Inflation, Stock Market, and Bond Market Returns

Below, Corrections depicts value-weighted one-year stock market returns (including distributions), one-year Treasury bond returns, and the one-year inflation rate (click to enlarge).  We display each one year lagged return by month, from 1951-2012 (inclusive).

Obviously, unexpected inflation takes away from an already-issued bond's return while having an unclear impact on already-owned stock returns.  Interestingly, simple regression on non-overlapping periods suggests a:

• 3.46% return on one-year bonds with 0.57% increase above and beyond that baseline for each one percent of inflation experienced that year.  
• 15.28% return on stocks with a -.76% loss for each one percent of inflation experienced that year

This may be seen in light of:

• One-year bond's arithmetic (geometric) average return of 5.57% (5.49%) with a standard deviation of 3.76%
• Value-weighted stock market's arithmetic (geometric) average return of 12.49% (11.13%) ( (including distributions) with a standard deviation of 16.36%
• The CPI's arithmetic (geometric) average level of 3.67% (3.68%) with a standard deviation of 3.00%

It is interesting and surprising that while bonds return less than stocks (on average) they return more in periods of higher inflation.  This is counter to the fact that a one log-point fall in unexpected inflation impacts the log return of already purchased bonds by one log-point.