Long Term Historical Correlation of S&P 500 with Interest Rates

In the previous post I highlighted how the correlation of rates and the S&P 500 has turned slightly negative, which is an infrequent occurrence judged over the last 10 years.  The risk on/risk off trade has thrived on the idea that rates and stocks are positively correlated (i.e. when stocks go down bonds rally (rates fall) and when stocks go up bonds sell off).  This is likely a function of the fact that the risk premium (as opposed to inflation expectations) is the primary driver of price fluctuation in the current environment.

For most of the 20th century, risk premium was less important than inflation premium though, which led to an inverse correlation of rates and equities.  Because inflation was a greater component of a company's cost of equity, as inflation expectations fell, interest rates fell (as did the cost of equity) and stocks rallied along with bonds.  If inflation ever becomes a dominant theme again, then one might expect the correlation that has been the heart of the risk on/risk off trade to get turned on its head.  What happens to the algo guys if that happens?