The market’s estimate of inflation can be derived simply from the spread of “regular” (nominal) treasuries and TIPS (treasury inflation-protected securities). As I write this, the 30-year treasury is at 1.4% and the 30-year TIPS is at -0.2% (per Bloomberg). So, very simplistically, inflation is expected to average 1.6% (the difference). That is *slightly* off though in three ways:

First, it doesn’t matter much at the current low rates, but subtraction isn’t technically correct. The returns on nominal bonds are given by this formula: (1 + yield) = (1 + real rate) * (1 + expected inflation) * (1 + risk premium)

Since we are talking about treasuries, the risk premium is (supposedly) zero so that term drops out. We can rearrange the remaining terms thus: (1 + inflation) = (1 + nominal yield) / (1+ real rate)

Plugging in the current rates we have: (1 + inflation) = 1.014/0.998 = 1.0160

Subtracting 1, we are left with 1.6% as the inflation expectation. (As I said, very close to just subtracting at these low rates.)

Second, since TIPS are slightly less liquid than nominal treasuries we would expect a small liquidity premium (much like the difference between on-the-run treasuries and off-the-run treasuries). In other words, the TIPS yield is a little higher due to being less liquid which means expected inflation is actually a little higher than the spread would indicate.

Third, since TIPS eliminate inflation risk, buyers should be willing to pay a small premium to avoid that risk. In other words, the TIPS yield is a little lower due to having less risk which means inflation is actually a little lower than the spread would indicate.

My astute readers will have noticed that the previous two items go in opposite directions, so they offset each other. They are also difficult to estimate and are likely small in magnitude. In practice that means I ignore them.

Also, a note for data nerds, inflation is:

- heteroskedastic – the volatility of inflation is correlated to the level of inflation
- autocorrelated – the current level of inflation is related to the previous level of inflation
- positively skewed – high inflation is further away from the median than low inflation