediate zone, and very pronounced in the high zone. We also perform a Markov switching test on the double-log function of gold prices and the exchange rate. The tests show a pronounced inverse relationship, i.e., substitution between assets, at normal market conditions. The relationship becomes significantly positive during episodes of financial distress, indicating complementarity between gold and U.S. dollar assets.