The impact of changing inflation on stocks depends on the initial level of inflation and the direction of travel.

The combination that tends to be most favorable for stock markets is when inflation is rising from very low levels (and deflation risks are receding) or when high inflation levels are moderating. As the chart shows, for stocks, bonds, and balanced funds, higher inflation (above, say, 3%) that is rising tends to be the worst outcome, while inflation above 3% that is falling is much more benign. 

For stocks in particular, the best returns tend to occur when inflation is below 1% but rising; this is often associated with a recovery from a recession and also with a decline in the risk of deflation (and is therefore not particularly favorable for bond markets).

Stable returns with inflation within range: reversal of extremes tends to be bullish