How does the consumer price index (CPI) affect the stock market?

The CPI is the measurement used by economists for tracking price changes in a typical basket of goods and services that urban consumers buy. Central banks monitor price changes to ensure economic growth remains stable, and they use monetary policy tools ( Lift or reduce interest rate) to intervene if it detects too much inflation or deflation. 

When the central bank moves to cool down an overheated economy, it is also temporarily limiting the pace of future economic growth. When this happens, corporate earnings can be expected to decline as business slows. Since each share of stock represents fractional ownership in the underlying company, if the company's business slows, its earnings per share of stock will decline. Thus, stock markets typically aren't moved directly as much by CPI data, but can be this way since higher interest rates can cause business activity to slow. In general stock markets prefer a lower CPI that allows consumers to keep spending, and businesses to continue investing.