GF500 Unit 4 Inverted Yield Curve Analysis Example

Inverted by 162 Basis Points: A Unit 4 Yield Curve Analysis of the Treasury Curve on June 30, 2023

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Purdue University Global

GF500: Financial Institutions and Markets

Unit 4 Yield Curve Analysis

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[Date]

Yields are the U.S. Treasury's published par yield curve rates and the New York Fed's published ACM estimates for June 30, 2023; the forward rates are computed from them as an approximation. The articles cited are real.

The Curve on June 30, 2023

The Treasury's par yield curve for June 30, 2023 read as follows: three months, 5.43 percent; six months, 5.47; one year, 5.40; two years, 4.87; three years, 4.49; five years, 4.13; seven years, 3.97; ten years, 3.81; twenty years, 4.06; and thirty years, 3.85 (U.S. Department of the Treasury, 2023).

The shape is unusual. Yields rise slightly from three to six months, then fall steadily to ten years, then rise again at twenty years before dipping at thirty. The front and middle of the curve are inverted: a lender could earn more by rolling three-month bills than by locking in a ten-year note.

Measuring the Slope Twice

Two spreads are widely watched. The ten-year minus two-year spread was 3.81 minus 4.87, or negative 1.06 percentage points. The ten-year minus three-month spread was 3.81 minus 5.43, or negative 1.62 points.

The two measures agree in sign but not in size, and they can disagree in other periods. The three-month rate tracks the Federal Reserve's current policy rate closely, while the two-year rate already embeds expectations of policy over the next two years. Research on recession forecasting has found the ten-year minus three-month spread to be a particularly useful predictor, which is one reason analysts report both (Estrella & Mishkin, 1998). On this date, the deeper inversion at the short end reflects a policy rate that markets did not expect to last.

The Forward Rates the Curve Implies

Treating the par yields as approximate spot rates, the curve implies the following forward rates: the one-year rate one year ahead at about 4.34 percent; the one-year rate two years ahead at about 3.73 percent; the average two-year rate starting in three years at about 3.59 percent; and the average five-year rate starting in five years at about 3.49 percent.

Read literally, the market was pricing a fall in short rates from about 5.4 percent to below 4 percent within three years. But forward rates mix two things: what investors expect short rates to be, and any premium they require for bearing the risk of longer bonds. Separating those is the central task of this analysis.

The forward curve on this date pointed to short rates falling about one and a half points, but a forward rate is an expectation plus a premium, so the inversion alone cannot say how much of the fall investors actually expected.

Three Theories Against the Shape

Pure expectations. A ten-year yield is simply the mean of the one-year rates investors anticipate over the decade, with nothing added for risk. On this view the inversion means investors expected the Fed to cut sharply. It explains the downward slope from one to ten years but not the rise at twenty years, which would require expected rates to rise again between years ten and twenty.

Liquidity premium. Long rates equal expected short rates plus a premium that rises with maturity. On this view an inverted curve requires expected rate cuts large enough to overwhelm a positive premium. It cannot easily explain a negative premium, which, as shown below, is what the estimates suggest.

Preferred habitat. Investors favor particular maturities, and rates in each segment depend partly on supply and demand there. This explains the twenty-year bump well: the Treasury had reintroduced the twenty-year bond in 2020, and it has traded at higher yields than its neighbors, consistent with weaker demand for that segment.

No single theory explains every feature. Expectations explain the main slope; preferred habitat explains the local kink.

Separating Expectations From the Term Premium

The New York Fed publishes daily estimates from a model that splits each Treasury yield into an expected path of short rates and a term premium (Adrian et al., 2013). For June 30, 2023, the model's fitted ten-year yield was 3.85 percent. It split that into a risk-neutral yield, the average expected short rate over ten years, of 4.62 percent, and a term premium of negative 0.77 percent. At two years, the term premium was negative 0.43 percent (Federal Reserve Bank of New York, 2023).

Those figures allow a rough decomposition of the 1.62-point gap between the three-month and ten-year yields. The expected average short rate over ten years, 4.62 percent, sat about 0.81 points below the three-month bill at 5.43 percent; that is the part of the inversion explained by expected rate cuts. The remaining 0.77 points came from the negative term premium: investors accepted a lower yield on ten-year notes than expected short rates alone would justify.

Interpretation

On this date, expected rate cuts explained slightly more than half of the inversion, and a negative term premium explained the rest. A negative term premium is unusual by historical standards. One reading is that investors valued long Treasuries as a hedge against recession, since bond prices rise when the economy weakens and rates fall, and were willing to pay for that protection. Another is that the model's estimates are uncertain, and different term premium models gave different answers in this period.

The practical lesson is that an inverted curve is not a direct readout of the market's rate forecast. A treasurer who read the forward rates as forecasts would have expected short rates to fall faster than investors in fact expected, by roughly the size of the premium.

What the Curve Meant for Decisions

For a borrower choosing between a floating-rate loan and a ten-year fixed rate on that date, the curve offered fixed money about 1.6 points cheaper than current short rates. If the term premium was genuinely negative, the fixed rate was cheaper than the expected cost of floating, and locking it in was attractive. For a saver, the reverse held: rolling bills paid more today, but only for as long as short rates stayed high. A bank funding long loans with short deposits faced a squeeze, earning less on new long assets than it paid on short liabilities. Each choice depends on whether the forward rates are read as forecasts or as forecasts plus a premium.

Conclusion

The June 30, 2023 curve was deeply inverted at the short end, with the three-month bill 1.62 points above the ten-year note. Forward rates implied a fall in short rates of about one and a half points, but a published decomposition attributes only about half of the inversion to expected cuts and the rest to a negative term premium. Expectations explain the curve's broad slope; preferred habitat explains its twenty-year kink.

References

Adrian, T., Crump, R. K., & Moench, E. (2013). Pricing the term structure with linear regressions. Journal of Financial Economics, 110(1), 110-138. https://doi.org/10.1016/j.jfineco.2013.04.009

Estrella, A., & Mishkin, F. S. (1998). Predicting U.S. recessions: Financial variables as leading indicators. The Review of Economics and Statistics, 80(1), 45-61. https://doi.org/10.1162/003465398557320

Federal Reserve Bank of New York. (2023). Treasury term premia [Data set]. Federal Reserve Bank of New York.

U.S. Department of the Treasury. (2023). Daily Treasury par yield curve rates [Data set]. U.S. Department of the Treasury.