Breakeven Inflation Rate vs Actual Inflation Rate Study

I am relatively new to the realm of TIPS and inflation rate and am working on a study. I wish to investigate the correlation between the breakeven inflation rate for (5Y, 10Y, 20Y) TIPS and actual inflation rate.

Based on my understanding, the BE rate is a market expectation of inflation. It is controlled by the spread between traditional bonds minus the corresponding TIP bonds. If the BE rate equals the average inflation rate over the term of the bond, then both bonds should carry roughly the same yield. Hence, a bet on TIPS is a hedge on inflation?

I am interested in seeing if there is any correlation between BE rate and actual inflation.

• I would start simple, by EX: taking BE rate for 5Y bond @ 2010 Jan. Then, calculating average inflation from 2010 - 2015.

• After that, checking how accurate the expectation was or are there any patterns or correlations.

I'm curious as to how to go about doing this. For example, how to calculate the bolded term average?(moving average, simple average, weighted average, EMA, etc.)

Any help and/or advice is greatly appreciated

I would compare the breakeven rate (yield of most recently issued nominal bond minus real yield of most recently issued TIPS) with the realized rate, with the latter determined as follows : $$(EndingTipsIndex/StartingTipsIndex)^{(1/n)} - 1$$