FIN435 • Chapter 6 — Interest Rates & Yield Curve Spring 2026
What you must be able to do
- Define SOFR and explain why it matters.
- Explain how the Fed influences short rates and how that reaches your borrowing rates.
- Use 2Y, 10Y, and the spread to discuss expectations about the economy (use FRED DGS2/DGS10).
- Interpret yield curve shapes using real data.
- Break down a corporate yield into components.
- Compute an implied future rate (expectations theory).
In class
Tip: if you can tell a coherent story from SOFR to the yield curve, you are prepared.
Interactive games (optional practice)
Opens in a new tab.
SOFR (Secured Overnight Financing Rate) — the modern benchmark
Video: LIBOR → SOFR Transition (Methodical Valuation)
Watch this to understand why LIBOR was replaced and how SOFR is used in modern floating-rate markets.
What SOFR is
SOFR is a broad measure of the cost of borrowing cash overnight collateralized by U.S. Treasury securities in the repo market. Think: “overnight funding rate backed by Treasuries.”
Why SOFR matters (click)
- It is widely used as a reference rate for many floating-rate instruments (institutional finance).
- It moves closely with the Fed’s policy stance and money-market conditions.
- It helps explain changes in borrowing costs across the economy.
SOFR → “Rates you feel” (rate transmission)
Policy changes affect very short-term rates first (overnight). Then the effect travels outward:
- Fed stance → money markets → SOFR
- SOFR & other short rates → bank funding costs
- Funding costs + competition + credit risk → Prime, credit cards, variable-rate loans
- Expectations about future short rates → 2Y/10Y Treasury yields → fixed-rate borrowing
Key idea: short rates are “policy-sensitive”; long rates embed expectations about inflation, growth, and future policy.
SOFR sandbox (simple approximations)
These are teaching approximations (not quotes). Use them to understand how benchmark moves can affect consumer rates.
Prime-rate approximation
Teaching rule of thumb: many bank rates move with a benchmark + a margin.
“What if rates rise?” quick impact
100 bps = 1.00%. A policy tightening cycle can move short rates by multiple percentage points.
Rates you pay: student loans, credit cards, and auto/mortgage
Credit card interest (monthly)
Assumes simple monthly interest for teaching (APR/12).
When benchmark rates rise, many variable consumer rates rise too.
Loan payment calculator (amortized)
Useful for student loans and auto loans.
Explain what drives the APR (benchmark + credit risk + term + fees/margins).
Mortgage intuition (10Y as an anchor)
Many fixed-rate borrowing costs are “anchored” by longer Treasury yields (especially the 10-year), plus risk/option/margin.
What students should say (click)
- 10Y Treasury reflects market expectations about inflation/growth/policy plus term premium.
- Mortgage rates embed: long-rate anchor + prepayment option + credit risk + servicer margin.
- Mortgage rates can move even if the Fed pauses because the 10Y can move.
Key benchmarks: 2-year, 10-year, and the spread (use FRED)
2-year Treasury (policy + expectations)
The 2Y is often viewed as the market’s “best guess” of the average short rate over the next ~2 years. It tends to move with expected Fed policy.
10-year Treasury (long-run + term premium)
The 10Y reflects expectations of inflation/growth over a longer horizon, plus a term premium. It anchors many long-term borrowing rates.
2s10s spread (signal)
Spread = (10Y − 2Y). When negative (“inverted”), markets may be pricing future rate cuts and slower growth.
Spread calculator + mini chart
Official daily “par yield” series (recommended source): FRED DGS2 (2Y) and FRED DGS10 (10Y).
Yield Curve Lab (2020–2025 snapshots)
Select a date below to plot the Treasury yield curve from the dataset. Reference page: Yield Curve (1/15/2025)
View dataset table (click to expand)
| Date | 1 Mo | 3 Mo | 6 Mo | 1 Yr | 2 Yr | 3 Yr | 5 Yr | 7 Yr | 10 Yr | 20 Yr | 30 Yr |
|---|
What determines interest rates? (short vs long)
Short-term rates (0–12 months)
- Central bank policy stance and money-market conditions
- Liquidity conditions and funding markets (repo, bank reserves)
- Near-term inflation prints and guidance that shifts expectations
Long-term rates (2–30 years)
- Expected inflation + expected real growth over the horizon
- Term premium (uncertainty compensation)
- Bond-market supply/demand (issuance, risk appetite, global demand)
Reality check
The Fed strongly influences short rates. The bond market prices long rates using expectations about the future. That is why the yield curve can move even when the Fed is “on hold.”
Bond yield breakdown: Treasury vs corporate
Corporate yields may include default and liquidity compensation relative to Treasuries.
Which components apply? (matrix)
Use this to explain why long corporates usually have the most “add-ons.”
| Interest Rate Parameter | Short-Term Treasuries | Long-Term Treasuries | Short-Term Corporates | Long-Term Corporates |
|---|---|---|---|---|
| r* | X | X | X | X |
| IP | X | X | X | X |
| MRP | X | X | ||
| DRP | X | X | ||
| LP | X | X |
Core decomposition (click to expand)
Required return formula
r = r* + IP + DRP + LP + MRP
| Component | Meaning | Simple analogy |
|---|---|---|
| r* | Real risk-free rate | Growth in purchasing power |
| IP | Inflation premium | Compensation for expected inflation |
| MRP | Maturity risk premium | More uncertainty at longer horizons |
| DRP | Default risk premium | Chance borrower does not repay |
| LP | Liquidity premium | Cost of not being able to sell quickly |
Simplified spread: Corporate – Treasury ≈ DRP + LP (holding maturity/real/inflation roughly comparable).
Spread calculator (quick)
Discussion: when does the spread widen?
- Higher recession risk → higher expected default risk → spread widens
- Lower market liquidity / risk-off periods → liquidity premium rises
- Credit quality differences (AAA vs BBB) show up in spreads
Expectations Theory (Implied Future Short Rate)
Big idea: a longer-term Treasury yield can be interpreted (roughly) as an average of expected future short-term yields. Under pure expectations theory (ignoring term premiums), investors should be indifferent between: (1) buying a longer-term bond now, or (2) buying a shorter-term bond and then “rolling over” into another short-term bond later.
Real-life interpretation
- Choice A: Lock in the N-year yield today (buy an N-year Treasury).
- Choice B: Buy an M-year Treasury today, then reinvest for (N−M) more years at the future short rate.
- If markets are efficient and there is no term premium, both choices should deliver about the same expected total return.
That means: the yield curve can imply what the market is “pricing in” for future short rates.
Concrete example (2-year vs rolling 1-year)
Suppose the 2-year yield is a and the 1-year yield is b. Expectations theory implies the market’s “implied” 1-year rate starting one year from now is c.
In plain English: If you buy a 2-year today, you earn the 2-year yield. If instead you buy a 1-year today and then buy another 1-year next year, the implied second-year rate is the one that makes those two strategies match.
Example (Exam-style): 2-year = 5%, 1-year = 4% → implied 1-year next year?
Quick approximation (teaching shortcut)
Treat yields like simple averages (ignores compounding):
This is the “5×2 = 4 + x” logic. It is fast and intuitive, but not exact.
Visual: Lock 2-year vs Roll 1-year (Expectations Theory)
Teaching graphic: two strategies should match in expected total return (ignoring term premium).
Exam example shown: 2-year = 5.00%, 1-year today = 4.00% ⇒ implied 1-year rate one year from now ≈ 6.01% (exact compounding).
Correct math (with compounding)
Pure expectations theory uses gross returns:
Result: implied 1-year next year is about 6.01% (very close to the shortcut’s 6%).
Formula
Let: a = N-year yield (as a decimal), b = M-year yield (as a decimal), c = implied future rate for years (N−M).
Indifference condition (gross returns):
Solving for c:
Important: in real markets, long rates also include a term premium, so this “implied future rate” is an approximation. Still, it is very useful for interpreting what the yield curve is signaling.
Implied Future Rate Calculator (in-page)
Enter annualized yields as percentages. This calculator computes the implied future rate c. Use it to interpret what the yield curve is pricing in.
How to “use” c (what it means)
- If c is lower than today’s short rate, the curve is often signaling expected easing / slower growth.
- If c is higher, the curve is often signaling expected tightening / stronger inflation pressure.
- The bigger the gap between long and short rates, the stronger the market’s implied path of future rates (plus any term premium).
Link to the full tool
If you prefer the dedicated calculator page (and want to experiment with more cases), use:
Recommendation: Try inputs from today’s yield curve (use FRED) and interpret what the curve “implies.”
Materials: Slides + Chapter 6 Case Study (Excel)
Chapter 6 Quizzes
Complete Quiz 1 first, then Quiz 2.
Market data links (recommended sources)
Treasuries & yields
Corporate & agency yields
Reading (optional)
“Who determines interest rates?” (high-level summary): Investopedia link