To understand how vulnerable municipal bonds are to inflation, consider this: the triple-A 10-year is the same price it was six months ago, and by one measure almost 100 basis points weaker.

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As bond investors once again bake inflation expectations into the market, the specter of eroding purchasing power has pulled the real return on bonds back to Earth from an unprecedented peak.

According to the Municipal Market Data yield curve scale, the 10-year triple-A yields 3.09%.

This is a “nominal” yield, meaning it only describes how much money the bondholder collects. It does not describe the “real” yield — or increase in purchasing power of the cash collected from the bond.

A “real” yield is the nominal yield subtracted by the rate of inflation. It conveys the increase in stuff the bondholder could buy with the money earned on the bond.

Measuring a real yield is tricky because nobody knows what the inflation rate will be until after the fact.

The Bureau of Labor Statistics each month measures prices on a basket of goods to approximate changes in what a dollar can buy.

Measuring municipal yields using this guideline, known as the consumer price index, shows real yields on munis at historic highs.

The latest CPI reading in May showed a 1.3% decline in prices. Shrinking prices add to the ­purchasing power of fixed income, pushing real yields higher than nominal yields because a dollar earned on a bond can buy more.

The most recent CPI number implies a real yield of 4.39% on the triple-A 10-year. That would be the highest real triple-A 10-year yield in 23 years, based on the MMD monthly nominal yield subtracted by the previous month’s CPI.

The yield on the triple-A 10-year has seldom been lower; the real return to bondholders has seldom been higher.

The reason for this is simple: this is the first time since the 1950s that the CPI declined.

Since 1981, the average yield on the triple-A 10-year is 5.5%. That 5.5% nominal yield, though, has been eroded by an average 3.5% inflation rate.

A negative inflation rate means a well-below-average nominal yield can deliver a well-above-average real yield.

Though munis are offering fewer cents per dollar in coupon payments, those fewer cents can buy more.

To put this into perspective, take the triple-A 10-year in July 1981. The nominal 11.25% yield that month seems far higher than anything plausible in today’s muni market.

An inflation rate of 10.7% that month left a real yield of 0.55%, a small fraction of today’s real yield.

It is for this reason few bond investors disagreed after President Gerald Ford declared inflation “Public Enemy Number One” in October 1974 — when the CPI rose 12%.

According to Federal Reserve data, state and local government debt that month yielded 6.57% — meaning bondholders were effectively losing 5.43% of their principal annually.

Chris Mier, managing director at Loop Capital Markets, likes to extract the real yield from a nominal yield using “core” CPI, which excludes food and energy from the basket of goods used in the index.

The thinking behind this measure is food and energy prices are volatile and can bound or tumble regardless of inflation. Core CPI reflects the “underlying” rate at which prices change, rather than short-term shocks caused by a crop shortage or an oil embargo.

Mier points out a few times when the real yield on the 20-year triple-A scale — based on the nominal yield minus core CPI — spiked. Anyone who bought on those spikes would have made money, he said.

For example, in December 1994, the real muni yield bloated to 3.9%, based on the 6.5% nominal yield from the MMD scale at 20 years subtracted by an increase in core CPI of 2.6% over the previous year.

A year later, the nominal yield had plunged 135 basis points.

Mier cited January 2000 and November-December 2003 as crests in real yields that marked buying opportunities.

December 2008, when the 20-year real yield touched 4.7%, was also one of those times, Mier said. This is not.

Measuring real yields based on core CPI shows municipal yields have resorted to a more normal range.

The 20-year triple-A yesterday yielded 4.17%. Subtracting core CPI shows a real yield of 2.37%. The median real yield since the early 1980s is 2.73%.

“When you look at CPI [excluding] food and energy, we’ve actually moved back to a very normal type spread,” Mier said.

Eric Lascelles, chief economics and rates strategist at TD Securities, said the trouble with using the index to determine real yields is that CPI is old news.

The CPI is a not a predictor of inflation. It is retrospective. A bondholder does not care about yesterday’s rate of inflation. He wants to know what his principal and interest will be worth when he collects it.

The Treasury market may offer better tea leaves, according to Lascelles.

The Treasury sells Treasury inflation-protected securities, or TIPS, whose principal adjusts by the magnitude of the change in CPI. The nominal Treasury yield minus the TIPS yield expresses the market’s anticipation for the rate of inflation.

Using the TIPS spread to determine the inflation adjustment also shows muni yields closer to the norm, at least since the Fed began tracking TIPS yields in 2003.

The 10-year TIPS spread — the 10-year Treasury yield at 3.4% minus 10-year TIPS yield at 1.83% — is 1.57%.

This represents investors’ collective forecast for the rate of inflation over the next 10 years. That implies a real 10-year triple-A yield of 1.52%.

The average since 2003 is 1.48%.

This, incidentally, is the example used in the first sentence of this story.

The triple-A muni yield is the same as it was six months ago at roughly 3.1%.

In the meantime, inflation expectations have swelled: the TIPS spread on Jan. 12 revealed an expected inflation rate of 0.59% over the next 10 years. Yesterday, the bond market projected a 1.57% rate.

Thus at the same nominal yield, bondholders in that four-month span lost 98 basis points in purchasing power.

If the TIPS spread is to be believed, real muni yields went from normal in mid-2008 to unprecedentedly elevated in late 2008 and are back to normal in 2009.

During the throes of the credit crisis, the bond market projected little inflation. The 10-year TIPS spread collapsed from more than 2% in early September to less than 1% for most of November, December and January.

The real yield on triple-A munis skyrocketed. Inflation shaved off only a few basis points from the nominal yield.

As inflation projected by the TIPS spread has crept back up, it has dragged the real yield on munis back into comportment with historical norms.

Guy LeBas, director of fixed income at Janney Montgomery Scott, said the mushrooming of real yields last year and their return to normal this year was not entirely due to inflation expectations.

The market’s outlook for almost no inflation late last year coincided with illiquidity and credit concerns about municipalities, LeBas said.

That is partly why the real 10-year triple-A yield, based on the nominal yield minus the TIPS spread, leaped to 4.11% in December, which would have been 11 standard deviations from the mean prior to the Lehman bankruptcy in September.

Real yields vary as compensation for credit risk and illiquidity.

LeBas said because of these factors, investors were hesitant to buy munis late last year even with expectations for inflation close to nil.

Now that “we haven’t seen the explosions, the fireworks of default that some have feared,” he said, “the market is pricing in a more realistic expectation of credit risk.”

That leads to a real yield that squares with history. The real yield on the 20-year triple-A based on the TIPS spread is still elevated compared with the past five years.

The 20-year TIPS spread is 2.02%. Taking that inflationary bite out of the 20-year triple-A yield of 4.25% shows a real yield of 2.23%.

The average real 20-year triple-A yield since the Treasury began selling 20-year TIPS is 1.87%.

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