Measuring Expected Inflation

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Copyright 2021, Tony Lima. All rights reserved.
[pdf version available after the endnotes]

This article was spurred by an entry in the Wall Street Journal (May 23, 2021).[1] Titled, “Inflation Forces Investors to Scramble for Solutions,” it is the usual combination of fearmongering and bad advice.  This seems like a good time to write about current inflation news. Along the way I’ll describe measuring expected inflation, look at the yield curve, and conclude with the term structure of expected inflation.

WSJ headline and photo current inflation newsThe last WSJ article I read with a scary headline like this completely failed to mention Treasury Inflation Protected Securities (TIPS).  I wrote a note about this omission to a friend who works at WSJ.  At least the most recent article mentions TIPS.

The challenge facing investors was apparent this month when new data showed a surprisingly large jump in consumer prices. Rather than rise, a collection of assets generally thought to safeguard investors against inflation fell after the report.

The price of the benchmark 10-year Treasury inflation-protected security logged its biggest one-day decline in a month. Shares of real-estate investment trusts slid the most since January. Commodities were generally flat but dropped the following day.

Once again, the Journal misreads the market.  The price of 10-year TIPS fell because the market had expected an even worse report.  And the data is cherry-picked, limited to one observation out of 25 days (assuming the “month” began Monday, April 15).  A very small sample out of an anemic larger sample drawn from a vast ocean of data contains a quantity of information of approximately equal to zero.

So let’s look at some longer term data.  A friend has an IRA account that includes a chunk of a TIPS mutual fund.  Over the last year, the price has appreciated 6.64%.  That ain’t chicken feed.  And it means the market’s fears about inflation have been rising steadily. 

Directly Measuring Expected Inflation

Luckily, we have a market-based measure of expected future inflation.[2] This is based on the Fisher Equation

Fisher Equation measuring expected inflation

Fisher Equation

where πe is the expected inflation rate, i is the nominal interest rate (the market interest rate) and r is the real interest rate (the interest rate adjusted for inflation expectations). We have direct measures of both variables. The nominal interest rate is the current yield on U.S. government securities. The real interest rate is the yield on TIPS. The Fed supplies historical data on these two variables for 5-, 7-, 10-, 20-, and 30-year maturities.[3]

An example will show how this works. Suppose our planning horizon is 10 years. On May 14, 2021, the nominal interest rate on 10-year Treasury notes was 1.65%. The real interest rate on 10-year TIPS was ⎯0.88%. Therefore, the expected annual inflation rate over the next ten years is

Expected ten year annual inflation measuring expected inflation

Expected ten year annual inflation

The Term Structure of Expected Inflation

The Fed data set presents an interesting possibility: the term structure of expected inflation. In the world of finance, the term structure of interest rates (yield curve) shows the relationship between the times to maturity of securities and their yields to maturity. Here’s an example from May 14, 2021.

Yield curve measuring expected inflation

(click for larger image)

A yield curve usually slopes upward because risk increases as the time to maturity lengthens. By definition, a 30-year security is riskier than a 10-year security because there are 20 more years of possible adverse events.[4]

At this point, you may be wondering about risk. There are two sources of uncertainty in the Fisher equation: the inflation rate and the real rate of return.

The actual future inflation rate is unknown because of many uncertainties. They include (but are not limited to) monetary and fiscal policy, external supply shocks, and international factors (exchange rates and asset flows). The previous equations take an ex-ante viewpoint in that they are predictions of the future. But ex-post this relationship must be true by definition:

Ex post real interest rate measuring expected inflationIn other words, looking into the past the real rate of return must equal the nominal interest minus the actual inflation rate. Continuing the previous example,

Ex post ten year real interest rate measuring expected inflation

Ex post ten year real interest rate

The real rate of return on that 10-year government bond will be 0.88% if the actual inflation rate is 2.53% per year over that period. That is the source of uncertainty about expected inflation. We simply do not know for sure what the actual inflation rate will be in the next ten years.

The risks in the real rate of return are less obvious. Some economists measure the risks arising from the real rate of return on physical capital. While that is a contributing factor, the assumption that the real rates of return on financial and physical assets are equal is an equilibrium condition, not necessarily true in the short run (even with a planning horizon of ten years). I prefer to think of the real return on financial assets as risk free since, by definition, it is the difference between the nominal return and the actual inflation rate.

What will inflation risk do to our model? Let’s look at the data. Here’s the May 14, 2021, version.

Inflation expectations term structure May 14, 2021 measuring expected inflation

(click for larger image)

The market expects 2.69% annual inflation over the next five years. From seven to 20 years maturity, expected inflation is slightly less than 2.55%. For a 30-year planning horizon, expected inflation drops to 2.36%. Several things are notable about this graph.

First, short-term inflation expectations are considerably higher than even slightly longer-term rates. Second, the stability of expectations from 7- to 20-year maturities is unexpected (at least by me). For additional information, let’s look at how the shape and location of the expected inflation curve have changed over the last year. (The Excel workbook contains monthly data. I picked four months that divide the period roughly into thirds.)

Inflation expectations term structure measuring expected inflation

(click for larger image)

There has been a consistent, steady upward shift of inflation expectations over the last year. One year ago, the five-year expectation was 0.82%. A few weeks ago, it was 2.69%. An upward shift of the expected inflation curve means markets expectations of inflation are 1.87 percentage points higher than they were a year ago.]

Time for some basic economics. A movement along a single yield curve is caused by changes in the planning horizon (time to maturity). When the term structure of expected inflation shifts, some other factor affecting inflation expectations must have changed. One possible factor is inflation risk. Higher inflation risk causes bond buyers to demand a higher rate of return to compensate for the additional risk. From our two-dimensional perspective the expected inflation curve shifts upward.

There’s something a bit more subtle going on here. The expected inflation term structure curve slopes upward in the two 2020 observations. In 2021, the curve slopes downward. A positively sloped curve means markets expect long-term inflation to be higher than short-term inflation. A negatively sloped curve means the opposite. Here’s a closer look at the two monthly observations closest to January 1, 2021.

Flat expected inflation curve measuring expected inflation

(click for larger image)

At some point between December 25, 2020, and January 29, 2021, the expected inflation curve inverted.[5] There are several possible complementary explanations.

One obvious fact is that long-term inflation expectations tend to be anchored in the 1.5% – 2.5% range. Short-term expectations may be above or below this anchor. While this is true, it does not really explain the facts.

A second hypothesis is that markets suddenly became aware of short-term inflation near the beginning of 2021. The most obvious event was President Biden announcing his cabinet selections and started laying out his legislative agenda. Treasury Secretary Dr. Janet Yellen is a died in the wool Keynesian. Her Ph.D. from Yale was under the watchful guidance of the late James Tobin. Do not expect supply side economics to have much traction in this administration. As evidence, consider their denial that high unemployment benefit payments contribute to lower labor force participation. Most economists worthy of the title disagree. I wrote about one example a few weeks ago. The markets (and I) correctly observed that this would add to inflationary pressure, especially over the next five years.

A third possibility is differences in inflation risk at different time horizons. It looks like markets are saying that inflation risk has risen by more in the five-to-seven-year range. It’s difficult to see this from the previous graph, so here’s the change in expected inflation.

Change in expected inflation measuring expected inflation

(click for larger image)

This makes it pretty clear that the largest increase in inflation risk has been in the five-to-seven-year maturities. After that the difference remains fairly constant (despite the changes in slopes of the two term structure lines).

Are Markets Correct?

With M2 growing over 20% per year, it’s difficult to understand why the five-year expectations are as low as they seem. My guess is that they are taking the Fed at its word. Board of Governors member Lael Brainard made this unusually frank statement in a May 11 speech (emphasis added).[6]

But recent experience suggests we should not lightly dismiss the risk on the other side. Achieving our inflation goal requires firmly anchoring inflation expectations at 2 percent. Following the reopening, there will need to be strong underlying momentum to reach the outcomes in our forward guidance. Remaining patient through the transitory surge associated with reopening will help ensure that the underlying economic momentum that will be needed to reach our goals as some current tailwinds shift to headwinds is not curtailed by a premature tightening of financial conditions.

Earlier in that same speech, Gov. Brainard used the Fed’s new favorite word: “transitory.” Inflation may rise this year, but it won’t last long. Just for laughs, let’s do a little number-crunching.

The Path of Inflation

Suppose inflation over the next 12 months is 10%. What inflation rates will lower the five year average to 2.69%? The answer is 0.9397% for each of the remaining four years.

Inflation required to meet 2.69% inflation expectations, 10% year one inflation measuring expected inflation

Inflation required to meet 2.69% inflation expectations, 10% year one inflation

The Excel workbook does the calculations for you. Pick values for the year 1 inflation rate (10% above) and the inflation goal. The software will calculate the required inflation rates over the subsequent four years.

What about 5% inflation? Here, at least, the Fed can tolerate additional inflation in years two through five.

Inflation required to meet 2.69% inflation expectations, 5% year one inflation measuring expected inflation

Inflation required to meet 2.69% inflation expectations, 5% year one inflation

That 2.12% inflation must look pretty attractive to the Fed. Sadly, I don’t believe inflation over the next 12 months will be that low.

One more example will make the point clear. Suppose inflation is 15% over the next year. In that case, achieving a 2.69% average rate over the five-year period requires slight deflation.

Inflation required to meet 2.69% inflation expectations, 15% year one inflation measuring expected inflation

Inflation required to meet 2.69% inflation expectations, 15% year one inflation


Are you depressed? Don’t be. If my forecasts are anywhere near correct, five-year TIPS securities are currently underpriced. Don’t put your entire retirement account into TIPS, but a chunk will be a useful hedge. For those who prefer conventional mutual funds, Vanguard’sShort-Term Inflation-Protected Securities Index Fund Admiral Shares (VTAPX)is one example. Vanguard and many others offer Exchange-Traded Funds of short-term TIPS.

Disclaimer: remember what you paid for this advice. I have a small piece of my retirement in a TIPS fund. But diversification remains essential.

  1. Goldfarb, Sam (May 23, 2021). “Inflation Forces Investors to Scramble for Solutions.” Wall Street Journal, May 23, 2021. Available at Accessed May 23, 2021.
  2. I did some reading after writing this draft. Apparently, it is now fashionable to call expected inflation “breakeven inflation.” While there are subtle differences between the two phrases, this blog is not now and has only rarely in the past pretended to include only academic research and publications.
  3. Board of Governors of the Federal Reserve System, “H.15 Selected Interest Rates.” Available at Accessed May 26, 2021.
  4. Tobin, James (1958). “Liquidity Preference as Behavior Towards Risk.” The Review of Economic Studies 25.2 (Feb 1958): 65-86. Available at: .
  5. Ordinary yield curves that slope upward are called “normal” because those curves usually slope upward. An inverted yield curve slopes downward. I have borrowed the terminology here even though I’m unsure about what “normal” means with respect to the expected inflation curve.
  6. Brainard, Lael (May 11, 2021). “Patience and Progress as the Economy Reopens and Recovers.” Presentation to “The Road to Recovery and What’s Next,” a virtual conference sponsored by the Society for Advancing Business Editing and Writing (via webcast). Available at Accessed May 24, 2021.

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About Tony Lima

Retired after teaching economics at California State Univ., East Bay (Hayward, CA). Ph.D., economics, Stanford. Also taught MBA finance at the California University of Management and Technology. Occasionally take on a consulting project if it's interesting. Other interests include wine and technology.