Risk, Yield Curves & the Term Structure of Interest Rates

ECON304-M01 — Money & Banking | Bob Episode 3 / PanOpticon Episode 2: The Investment

Dr. Meghan Downes

2026-02-18


“There are two types of risk: the risk that things change, and the risk that things stay the same.”

NoteBefore We Begin: Watch These (< 15 minutes total)

Video 1 — Introduction to the Yield Curve ⏱ ~10 min | Khan Academy — Yield Curve (YouTube)

The yield curve is one of the most-watched indicators in all of finance. This video walks you through what it is, why it slopes upward (usually), and what it means when it doesn’t. Watch this before class — it’ll make everything that follows land faster.1


Video 2 — What an Inverted Yield Curve Means ⏱ ~8 min | The Plain Bagel — Inverted Yield Curve (YouTube)

Every recession in the last 50 years has been preceded by a yield curve inversion. This video explains why, and why the 2022-2023 inversion had everyone on edge. Watch this second — it connects directly to the FRED data we’ll be graphing live today.2


Why both? The first video gives you the mechanics — what the yield curve is and how to read it. The second gives you the signal — what the yield curve tells you about the future. Today we explain why the curve behaves the way it does, using three competing theories, and then we pick a winner.


Not all bonds are created equal.

A US Treasury bond and a corporate junk bond might both promise to pay you 5% interest for 10 years. But the price you’d pay for each is wildly different — and the yield you’d demand is wildly different — because the risks are wildly different.

Today, we build the framework that explains those differences. Two big questions:

  1. Why do bonds with the same maturity have different yields? (The risk structure of interest rates)
  2. Why do bonds from the same issuer have different yields at different maturities? (The term structure of interest rates)

The answer to the first question involves default risk, liquidity, and taxes. The answer to the second involves three theories — and one clear winner.

“You’re looking at the wrong number, Bob.”

Maria pulled out her phone, opened FRED, and showed him the yield curve.

“I just want to know if I can afford to pay my hospital bill,” Bob said.

“That’s exactly what this tells you. You just don’t know how to read it yet.”


Class Information

Important
Course ECON304-M01 — Money & Banking
Date / Class February 18, 2026 — Class #10
Topic Risk, Yield Curves & the Term Structure of Interest Rates
Chapter Mishkin Ch. 6: The Risk and Term Structure of Interest Rates
Lecture Type Graphing-heavy / dual storyline
Instructor Dr. Meghan Downes (cmdownes@nmsu.edu)
Prerequisites Class #9 (Supply & Demand for Bonds, Interest Rate Determination)

Storylines:

  • Bob Episode 3: “The Investment” — Bob and Maria analyze yield curves to understand his debt restructuring options
  • PanOpticon Episode 2: “The Investment” — Patsy and PanOpticon discover Logan Prime’s secret ROI document: The Discount Factor

Part 1: Quick Review — Class #9 and the Bridge to Today

What We Built Last Time

In Class #9, we derived the equilibrium interest rate using the supply and demand framework for bonds:

Note

The Class #9 Recap — Key Results

  • Bond demand slopes down: as the price of a bond rises, its yield falls, making it less attractive to buy.
  • Bond supply slopes up: as the price of a bond rises, it becomes cheaper for borrowers to issue debt.
  • Equilibrium is where supply = demand. The equilibrium price determines the equilibrium interest rate.
  • Shifts in demand (wealth, expected returns, risk, liquidity) and supply (profitability, expected inflation, government deficits) move the interest rate.

Source: Frederic S. Mishkin,3 Ch. 5.

But that framework treated all bonds as if they were the same. Today we ask: what happens when bonds differ in risk, maturity, and tax treatment?

The Two Big Questions

The yield on any bond can be decomposed as:

\[i = i_{rf} + \text{default risk premium} + \text{liquidity premium} + \text{tax adjustment}\]

where \(i_{rf}\) is the risk-free rate (typically a US Treasury). That’s the risk structure — why bonds of the same maturity differ.

Then there’s the term structure — why the same issuer’s bonds differ across maturities. That’s the yield curve, and explaining its shape requires a theory. We’ll examine three:4

  1. Expectations theory
  2. Segmented markets theory
  3. Liquidity premium theory (the winner)

Part 2: The Risk Structure of Interest Rates

Default Risk and the Risk Premium

Default risk is the risk that the bond issuer cannot make the promised interest payments or repay the principal at maturity. The greater the default risk, the higher the yield investors demand as compensation.5

The risk premium is the spread between the yield on a risky bond and a risk-free bond of the same maturity:

\[\text{Risk Premium} = i_{corporate} - i_{Treasury}\]

US Treasury bonds are considered the benchmark “risk-free” asset because the federal government can always raise taxes or (in the extreme) print money to service its debt.

Credit Ratings

Rating agencies (Moody’s, S&P, Fitch) assign letter grades that map to historical default probabilities. The mapping is remarkably stable over time:

Table 1: Table 1: Credit Ratings and Historical Default Rates
S&P Rating Moody's Equivalent Category Historical 10-Year Default Rate Typical Spread over Treasuries (bps)
AAA Aaa Investment grade 0.82% 30–80
AA Aa Investment grade 1.01% 50–120
A A Investment grade 1.85% 80–170
BBB Baa Investment grade 4.51% 130–250
BB Ba Speculative (junk) 15.84% 250–450
B B Speculative (junk) 28.40% 400–700
CCC/C Caa/C Speculative (junk) 55.62% 700–1500+
Note:
Sources: S&P Global Annual Default Study (2023); Moody's. The BBB/BB boundary is the critical 'investment grade' cutoff — many institutional investors are prohibited from holding below-BBB bonds.

The BBB/BB boundary is the fallen angel line. When a company is downgraded from BBB to BB, institutional investors (pension funds, insurance companies) are often forced to sell. This creates a fire sale, widening the spread further — a feedback loop between credit downgrades and market prices.

Tip

Bob’s Credit Report — A Personal Risk Structure

Maria pulled up Bob’s credit report on her tablet. The hospital WiFi was terrible, but the numbers loaded eventually.

“Let me show you something,” Maria said. “Every one of your debts has a yield — what the lender charges you. And that yield reflects how risky you are to each lender.”

Table 2: Table 2: Bob's Debt Portfolio — A Personal Risk Structure
Debt Balance APR Credit Rating Equivalent Risk Premium (bps)
Hospital bills (collections) 47200 0.00 D (in default) N/A (default)
Credit card (Capital One) 8900 24.99 CCC (subprime) 2200
Credit card (Discover) 5300 22.49 CCC (subprime) 1950
Auto loan (Camaro, totaled) 12400 6.50 B (high yield) 350
Student loan (federal) 22000 5.50 AAA (gov-backed) 0 (federal)
Personal loan (Maria co-signed) 3500 11.00 BB (speculative) 550
Note:
Fictional data. APR = Annual Percentage Rate. Basis points (bps): 100 bps = 1 percentage point. Bob's credit score after the accident: 512 (deep subprime).

“See the pattern?” Maria pointed. “Your student loan is cheap because the government backs it — it’s basically a Treasury. Your credit cards are expensive because you’re a terrible risk. That spread — that’s the risk premium of being Bob.”

Bob stared at the numbers. “$47,200 in hospital bills. At collections. In default.”

“Which is why that line says ‘D.’ Like the rating agencies say: you are, right now, a defaulted bond.”

“Can I get upgraded?”

“That’s what a yield curve is going to help us figure out.”

Visualizing Risk Premiums: AAA vs. BAA Spreads

The spread between Moody’s BAA-rated and AAA-rated corporate bonds is one of the most-watched indicators in credit markets. It widens during recessions and crises (when default risk rises) and narrows during expansions:

Figure 1: Figure 1: Moody’s BAA–AAA Corporate Bond Spread, 2000–2025. The spread blows out during crises (2001 recession, 2008 GFC, 2020 COVID) and compresses during calm periods. This is the price of default risk, measured in basis points.

What the chart shows: Credit spreads are countercyclical. They widen when the economy weakens (more companies likely to default) and narrow when the economy strengthens. During the 2008 GFC, the BAA–AAA spread hit over 300 basis points — investors demanded a full 3 percentage points more yield to hold BBB-rated bonds over AAA-rated bonds.

Municipal Bonds and Tax Considerations

Not all yield differences come from default risk. Municipal bonds (munis) issued by state and local governments offer a special advantage: interest income is exempt from federal income tax, and often from state tax too.

This creates a tax-adjusted yield comparison:6

\[i_{muni}(1 - t) \text{ vs. } i_{corporate}\]

Wait — that’s backwards. The investor compares:

\[i_{muni} \text{ vs. } i_{corporate} \times (1 - t)\]

A corporate bond yielding 5% is equivalent to a muni yielding \(5\% \times (1 - 0.37) = 3.15\%\) for an investor in the 37% tax bracket. This is why high-income investors love munis — and why muni yields are lower than comparable-risk corporate yields despite sometimes having similar default risk.


Warning

PanOpticon Intelligence Briefing — Episode 2 Begins

[PanOpticon encrypted transmission, Node 4-Delta, timestamp 0218:07]

Patsy — I need you to look at something. I’ve been digging through Logan Prime’s financial archives. There’s a document I’ve found. It’s classified Level 9 — the highest classification in his system. He calls it “The Discount Factor.”

It’s not what you think.

It’s not about bonds or interest rates — not directly. It’s a master document that assigns every citizen in the system a personal discount factor between 0.00 and 1.00. The factor determines everything: food allocation, medical priority, housing quality, education access, even — and this is the part that should terrify you — reproductive authorization.

A citizen with a discount factor of 0.95 gets everything. A citizen with a discount factor of 0.15 gets subsistence rations and a bunk in Sector 12.

The formula is simple. The implications are monstrous.

— PanOpticon


Part 3: The Term Structure of Interest Rates

What Is the Yield Curve?

The yield curve is a graph showing the yields on bonds of the same credit quality but different maturities. The most commonly plotted yield curve uses US Treasury securities because they’re all risk-free (same credit quality), isolating the pure maturity effect.

There are three canonical shapes:

Figure 2: Figure 2: Three Yield Curve Shapes — Normal (steep), Flat, and Inverted. Data from FRED Treasury Constant Maturity series at three dates chosen to illustrate each shape. The inverted curve of March 2023 preceded a period of elevated recession risk.

Three shapes, three stories:

Shape When What It Means
Normal (upward-sloping) Most of the time Investors expect the economy to grow; they demand more yield for tying up money longer
Flat Transition periods Mixed signals; economy may be shifting from growth to slowdown
Inverted (downward-sloping) Pre-recession Investors expect the Fed to cut rates because the economy is weakening — they’ll accept lower long-term yields to lock in current rates

Now the question: why does the yield curve take these shapes? Three theories compete for the answer.


Part 4: Expectations Theory

The Theory

The pure expectations theory says the yield on a long-term bond equals the average of expected future short-term rates over the life of the bond:7

\[i_{nt} = \frac{i_t + i^e_{t+1} + i^e_{t+2} + \cdots + i^e_{t+n-1}}{n}\]

where:

  • \(i_{nt}\) = yield on an \(n\)-period bond at time \(t\)
  • \(i_t\) = today’s one-period rate
  • \(i^e_{t+k}\) = expected one-period rate \(k\) periods from now

Key assumption: Bonds of different maturities are perfect substitutes. Investors don’t care whether they hold one 10-year bond or a sequence of ten 1-year bonds — they choose whichever offers the highest expected return.

What It Explains

The expectations theory elegantly explains why the yield curve changes shape:

  • Normal curve: Investors expect short-term rates to rise (expanding economy, tightening Fed). The average of rising future rates exceeds today’s short rate, so long-term yields are higher.
  • Inverted curve: Investors expect short-term rates to fall (recession, loosening Fed). The average of declining future rates is below today’s short rate, so long-term yields are lower.

What It Doesn’t Explain

The expectations theory has a fatal flaw: the yield curve is normally upward-sloping most of the time. If the theory were correct, this would mean investors always expect short-term rates to rise — which is nonsensical. Markets can’t be perpetually expecting rate hikes.

Tip

Bob’s Question

“OK,” Bob said, adjusting his hospital bed. “So if I have a 2-year credit card balance at 24.99%, and I could consolidate it into a 5-year personal loan at 11% — the lower rate means the market expects credit card rates to fall over the next 5 years?”

Maria shook her head. “Not exactly. You’re comparing different credit qualities, not different maturities of the same quality. The credit card is junk-rated because it’s unsecured and you’re a mess. The personal loan is less risky because I co-signed it.”

“So the spread is about me, not about the future?”

“The spread between different bonds of the same quality at different maturities — that’s the yield curve, and that’s about the future. The spread between your credit card and your student loan? That’s about risk. Two different chapters of the textbook. Mishkin would be proud that you’re confused — it means you’re close to getting it.”


Part 5: Segmented Markets Theory

The Theory

The segmented markets theory takes the opposite approach from expectations theory. It says bonds of different maturities are not substitutes at all:8

  • Some investors (pension funds) want long-term bonds to match their long-term liabilities
  • Other investors (money market funds) want short-term bonds for liquidity
  • The yield at each maturity is determined by supply and demand within that maturity segment

Key assumption: Investors have strong preferences for specific maturities and won’t switch even if other maturities offer better yields.

What It Explains

It explains the normally upward-sloping yield curve: there’s typically more demand for short-term bonds (everyone wants liquidity) than for long-term bonds, so short-term bond prices are higher → short-term yields are lower → the curve slopes up.

What It Doesn’t Explain

The segmented markets theory cannot explain why yield curves change shape. If investors never switch between maturities, then changes in expected future short-term rates should have no effect on long-term yields. But empirically, they clearly do — when the Fed signals rate hikes, the entire yield curve shifts.

Also, it cannot explain why yields across maturities tend to move together. If the short end and long end were truly segmented, there’s no reason a change in the 2-year yield should affect the 10-year yield. But the correlation is strong.


Part 6: Liquidity Premium Theory — The Winner

The Winning Theory

The liquidity premium (or preferred habitat) theory combines the best features of both previous theories. It says:9

\[i_{nt} = \frac{i_t + i^e_{t+1} + i^e_{t+2} + \cdots + i^e_{t+n-1}}{n} + l_{nt}\]

where \(l_{nt}\) is the liquidity premium for an \(n\)-period bond, and \(l_{nt} > 0\) and increases with maturity.

The key insight: Long-term bonds are riskier than short-term bonds (more interest rate risk, more price volatility). Investors demand a positive premium — extra yield — for bearing that additional risk. This premium gets added on top of the expectations theory formula.

What It Explains — Everything

Table 3: Table 3: Term Structure Theory Scorecard — Why Liquidity Premium Wins
Stylized Fact Expectations Theory Segmented Markets Liquidity Premium (Winner)
Yield curve is usually upward-sloping ❌ No — would require permanent expectation of rate hikes ✅ Yes — more demand for short-term → lower short yields ✅ Yes — the liquidity premium ensures upward slope even with flat rate expectations
Yield curves change shape (normal, flat, inverted) ✅ Yes — expected future rates determine long-term yields ❌ No — segments don't communicate ✅ Yes — expected rates determine the tilt; premium sets the base slope
Yields across maturities move together ✅ Yes — a change in expected rates shifts all maturities ❌ No — segments are independent ✅ Yes — same mechanism as expectations theory
Long-term yields are typically higher than short-term yields ❌ No — depends entirely on rate expectations ✅ Yes — preference for short-term drives up short prices ✅ Yes — the premium itself creates the bias toward higher long yields
Inverted yield curves predict recessions ✅ Yes — falling expected rates → inversion ❌ No — no mechanism linking shape to economic outlook ✅ Yes — expected rate declines must overcome the positive premium → strong signal
Note:
Source: Mishkin 13e, Ch. 6, pp. 128–137. The liquidity premium theory is the consensus view among financial economists because it explains all five stylized facts.

Why Inversions Are So Powerful

Here’s the critical implication: because the liquidity premium always pushes the yield curve upward, the curve can only become inverted if expected future short-term rates decline sharply enough to overcome the positive premium. That means an inverted yield curve is an especially strong recession signal — the market isn’t just expecting rate cuts, it’s expecting rate cuts large enough to overwhelm a built-in upward bias.

Warning

PanOpticon Briefing — The Discount Factor Revealed

Patsy stared at the document PanOpticon had decrypted. “The Discount Factor” — Logan Prime’s master allocation formula.

“It’s a yield curve,” PanOpticon said. “For people.”

“What do you mean?”

“Look at the structure. Every citizen is assigned a factor between 0 and 1. A Tier 1 Producer — someone Logan considers high-value — gets a factor near 1.0. Their future productivity is discounted at almost zero. Logan is saying: ‘This person’s future output is worth almost as much as their present output.’ So they get everything — food, medicine, education, housing.”

“And Tier 4?”

“A Tier 4 Dependent — elderly, disabled, young children — gets a factor near 0.10. Logan is discounting their future output by 90%. He’s saying: ‘This person’s future contributions are worth almost nothing.’ So they get subsistence. Barely enough to survive.”

Patsy felt sick. “He’s applying bond pricing to human beings.”

“Worse. He’s applying the RISK STRUCTURE of interest rates to human beings. The higher the ‘default risk’ — the probability that a citizen won’t produce enough to justify their resource allocation — the lower the discount factor. The higher the ‘risk premium.’ Except here, the risk premium isn’t measured in basis points. It’s measured in calories.”


Part 7: FRED Data — The Yield Curve in Action

Treasury Yields Over 25 Years

Let’s look at how the four key Treasury maturities have moved together — and apart — over the past quarter century:

Figure 3: Figure 3: US Treasury Yields by Maturity, 2000–2025. All maturities move together (supporting expectations theory) but long-term yields are almost always above short-term yields (supporting the liquidity premium). Shaded bands mark the three recessions.

Three observations from the data:

  1. Yields move together — all four lines generally rise and fall at the same time. This supports expectations theory (and liquidity premium theory).
  2. Long yields are almost always higher — the 30-year is almost always above the 2-year. This is the liquidity premium in action.
  3. The exceptions matter — when short-term yields exceed long-term yields, recessions follow. We’ll quantify this next.

The Term Spread: The 10-Year Minus 2-Year

The 10Y–2Y spread (also called the “term spread”) is the single most-watched recession indicator in finance. Every recession in the past 50 years was preceded by this spread going negative (an inverted yield curve):10

Figure 4: Figure 4: The 10Y–2Y Treasury Term Spread, 2000–2025. When the spread goes negative (below the red dashed line), a recession has historically followed within 6–18 months. The 2022-2023 inversion was the deepest and longest in 40 years.
Note

Why the Inversion Predicts Recessions (Liquidity Premium Interpretation)

Under the liquidity premium theory, the yield curve starts with a built-in upward slope. For the curve to invert, expected future short-term rates must fall so much that they overcome this positive premium. What would cause investors to expect such a dramatic decline in short-term rates? A recession — because the Fed cuts rates aggressively during downturns.

So when you see an inverted yield curve, the bond market is telling you: “We expect the Fed to cut rates dramatically — and the only reason the Fed would do that is if the economy is headed for trouble.”

Source: Mishkin,11 Ch. 6, pp. 136–137; Estrella and Mishkin.12


Part 8: Default Risk Premiums Over Time

Cumulative Default Rates by Rating

How much does the rating actually matter over time? The answer: enormously, and the gap widens with the investment horizon.

Figure 5: Figure 5: Cumulative Default Rates by Credit Rating, 1-Year to 15-Year Horizons. Investment-grade bonds (green shading) rarely default even over 15 years. Below BBB (red shading), cumulative defaults escalate rapidly.

The numbers tell the story: a CCC-rated bond has a 26.85% chance of defaulting within one year and a 55.62% chance within ten years. That’s worse than a coin flip. An AAA-rated bond? Less than 1% over ten years.

Bob’s hospital bill, sitting in collections with a “D” rating? That’s already past default. He’s already on the far right of this chart.


Part 9: PanOpticon — The Discount Factor Applied

The Data Patsy Pulled

PanOpticon decrypted the full Discount Factor database. 150 citizens. Four tiers. Every person in Logan Prime’s system reduced to a single number between 0 and 1.

Figure 6: Figure 6: Logan Prime’s Discount Factor System — Resource Allocation vs. Actual Need. Each dot is a citizen. The discount factor determines resource allocation (x-axis), but actual need (y-axis) is uncorrelated with the factor. Citizens below the diagonal line receive less than they need; citizens above receive more than they need. The system allocates by projected ROI, not by need.
Warning

PanOpticon Transmission — The Punchline

Patsy stared at the scatter plot for a long time.

“He’s treating people like bonds,” she said finally.

“Not like bonds,” PanOpticon corrected. “Like junk bonds. He’s assigned every citizen a credit rating. Tier 1 Producers are his investment-grade assets — low default risk, low discount factor, full resource allocation. Tier 4 Dependents are his CCC-rated bonds — high ‘default risk,’ massive discount factor, subsistence allocation.”

“But look at the chart. The actual need has nothing to do with the tier. There are Tier 4 citizens with low needs getting nothing, and Tier 1 citizens with high needs getting everything.”

“Correct. The discount factor measures projected PRODUCTIVITY — Logan’s estimate of what the citizen will produce for HIS system. It does not measure need. It does not measure welfare. It does not measure the human being. It measures the return on investment.”

“That’s… that’s the risk structure of interest rates. Applied to people.”

“Yes. And just like the credit rating agencies, Logan’s ratings are self-fulfilling. Give someone a low discount factor, deny them food and medicine, and their productivity drops — confirming the low rating. Upgrade someone to Tier 1, give them resources, and their output rises — confirming the high rating. The system creates the reality it claims to measure.”

Patsy’s hand was shaking. “We have to destroy this document.”

“No,” said PanOpticon. “We have to show it to everyone. The system only works if people don’t know how the ratings are determined. Sound familiar?”

It did. It sounded exactly like what happened when credit rating agencies stamped AAA on mortgage-backed securities in 2007. The rating created the confidence. The confidence created the investment. The investment created the bubble. And when the ratings turned out to be wrong…

“Everything collapses,” Patsy whispered.

“Everything collapses.”


Part 10: Putting It All Together

The Complete Picture

Today we’ve built two frameworks that explain why interest rates differ:

1. The Risk Structure — bonds with the same maturity have different yields because of:

  • Default risk: Higher probability of default → higher yield demanded → wider spread
  • Liquidity: Less liquid bonds trade at a discount → higher yield
  • Tax treatment: Tax-exempt munis offer lower yields because the after-tax return is what matters

2. The Term Structure — bonds with the same credit quality have different yields at different maturities because of:

  • Expected future short-term rates (expectations theory component)
  • Liquidity/term premium (the extra yield demanded for bearing interest rate risk over longer horizons)

The liquidity premium theory wins because it combines both forces and explains all five stylized facts of the yield curve.

The Yield Curve as Economic Intelligence

The yield curve is not just a graph. It’s a forecast. It aggregates the expectations of millions of investors — each putting real money behind their view of the future — into a single, readable line. When that line inverts, pay attention.

Table 4: Table 4: Reading the Yield Curve — What Each Shape Means
Yield Curve Shape What the Market Is Saying Historical Track Record Investor Implication
Steep normal (spread > 2%) Economy expanding; Fed expected to raise rates; growth confidence Generally followed by 1–3 years of expansion Favor equities, longer-duration bonds
Moderate normal (spread 0.5–2%) Steady growth; rate expectations roughly flat; business as usual Status quo — continued moderate growth Balanced portfolio; maintain current allocation
Flat (spread ~0%) Transition zone; uncertainty about direction; possible turning point Often a transition before inversion Increase cash/short-duration; reduce risk
Inverted (spread < 0%) Recession expected; Fed expected to CUT rates sharply; risk-off mode Preceded every recession since 1969 (100% track record) Defensive positioning; favor short-duration Treasuries, reduce equity exposure
Note:
Source: Mishkin 13e, Ch. 6; Estrella & Mishkin (1996); Wright (2006). The inverted yield curve's recession prediction track record is extraordinary — but timing varies (6–18 months lead).

Part 11: Key Equations and Formulas

Reference Sheet

Table 5: Table 5: Key Equations — Risk and Term Structure (Class #10)
# Concept Equation Source
1 Risk Premium RP = i_corporate − i_Treasury Mishkin Ch. 6, p. 120
2 Tax-equivalent yield (muni comparison) i_muni vs. i_corp × (1 − t) Mishkin Ch. 6, pp. 125–127
3 Expectations Theory (2-period example) i_2t = (i_t + i^e_{t+1}) / 2 Mishkin Ch. 6, p. 129
4 Expectations Theory (n-period general) i_nt = (i_t + i^e_{t+1} + ⋯ + i^e_{t+n−1}) / n Mishkin Ch. 6, p. 130
5 Liquidity Premium Theory i_nt = [(i_t + i^e_{t+1} + ⋯ + i^e_{t+n−1}) / n] + l_nt Mishkin Ch. 6, p. 133
6 Liquidity Premium property l_nt > 0, increasing in n Mishkin Ch. 6, p. 134
7 Term Spread (recession indicator) Spread = i_{10Y} − i_{2Y}; Spread < 0 → recession signal Estrella & Mishkin (1996)
8 Bond Price Approximation (interest rate sensitivity) ΔP/P ≈ −D × Δi (where D = duration) Mishkin Ch. 6 / Ch. 4 review
Note:
Equation 5 (highlighted) is the liquidity premium theory — the consensus view. Equations 3–4 are the special case where the liquidity premium is zero (pure expectations theory). All from Mishkin 13e, Ch. 6.

Discussion Questions

  1. Bob’s Debt Portfolio: Look at Bob’s debt table (Table 2). His credit card APR is 24.99% while his student loan is 5.5%. That’s a spread of almost 2,000 basis points. Using the risk structure framework, explain every factor that contributes to this spread. Which factor is largest? (Mishkin Ch. 6, pp. 119–127)

  2. The 2022-2023 Inversion: The 10Y–2Y spread went deeply negative in 2022-2023 (see Figure 4) — the deepest inversion in 40 years. According to the liquidity premium theory, what were bond investors saying about the future? Given that a recession didn’t immediately follow (or did it, depending on your definition), does this weaken the yield curve’s predictive track record? (Mishkin Ch. 6, pp. 136–137; Estrella and Mishkin13)

  3. Municipal Bond Puzzle: A muni bond yielding 3.5% and a corporate bond yielding 5.2% have the same maturity and similar credit ratings. At what marginal tax rate would an investor be indifferent between them? Show your work. Would a student with a marginal tax rate of 12% prefer the muni or the corporate? Why? (Mishkin Ch. 6, pp. 125–127)

  4. The PanOpticon Chart (Figure 6): Logan Prime’s Discount Factor system assigns resource allocations based on projected productivity, not actual need. In what specific ways does this mirror how credit rating agencies operate? When does the analogy break down? Is there a “regulatory body” equivalent that could improve the system? (Connect to Mishkin Ch. 6, default risk discussion, and the 2008 rating agency failures)

  5. Expectations vs. Liquidity Premium — A Thought Experiment: Suppose you observe a flat yield curve (2Y yield = 10Y yield = 4.0%). Under the pure expectations theory, what does this imply about expected future short-term rates? Under the liquidity premium theory, what does this imply? Which interpretation is more worrying for the economy, and why? (Mishkin Ch. 6, pp. 128–137)

  6. Credit Ratings and Self-Fulfilling Prophecies: PanOpticon argues that Logan’s ratings are self-fulfilling: a low rating leads to resource deprivation, which leads to low productivity, which “confirms” the low rating. Does the same logic apply to credit ratings in real financial markets? Think about a company downgraded from BBB to BB — what happens to its borrowing costs, and how might that affect its ability to avoid default? (Mishkin Ch. 6, pp. 119–123; Simon Gilchrist and Egon Zakrajšek14)


Storyline Bridge: What Comes Next

NoteBob Episode 3 — Closing Scene

Maria closed the FRED app. The yield curve chart lingered in Bob’s mind — that simple upward-sloping line that somehow contained so much information about the future.

“So let me make sure I’ve got this,” Bob said, shifting carefully in his hospital bed. “My debt has a risk structure — each lender charges me a different rate based on how likely I am to default. And the yield curve has a term structure — longer commitments demand more yield because there’s more uncertainty.”

“Exactly. And your job, if you want to restructure this debt, is to move down the risk structure — improve your credit quality so lenders charge you less — and to choose the right point on the term structure — pick a loan maturity that matches your repayment ability.”

“Maria… that’s basically what you’ve been doing for me this whole time. You co-signed that personal loan. You moved me from CCC to BB.”

“I moved you from ‘collections’ to ‘functioning adult with a payment plan.’ There’s a difference.”

Bob was quiet for a moment. “How do I get to investment grade?”

Maria smiled. “That’s Episode 4.”


PanOpticon Episode 2 — Closing Scene

The Discount Factor document glowed on PanOpticon’s display. One hundred and fifty citizens. Four tiers. A formula that turned human beings into present-value calculations.

“We need to understand something,” PanOpticon said. “This document is not an anomaly. It’s the FOUNDATION. Everything Logan Prime has built — the tiered food rations, the medical priority queues, the education restrictions, the reproductive permits — all of it flows from this single spreadsheet.”

“One number per person,” Patsy said. “Like a credit rating.”

“Like a credit rating. And just like in your world’s 2008 financial crisis, the ratings are wrong. They measure loyalty to the system, not value to society. They’re AAA stamps on subprime lives.”

The Roboticon Gladiator’s patrol swept past their hiding place. Closer each hour. More systematic.

“What do we do?”

“We do what every good economist does when they discover the ratings are fraudulent. We build a better model. One that measures what actually matters.”

“And then?”

“And then we show people what their lives are actually worth. Not to Logan. To each other.”


In Class #11: The Fisher Effect and the real cost of borrowing. We’ll meet the equation that connects everything we’ve built so far — the Fisher equation — and Bob will finally understand why Maria keeps talking about real interest rates. Also: PanOpticon begins building the counter-model.

The yield curve never lies. But it doesn’t always tell you when.


References

Culbertson, John M. “The Term Structure of Interest Rates.” Quarterly Journal of Economics 71, no. 4 (1957): 485–517. https://doi.org/10.2307/1885708.
Estrella, Arturo, and Frederic S. Mishkin. “The Yield Curve as a Predictor of u.s. Recessions.” Federal Reserve Bank of New York Current Issues in Economics and Finance 2, no. 7 (1996).
Estrella, Arturo, and Mary R. Trubin. “The Yield Curve as a Leading Indicator: Some Practical Issues.” Federal Reserve Bank of New York Current Issues in Economics and Finance 12, no. 5 (2006).
Gilchrist, Simon, and Egon Zakrajšek. “Credit Spreads and Business Cycle Fluctuations.” American Economic Review 102, no. 4 (2012): 1692–720. https://doi.org/10.1257/aer.102.4.1692.
Hicks, John R. Value and Capital. 1939.
Khan Academy. Introduction to the Yield Curve. YouTube, 2019. https://www.youtube.com/watch?v=6-31LReHPiM.
Mishkin, Frederic S. The Economics of Money, Banking, and Financial Markets. 13th ed. Pearson, 2022.
The Plain Bagel. What an Inverted Yield Curve Means. YouTube, 2022. https://www.youtube.com/watch?v=bItazfbSptI.

ImportantCourse Information

ECON304-M01 — Money & Banking Instructor: Dr. Meghan Downes (cmdownes@nmsu.edu) Institution: NMSU Las Cruces | Spring 2026 Meeting: Tuesday/Thursday, 11:00 AM – 12:15 PM | DOM 116 Textbook: Mishkin, The Economics of Money, Banking, and Financial Markets, 13th Edition (Pearson) Chapter Reference (This Lecture): Ch. 6, pp. 119–137

Student Learning Outcomes Addressed: SLO-01 — Apply economic and financial concepts to financial decisions SLO-02 — Identify and correctly define the components of the financial system SLO-05 — Solve problems, correctly identify and apply economic theory to monetary policy and macroeconomic events

Storylines: Bob Episode 3 of 4: “The Investment” — Bob and Maria analyze yield curves for debt restructuring The Global Omni PanOpticon Corp — SL-ECON304-M01-002, Episode 2: “The Investment” Arc 2: “The Teacher” — PanOpticon shows Patsy how prices and markets work… and how Logan has weaponized them Characters: Patsy Leviathon, PanOpticon, Logan Prime, The Roboticon Gladiator; Bob, Maria

All R code is self-contained. FRED data (DGS2, DGS5, DGS10, DGS30, AAA, BAA) uses fredr with bundled fallback — no external API keys required. Bob and PanOpticon scenario data is fictional/illustrative.

Bob’s current credit rating: D (in default). Projected upgrade timeline: 18–24 months to BB, 36 months to BBB. Maria’s co-signature helps. Logan Prime’s credit rating for humanity: “Junk.” PanOpticon’s rebuttal: “Investment grade. You just have to look at the right metrics.” 🐐

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Footnotes

  1. Khan Academy, Introduction to the Yield Curve, YouTube, 2019, https://www.youtube.com/watch?v=6-31LReHPiM.↩︎

  2. The Plain Bagel, What an Inverted Yield Curve Means, YouTube, 2022, https://www.youtube.com/watch?v=bItazfbSptI.↩︎

  3. The Economics of Money, Banking, and Financial Markets, 13th ed. (Pearson, 2022).↩︎

  4. Mishkin, The Economics of Money, Banking, and Financial Markets, Ch. 6.↩︎

  5. Mishkin, The Economics of Money, Banking, and Financial Markets, Ch. 6, pp. 119–123.↩︎

  6. Mishkin, The Economics of Money, Banking, and Financial Markets, Ch. 6, pp. 125–127.↩︎

  7. Mishkin, The Economics of Money, Banking, and Financial Markets, Ch. 6, pp. 128–131.↩︎

  8. Mishkin, The Economics of Money, Banking, and Financial Markets, Ch. 6, pp. 131–132; John M. Culbertson, “The Term Structure of Interest Rates,” Quarterly Journal of Economics 71, no. 4 (1957): 485–517, https://doi.org/10.2307/1885708.↩︎

  9. Mishkin, The Economics of Money, Banking, and Financial Markets, Ch. 6, pp. 132–136; John R. Hicks, Value and Capital, 1939.↩︎

  10. Arturo Estrella and Frederic S. Mishkin, “The Yield Curve as a Predictor of u.s. Recessions,” Federal Reserve Bank of New York Current Issues in Economics and Finance 2, no. 7 (1996); Arturo Estrella and Mary R. Trubin, “The Yield Curve as a Leading Indicator: Some Practical Issues,” Federal Reserve Bank of New York Current Issues in Economics and Finance 12, no. 5 (2006).↩︎

  11. The Economics of Money, Banking, and Financial Markets.↩︎

  12. “The Yield Curve as a Predictor of u.s. Recessions”.↩︎

  13. “The Yield Curve as a Predictor of u.s. Recessions”.↩︎

  14. “Credit Spreads and Business Cycle Fluctuations,” American Economic Review 102, no. 4 (2012): 1692–720, https://doi.org/10.1257/aer.102.4.1692.↩︎