There has been talk about 5 by 5 rates a number of different places recently. I had a conversation in the comments of a TheMoneyIllusion post a couple of weeks back about 5 by 5 rates. A few days ago Tim Duy had a post about them as well.
First, what is this all about? Essentially, you can get a quick and easy estimate of what market participates think inflation will average for five years starting 5 years from now, using conventional 10 year and 5 year Treasury data and 10 year and 5 year TIPS data. The TIPS is a Treasury security that compensates for inflation, so that its yield is essentially a measure of the real interest rate. Differencing the two types of Treasuries gets you a measure of the average inflation implied up until the maturity of the security by the Fisher Equation. So the difference between the yields of the two 5 year Treasuries is average inflation over the next five years, and the difference between the yield of the two 10 year Treasuries is the average inflation for 10 years. Note that there is a number of different ways inflation could play out that could give rise to the average. It could be relatively constant over all the years, or might be low and then become higher. Also, these are expectations conditional on market participants current knowledge.
The useful point about looking at both the 5 year and 10 year average inflation expectations is that you can back out what the implied inflation is for years 6 through 10. There is more about how this is done in the comments linked to above, but using the magic of natural logs, you can get a very good approximation by the 10 year average inflation being the weighted average of the two five year averages. (James Hamilton had a very good post on the usefulness of logs in economics). The picture below is the implied average inflation for five years starting in five years using daily data from FRED starting with the earliest available date.
The first thing that is easily noticed is that there is increase in volatility in the expectations in the latter half of the series. The variance up the end of 2006 is around 0.027, while the variance after June 2009 is 0.053.
A plausible reason for this is Fed policy. I borrowed the idea from to plot expansionary or contraction changes in Fed policy on the 5 by 5 rates. Marcus at the link looks at other data. However, when looking at the 5 by 5 rates below, the Fed generally turns off QE after a period of future inflation exceptions rising. How likely is it that the FOMC (Federal Open Market Committee) would look at the 5 by 5 in its decision making process? Recent Fed transcripts reveal that they went into the decision making process in Sept 2008. Obviously, the FOMC is going to be looking at a number of other things as well. However, this serves as some indication that the FOMC is still very much concerned with long run price stability, possibility at the expense of the slowly improving job market. With all this in mind it is not surprising that Bernanke recently stated that “Although we have been very aggressive, I think on the monetary policy front we could have been even more aggressive.”