Alternative Yield Discount (Inflation) Rates

Investors arguably expect that investments generate returns in excess of the inflation rate. Do different measures of the inflation rate indicate materially different yield discounts? To investigate, we relate 12-month trailing S&P 500 annual operating earnings yield (E/P), S&P 500 12-month trailing annual dividend yield, 10-year U.S. Treasury note (T-note) yield and 3-month U.S. Treasury bill (T-bill) yield to four measures of annual U.S. inflation rate:

1. Non-seasonally adjusted inflation rate based on the total Consumer Price Index (CPI) from the Bureau of Labor Statistics (retroactive revisions of seasonal adjustments interfere with historical analysis).
2. Non-seasonally adjusted inflation rate based on core CPI from the Bureau of Labor Statistics.
3. Inflation rate based on the Personal Consumption Expenditures: Chain-type Price Index (PCE) from the Federal Reserve Bank of St. Louis.
4. Trimmed mean PCE from the Federal Reserve Bank of Dallas.

The CPI measurements have a delay of about two weeks, and the PCE measurements have a delay of about a month. Using monthly data for all variables during March 1989 (limited by earnings data) through January 2022, we find that...