Promised cash flows are not guaranteed cash flows.
Treasury bonds let us focus on time value and interest-rate risk. Corporate bonds and structured credit add another layer: the issuer may not pay. Once default risk enters, yield is no longer just a time-value number.
- Treasury bond → corporate bond → structured credit
- Promised payoff ≠ expected payoff
- Default premium, risk premium, and what spreads contain
- Securitization reallocates risk — it does not destroy it
By the end of this lesson, you should be able to:
- 1Explain why non-government bonds carry default risk.
- 2Define default and distinguish promised payoff from expected payoff.
- 3Read the simplified Moody's, S&P, and Fitch rating scale.
- 4Distinguish investment grade from non-investment grade.
- 5Interpret a corporate bond spread over Treasuries.
- 6Explain why a corporate spread is not just default probability.
- 7Distinguish promised YTM from expected YTM.
- 8Define default premium and risk premium.
- 9Calculate promised YTM and expected YTM for a risky zero-coupon bond.
- 10Explain why securitization can repackage risk and what it requires.
- 11Explain why senior structured claims can lose value when correlation, liquidity, and model assumptions change.
Fixed-Income Securities
Bonds move the financial system. Two lessons build the valuation machinery now; duration, convexity, credit risk, and securitization arrive in upcoming lessons.
From interest-rate risk to default risk
Lesson 3.3 measured how bond prices move when yields move. Duration and convexity approximate the price effect of a yield change. But for corporate bonds, a yield change may not be only an interest-rate movement. A corporate yield can rise because investors are less confident the issuer will pay. That is a different kind of risk — and it requires a different set of tools.
Same yield move, different cause
If a Treasury yield rises, the move may reflect interest rates, inflation expectations, or liquidity. If a corporate bond yield rises, the move may also reflect credit fear: investors are demanding more compensation because they are less confident the issuer will pay.
Both yields rose 1%. Why?
The two bonds sit side by side. Each shows the same +1% yield move. Toggle between them to see which causes could be behind the move.
| Possible driver of the +1% move | Treasury | Corporate |
|---|---|---|
| Interest-rate expectations | ✓ | ✓ |
| Inflation expectations | ✓ | ✓ |
| Liquidity / flight-to-safety | ✓ | ✓ |
| Credit / default risk | · | ✓ |
| Market risk premium | · | ✓ |
| Issuer-specific fear | · | ✓ |
What changes when debt is risky?
For riskless debt, promised cash flows are treated as arriving with certainty. For risky debt, the promised payment is not the same as the expected payment. The promised payoff is what the contract says. The expected payoff is the probability-weighted payoff after accounting for default and recovery. The price is what investors pay today for that uncertain payoff.
The expected payoff weights the full payment by the probability of receiving it, and the recovery value by the probability of default.
- probability of full payment
- promised face value
- recovery value in default
Promised payoff stays fixed at F. Expected payoff changes as probability and recovery change.
What you are promised vs what you expect
Dial the probability of full payment and the recovery value. The expected payoff updates live. Notice how a high promised payoff can hide a much lower expectation once default risk is included.
The face value written into the bond contract — paid if default does not occur.
Probability-weighted blend of full payment and recovery.
“Promised yield is what I will earn.”
No. Promised yield is what you earn if default does not occur. It is computed from the promised payoff, not the expected payoff. Expected yield is lower whenever default risk is real.
- probability of full payment
- promised face value
- recovery value in default
Expected / Promised = 93.0% of face
The expected payoff is what a risk-neutral investor would weigh against the price. It is always at or below the promised payoff whenever default is possible.
Ratings, spreads, and what the premium contains
Credit ratings
Non-government bonds carry default risk. Credit ratings by agencies provide indications of the likelihood of default by each issuer. Ratings are opinions, not guarantees. Investment grade generally means Baa3 / BBB− or higher. Non-investment grade is also called speculative grade or high yield.
Ride the ladder down
Move the elevator from the safest rating toward default. Watch the default-risk meter climb and the promised-yield pressure build.
| Moody's | S&P | Grade | Default risk | Promised yield |
|---|---|---|---|---|
| Aaa | AAA | Investment | 4 | 8 |
| Aa | AA | Investment | 8 | 12 |
| A | A | Investment | 14 | 18 |
| Baa | BBB | Investment | 24 | 28 |
| Ba | BB | Non-Investment | 40 | 45 |
| B | B | Non-Investment | 58 | 62 |
| Caa | CCC | Non-Investment | 75 | 78 |
| Ca | CC | Non-Investment | 86 | 88 |
| C | C | Non-Investment | 93 | 94 |
| C | D | Non-Investment | 100 | 100 |
Which is riskier: A or Baa?
Which usually offers higher promised yield: AAA or BB?
Lower rating, higher promised yield — but not automatically better return
Lower-rated bonds usually promise higher yields. But a higher promised yield is not automatically a higher expected return. The extra yield may compensate for a higher probability of not receiving the promised cash flow. As debt becomes very risky, it starts to behave more like equity: payoffs become uncertain, bondholders may become residual claimants in distress, and promised fixed-income cash flows become economically less "fixed."
From bond-like to equity-like
The further right you go, the more the bond's return depends on the issuer's survival — exactly the question equity holders ask.
Effectively risk-free benchmark. Return is about time value of money.
Corporate bond spreads
A common measure of credit compensation compares a corporate bond yield to a Treasury yield of similar maturity. For example, the Moody's Baa yield minus the 10-year Treasury yield. This spread measures extra promised yield investors require for Baa corporate bonds over Treasuries. But a corporate spread can reflect many things: expected default loss, risk aversion, liquidity, taxes, systematic risk, embedded options, market stress, and pricing or model error.
Spreads breathe with fear
Below is a stylized teaching chart of how credit spreads behaved in notable episodes. Switch regimes to see how the spread widens or narrows.
Spreads compensate for expected default loss plus a moderate risk premium. Markets function, credit is reasonably available.
What is inside the premium?
A corporate spread is not "just default probability." Empirical research has examined what drives corporate spreads. The findings consistently show that default explains only part of the spread — the rest includes liquidity, taxes, systematic risk, embedded options, market segmentation, and model or pricing error.
What is the spread made of?
Allocate the 300 bps spread across its possible drivers. The total updates live. Exceed the target and you get a warning — because the pieces cannot sum to more than the whole.
Promised yield, expected yield, default premium, and risk premium
Decomposition of corporate bond yields
Promised YTM is the yield if default does not occur. Expected YTM is the probability-weighted average of all possible yields. Default premium is the difference between promised yield and expected yield. Risk premium is the difference between the expected yield on a risky bond and the yield on a risk-free bond of similar maturity.
Split the bond into its yield branches
The same bond supports four related but distinct yields. Promised yield uses the promised payoff. Expected yield uses the expected payoff. The gap between them is the default premium; the gap from expected to risk-free is the risk premium.
Computed from the promised payoff. This is the headline yield you see quoted — but it assumes no default.
Computed from the expected (probability-weighted) payoff. This is the yield investors actually expect to earn on average.
The extra promised yield that compensates for the possibility of default. It is the gap between what is promised and what is expected.
The extra expected yield over the risk-free rate. This is the reward for bearing the bond's risk — on top of just being compensated for expected default loss.
XYZ risky zero-coupon example
All bonds have par value $1,000. A risk-free 10-year Treasury STRIPS costs $463.19 (yielding 8%). A risky 10-year zero from XYZ Inc. costs $321.97, promises $1,000, and has an expected payoff of $762.22. From these numbers we can compute the promised YTM, expected YTM, default premium, and risk premium.
≈ 8.00%
The risk-free benchmark: what a default-free zero yields over 10 years.
≈ 12.00%
The return if XYZ pays as promised. This is the number quoted in the market — but it is not the expected return.
≈ 9.00%
The probability-weighted return after accounting for default and recovery. This is lower than the promised yield.
The default premium (3%) compensates for the possibility of not receiving the promised payoff. The risk premium (1%) compensates for bearing default risk above the risk-free rate.
A high promised yield can simply be compensation for not receiving the promised payoff.
From risk-free to promised yield
The waterfall starts at the risk-free rate (8%), adds a risk premium to reach expected YTM (9%), then adds a default premium to reach promised YTM (12%). Adjust the inputs to see the layers shift.
“12.00% promised yield means investors expect to earn 12.00%.”
No. Expected YTM is 9.00%, risk premium is 1.00%. The default premium (3.00%) compensates for the chance you never receive the promised payoff.
The baseline: what a default-free Treasury promises for the same maturity.
The headline corporate yield — computed from the promised face value, ignoring default.
The yield investors actually expect, blending full payment and recovery scenarios.
As expected payoff falls, expected YTM falls and the default premium widens. As the corporate price falls, promised yield rises.
Securitization, structured credit, and model stress
Why securitize loans?
The core idea of securitization is that loans can be pooled and repackaged into new claims. Each of those claims is a tranche — a layer that takes losses in a set order. The junior tranches absorb the first losses; the senior tranches take losses only once the junior ones are wiped out. Why securitize? To repack risks to yield more homogeneity within categories, achieve more efficient allocation of risk, create more risk-bearing capacity, provide greater transparency, support economic growth, and extend credit to more borrowers.
But successful securitization requires: diversification, accurate risk measurement, normal market conditions, and reasonably sophisticated investors.
Loans in, tranches out
Many loans enter the machine. They are pooled and repackaged into tranches with different risk. The factory runs smoothly only when its assumptions hold. Flip a requirement off and watch the warning appear.
All four requirements are met. Risk is allocated across tranches and the structure behaves as designed — for now.
What securitization does and does not do
Securitization can reallocate risk. It can create claims that look safer and claims that absorb more risk. But pooling and tranching do not make underlying risk disappear. If the underlying loans are risky, the total pool is still risky. The structure decides who absorbs losses first.
Before and after securitization
Before securitization, every investor in the loan pool bears the same risk. After securitization, losses are layered: Junior takes the first hit, Mezzanine the next, Senior last. Increase the underlying loan stress to watch losses climb the stack.
Junior has absorbed 28 of the pool's losses. Senior is untouched — so far.
Risk moved. Risk did not vanish.
Why senior does not always mean safe
A bank risk manager described holding highly rated AAA and super-senior CDO tranches while trying to eliminate exposure to lower-rated tranches. The logic seemed conservative: keep the supposedly low-risk senior pieces and reduce the risky junior exposure. But during the crisis, senior structured tranches fell in value while some non-investment-grade tranches were squeezed upward. What seemed low-risk under the model became vulnerable once correlation, liquidity, and market stress changed.
Stress the senior tranche
The senior tranche starts AAA. A protection layer (Junior + Mezzanine) sits beneath it. Push the stress levers up and watch senior value fall, the badge crack, liquidity dry, and mark-to-market losses climb.
How much loans default together.
Whether buyers remain for the tranches.
Underlying collateral value.
Fire-sale pressure on prices.
As one risk manager later put it: the instruments were new, the losses came from familiar sources — housing, leverage, liquidity, and correlated defaults. The AAA badge was a conclusion drawn from assumptions, not a guarantee written into the assets.
Correlation is the hidden stress point
A senior tranche may look safe when defaults are assumed to be diversified. But if defaults become correlated, many loans fail together. Then losses can reach the senior tranche. Diversification works when defaults are not all driven by the same shock. When correlation rises, diversification can disappear exactly when it is needed most.
20 loans, two worlds
Toggle between independent and correlated defaults. In independent mode, defaults scatter and Junior absorbs them. In correlated mode, defaults cluster and losses can jump straight to Senior.
Disabled in independent mode.
Diversification works when defaults are not all driven by the same shock. When correlation rises, diversification can disappear exactly when it is needed most.
Can this securitization survive?
Four scenarios, four requirement lights
Each scenario starts with a realistic setup. Flip the requirement lights to explore what happens when assumptions break. The survival rating updates instantly.
Diverse, well-measured, stable
Loans spread across many regions and sectors. Risk models are calibrated. Markets are liquid. Buyers are sophisticated.
Geographically concentrated
Loans concentrated in one region. Correlations rise as the local economy weakens. Buyers rely on ratings only. Liquidity dries up.
Senior insured, insurer stressed
The senior tranche is wrapped by a mono-line insurer. But the insurer itself is under capital stress.
Junior absorbs — but losses exceed expectations
Junior is designed to absorb first losses. But realized losses are far larger than the models predicted.
From corporate default to structured-credit stress
Corporate bonds introduced default risk: the issuer might not pay. Credit ratings and spreads try to summarize that risk. But spreads contain more than expected default loss. Promised yield is not expected yield. Securitization then repackages risky loans into new claims, but the structure depends on diversification, measurement, normal markets, and investor understanding. When correlation and liquidity assumptions break, even senior claims can lose value.
Five layers of fixed-income risk
Each layer was introduced somewhere in this module. Click a layer to see where it came from and what it means. The stack grows from unavoidable time value up to the most assumption-dependent structure risk.
Lesson 3.1 · Pricing a single future payment
A dollar today is worth more than a dollar tomorrow. Even a default-free Treasury embeds the opportunity cost of waiting — the risk-free rate.
Fixed income is not risk-free. It is risk-specified.
Each instrument specifies which layers of risk it carries — and which it does not. Understanding the stack is understanding fixed income.
Summary and mastery check
Answer all questions, then check your work. You can retry any time — mastery is based on correctness, not speed.
- 01
What is default?
- 02
What is the lowest broad investment-grade category in the simplified table?
- 03
Why do lower-rated bonds usually promise higher yields?
- 04
True or false: a corporate bond spread is entirely default probability.
- 05
XYZ 10-year zero costs $321.97 and promises $1,000. What is the promised YTM?
- 06
XYZ expected payoff is $762.22 and price is $321.97. What is the expected YTM?
- 07
If promised YTM is 12% and expected YTM is 9%, what is the default premium?
- 08
If expected YTM is 9% and risk-free yield is 8%, what is the risk premium?
- 09
What four conditions does successful securitization require?
- 10
Why can a senior structured tranche still lose value?
- 11
What does securitization do to risk?
- 12
Why is relying only on ratings dangerous?
- 1Corporate bonds add default risk: the issuer might not pay.
- 2Default means a missed promised interest or principal payment.
- 3Ratings summarize credit quality but are opinions, not guarantees.
- 4Investment grade and non-investment grade differ by perceived credit quality.
- 5Lower-rated bonds usually require higher promised yields.
- 6Corporate spreads contain default risk, liquidity, taxes, systematic risk, and other components — not just default probability.
- 7Promised YTM is not the same as expected YTM.
- 8Default premium equals promised YTM minus expected YTM.
- 9Risk premium equals expected YTM minus risk-free yield.
- 10Securitization can repackage risk, but it relies on diversification, accurate measurement, normal markets, and sophisticated investors.
- 11Senior structured claims can still lose value when correlations, liquidity, and model assumptions change.