Local stock markets adjust sluggishly to changes in local inflation. When the local rate of inflation increases, local investors subsequently earn lower real returns on local stocks, but not on local bonds or foreign stocks, suggesting that local stock market investors use 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. 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.