Relation between price of gold and FED's balance sheet.

Seems to exists a relation between those two. In the long run, gold price seems to follow the expansion movements of the FED. In 08, prior to the GFC, the size of the BS was 800 times bigger than the price of a gold ounce. In 2012, it was 1,800 times bigger than the ounce of gold.

In both cases, the FED's BS was bigger than the ounce of gold by a factor that equals the price of that ounce.

After a growth in the BS size, it seems that it takes some time for gold to reach the value that matches the relation described above. It seems to require some time of keeping a steady not growing BS to reach it. In 2019, the FED failed in its attempt to reduce the BS, so gold wouldn't reach the desired value.

Would the FED be able to taper now? Would we see the ounce of gold at $3,600?