Negative. Correlation does not imply causation. There are plenty of examples in history where both interest rates were increasing along with the POG. Most of the 1970s would be one such example.
If one views gold as a currency, then the only guaranteed future exchange rate US$/Au is that which can be predicted by the interest rate differential i.e. the 'market prediction'. The more the US$ interest rates rises relative to the gold lease rate, the higher the future US$/Au rate i.e. an increase in the POG. Many will point out that there are many cases where the market prediction of future US$/Au exchange rate was wrong and they would be correct. Yes, the market is often wrong as carry trades demonstrate. However, I point out if someone believes that US$ interest rates are going up and thus gold will get cheaper in US$ terms, then they are welcome to short gold and buy US$ and thus get rich bucking the market. One wouldn't recommend US$ bonds for obvious reasons (rising rate environment).
A lot of people don't understand the origin of interest rates. They think Janet at the Fed is pulling levers and pushing buttons that actually do something. The only thing they can really do is buy or sell bonds. The QE experiment demonstrated that one can monetise a lot of debt but one cannot guarantee where the new money goes. In the US$ case in the last ten years, thanks to bond speculation, it went right back into the bond market further lowering interest rates and causing more deflation. Exactly what the Fed did not want.
Interest rates are a market phenomenon and the Fed gets its cue to "set" rates from the bond market. Interest rates rise because the marginal bondholders offload overpriced bonds because the interest these bonds pay no longer sufficiently compensates them for the ongoing currency debasement. Rising interest rates and falling bonds are thus a signal of rising inflation (sensu lato). I would not say this is "good for gold", rather bad for the currency as it now needs a higher interest rate to compensate investors to hold US$ bonds. Thus killing the argument that US$ bonds pay interest whereas gold is a 'dead' investment.
Certainly, I would not use rumours of rising US$ interest rates as a reason to short gold and invest in US$ cash.
