Local stock markets adjust sluggishly to changes in local inflation. When the local rate of inflation increases, local investors subsequently earn significantly lower real returns on local stocks, but not on local bonds or foreign stocks. Our findings are consistent with local stock market investors using sticky long-run nominal discount rates that are too low when inflation increases, because they are slow to update the inflation expectations in discount rates in response to aggregate inflation news. Small amounts of stickiness in inflation expectations suffice to match the real stock return predictability induced by inflation in the data. We also consider other explanations, such as nominal cash flow extrapolation.