That relationship is totally untrue. let's look at the chart below:
Look at the period from 1972 to 1975. Interest rates moved up to approximately 13% while gold moved up in tandem.
Then look again at the period from 1977 to 1981. Interest rates moved up to almost 19% and gold moved up to its highest price ever during the same period.
Look again at the period from 2004 to 2007. Interest rates were up and so was gold.
The last example was the recent December 2015 hike. Gold went into a bull market .
So gold remains an excellent hedge in times of inflation and deflation.
As for deflation just look at the price of gold when interest rates are near zero from 2008 onwards.
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