3.4Lesson 3.4 · Module 3

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
Learning objectives

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.
01Chapter 1

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.

1.1Section 1

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.

Professor's note
Before asking what a yield is, ask what risk the yield is compensating you for.
Definition · Same move, different meaning
When a Treasury yield and a corporate yield both rise by 1%, the number is identical. The economic story is not. A Treasury move is mostly about rates, inflation, and liquidity. A corporate move can also carry credit risk, a market risk premium, and issuer-specific fear.
Try itYield move · different cause
Tap a bond to inspect its drivers

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% moveTreasuryCorporate
Interest-rate expectations
Inflation expectations
Liquidity / flight-to-safety
Credit / default risk·
Market risk premium·
Issuer-specific fear·
1.2Section 2

What changes when debt is risky?

Definition · Default
Default occurs when a debt issuer fails to make a promised payment of interest or principal.

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.

Expected 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.

Definition · Promised is not expected
A corporate zero-coupon bond promises a fixed face value at maturity. But promised cash is not the same as expected cash. If default is possible, the expected payoff blends the full-payment scenario with the recovery-in-default scenario — weighted by their probabilities.
Try itPromised vs expected payoff
Corporate zero · face $1,000.00 · 10yr

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.

Promised payoff
$1,000.00

The face value written into the bond contract — paid if default does not occur.

Expected payoff
$930.00

Probability-weighted blend of full payment and recovery.

Probability of full payment (p)90%
Recovery in default (R)$300.00
Common misconception

“Promised yield is what I will earn.”

Correction

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.

Expected payoff
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.

02Chapter 2

Ratings, spreads, and what the premium contains

2.1Section 3

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.

Definition · The rating ladder
Rating agencies (Moody's, S&P) sort issuers from the safest (“Aaa / AAA”) down to default. The split between Investment Grade and Non-Investment Grade falls at the Baa / BBB boundary. As you descend the ladder, default-risk pressure rises and investors demand more promised yield.
Try itRating elevator
Use arrows or buttons · Aaa → D

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.

Selected rating
Aaa / AAA
Investment Grade
Default-risk pressure4
Promised-yield pressure8
Moody'sS&PGradeDefault riskPromised yield
AaaAAAInvestment48
AaAAInvestment812
AAInvestment1418
BaaBBBInvestment2428
BaBBNon-Investment4045
BBNon-Investment5862
CaaCCCNon-Investment7578
CaCCNon-Investment8688
CCNon-Investment9394
CDNon-Investment100100
Relative teaching meters, not historical default rates. Click any row to select it.

Which is riskier: A or Baa?

Which usually offers higher promised yield: AAA or BB?

2.2Section 4

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."

Professor's note
High promised yield can be attractive, but the word "promised" is doing a lot of work.
Definition · The debt–equity risk spectrum
Bonds are not all equally bond-like. A Treasury or AAA sits at the safe end — lower promised yield, high expected payoff, low equity character. As ratings fall, promised yield rises and the security behaves more like equity: the payoff depends increasingly on whether the issuer survives.
Try itDebt–equity risk spectrum
Select a rating to move the security

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.

← Bond-like · lower yieldEquity-like · higher yield →
Selected security
Treasury / AAA

Effectively risk-free benchmark. Return is about time value of money.

Promised-yield meter8
Expected-payoff meter99%
Equity-like character5
Professor's note
High promised yield can be attractive, but the word “promised” is doing a lot of work. As you slide toward the equity-like end, the promised yield rises because the expected payoff falls — not because the issuer is being generous.
2.3Section 5

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.

Professor's note
Do not read a spread as "the market's default probability." It is a price difference that contains several components.
Definition · The credit spread thermometer
A credit spread is the extra yield a corporate bond offers over a comparable Treasury. It widens when investors fear default, illiquidity, or risk aversion — and narrows when credit feels safe. The spread is a market price, and like other prices it tells a story about fear and compensation.
Try itCredit spread thermometer
Pick a regime to move the spread

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.

Current regime spread (stylized)60 bps
Stylized episodes (teaching only)
1930sGreat Depression
1987Crash
1998LTCM
2001Recession
2005Boom
2006Peak boom
Stylized teaching chart based on MIT 15.401 credit-spread discussion. Not current market data.
Interpretation · Normal

Spreads compensate for expected default loss plus a moderate risk premium. Markets function, credit is reasonably available.

2.4Section 6

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.

Definition · The spread is a market price
A 300 bps corporate spread is not a single number with a single cause. It bundles expected default loss, a liquidity premium, a tax premium, a systematic risk premium, optionality, and pricing noise. Decomposing it is hard — and the decomposition itself is uncertain.
Try itSpread decomposition mixer
Total spread target: 300 bps

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.

Allocated so far250 / 300 bps
Expected default loss60 bps
Liquidity premium50 bps
Tax premium30 bps
Systematic risk premium70 bps
Option / structure premium25 bps
Pricing / model error15 bps
Professor's note
The spread is a market price. Like other prices, it contains several stories at once — default, liquidity, taxes, risk premia, and noise. No single decomposition is definitive.
03Chapter 3

Promised yield, expected yield, default premium, and risk premium

3.1Section 7

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.

Definition · One bond, four views of yield
A risky bond can be split into branches: the promised payoff, the default/recovery scenario, the expected payoff, and the risk-free benchmark. Each produces a different “yield” — and confusing them is one of the most common fixed-income mistakes.
Try itPromised vs expected yield splitter
P=$700 · F=$1,000 · E[Payoff]=$900 · T=10yr

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.

Risky bond
P = $700
Promised yield

Computed from the promised payoff. This is the headline yield you see quoted — but it assumes no default.

Expected yield

Computed from the expected (probability-weighted) payoff. This is the yield investors actually expect to earn on average.

Default premium

The extra promised yield that compensates for the possibility of default. It is the gap between what is promised and what is expected.

Risk premium

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.

3.2Section 8

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.

Risk-free Treasury STRIPS yield

≈ 8.00%

The risk-free benchmark: what a default-free zero yields over 10 years.

XYZ promised YTM

≈ 12.00%

The return if XYZ pays as promised. This is the number quoted in the market — but it is not the expected return.

XYZ expected YTM

≈ 9.00%

The probability-weighted return after accounting for default and recovery. This is lower than the promised yield.

Default premium and risk premium

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.

Definition · The corporate yield waterfall
A corporate promised yield is built in layers: start at the risk-free rate, add a risk premium to reach the expected yield, then add a default premium to reach the promised yield. The headline 12% sits on top of a much smaller expected return.
Try itCorporate yield waterfall
MIT XYZ · 10yr zero · face $1,000.00

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.

8.00%
Risk-free
+1.00%
+ Risk premium
9.00%
= Expected YTM
+3.00%
+ Default premium
12.00%
= Promised YTM
Treasury STRIPS price$463.19
XYZ corporate price$321.97
Expected payoff$762.22
Common misconception

12.00% promised yield means investors expect to earn 12.00%.”

Correction

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.

Risk-free yield (Treasury STRIPS)

The baseline: what a default-free Treasury promises for the same maturity.

Promised yield (XYZ)

The headline corporate yield — computed from the promised face value, ignoring default.

Expected yield (XYZ)

The yield investors actually expect, blending full payment and recovery scenarios.

Default premium and risk premium

As expected payoff falls, expected YTM falls and the default premium widens. As the corporate price falls, promised yield rises.

04Chapter 4

Securitization, structured credit, and model stress

4.1Section 9

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.

Definition · Securitization factory
Securitization pools many loans into a single structure, then slices the pool's cash flows into tranches: Senior (paid first, safest), Mezzanine (middle), and Junior / equity (paid last, absorbs first losses). The structure reallocates risk — it does not eliminate it.
Try itSecuritization factory
Toggle the requirements

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.

Loans in
POOL
securitize
Senior
paid first
Mezzanine
middle
Junior / equity
absorbs first loss
Running smoothly

All four requirements are met. Risk is allocated across tranches and the structure behaves as designed — for now.

4.2Section 10

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.

Professor's note
The genius of securitization is risk allocation. The danger is forgetting that allocation depends on assumptions.
Definition · Risk reallocation, not elimination
Securitization moves risk from one place to another. The pool's total risk is split across tranches so that Junior absorbs the first losses, Mezzanine the next, and Senior is protected until the lower layers are exhausted. Risk moved. Risk did not vanish.
Try itRisk reallocation panel
Drag stress to hit the tranches

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.

Before · untranched pool
All investors share the same risk
After · tranched
Seniorprotected
Mezzanineprotected
Junior / equityfirst lossprotected
Underlying loan stress20
CalmStressCrisis
Senior still protected

Junior has absorbed 28 of the pool's losses. Senior is untouched — so far.

Risk moved. Risk did not vanish.

Professor's note
The genius of securitization is risk allocation. The danger is forgetting that allocation depends on assumptions — how big losses are, and how correlated the underlying loans turn out to be.
4.3Section 11

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.

Professor's note
"AAA" in a structured product depends heavily on model assumptions. Senior tranches can still lose value when underlying defaults become more correlated or liquidity disappears.
Definition · The label is not the exposure
A senior tranche may carry an AAA badge because Junior and Mezzanine sit beneath it. But that badge depends on assumptions about correlation, liquidity, and collateral. When stress rises, the badge can crack even though the underlying loans are the same.
Try itSenior tranche stress room
Raise each stress lever

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.

Senior trancheAAA
Senior value
83
Protection intact. Badge holds.
Mezzanine
Junior
protection layer
Default correlation20

How much loans default together.

Liquidity20

Whether buyers remain for the tranches.

Housing market20

Underlying collateral value.

Forced selling / mark-to-market20

Fire-sale pressure on prices.

Mark-to-market loss-12
LiquidityOk
The label did not change the underlying exposure

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.

4.4Section 12

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.

Definition · Diversification depends on correlation
Pooling many loans reduces risk only when defaults are independent. If defaults are driven by a common shock — a recession, a housing crash — they cluster together. Then diversification disappears exactly when it is needed most, and losses punch through to the senior tranche.
Try itDefault correlation demonstrator

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.

6 of 20 loans defaulted · pool loss 30%
Default probability (per loan)20%
Correlation / common shock50%

Disabled in independent mode.

Junior15 / 15
Exhausted
Mezzanine15 / 25
Absorbing losses
Senior0 / 60
Protected
Senior protected

Diversification works when defaults are not all driven by the same shock. When correlation rises, diversification can disappear exactly when it is needed most.

4.5Section 13

Can this securitization survive?

Definition · Stress-test the structure
A securitization survives only when its assumptions hold. Four requirements matter most: diversification, accurate risk measurement, normal markets, and sophisticated investors. Mark each satisfied or violated and watch the survival rating react.
Try itSecuritization stress test
Tap each light to toggle satisfied / violated

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.

Scenario
Diverse, well-measured, stable
Stable

Loans spread across many regions and sectors. Risk models are calibrated. Markets are liquid. Buyers are sophisticated.

All four requirements hold. The structure is likely to behave as designed.
Scenario
Geographically concentrated
Failing

Loans concentrated in one region. Correlations rise as the local economy weakens. Buyers rely on ratings only. Liquidity dries up.

Concentration + rising correlation + ratings-only buyers + no liquidity → high risk of failure.
Scenario
Senior insured, insurer stressed
Fragile

The senior tranche is wrapped by a mono-line insurer. But the insurer itself is under capital stress.

The insurance is only as good as the insurer. If the insurer is stressed, the wrap loses value.
Scenario
Junior absorbs — but losses exceed expectations
Fragile

Junior is designed to absorb first losses. But realized losses are far larger than the models predicted.

Losses are biting into Mezzanine. Senior is not yet hit but the cushion is thin.
4.6Section 14

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.

Definition · The fixed-income risk stack
Fixed income is not one risk — it is a stack. Each layer sits on top of the one below. A Treasury carries the first two layers; a corporate bond adds default and spread; a structured product adds model and correlation risk. The deeper you go, the more the risk depends on assumptions.
Try itRisk stack summary
Click a layer to expand

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.

Introduced in

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.

The stack, summarized

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.

05Mastery

Summary and mastery check

Try itLesson 3.4 mastery check
Pass with 9 of 12 correct

Answer all questions, then check your work. You can retry any time — mastery is based on correctness, not speed.

  1. 01

    What is default?

  2. 02

    What is the lowest broad investment-grade category in the simplified table?

  3. 03

    Why do lower-rated bonds usually promise higher yields?

  4. 04

    True or false: a corporate bond spread is entirely default probability.

  5. 05

    XYZ 10-year zero costs $321.97 and promises $1,000. What is the promised YTM?

  6. 06

    XYZ expected payoff is $762.22 and price is $321.97. What is the expected YTM?

  7. 07

    If promised YTM is 12% and expected YTM is 9%, what is the default premium?

  8. 08

    If expected YTM is 9% and risk-free yield is 8%, what is the risk premium?

  9. 09

    What four conditions does successful securitization require?

  10. 10

    Why can a senior structured tranche still lose value?

  11. 11

    What does securitization do to risk?

  12. 12

    Why is relying only on ratings dangerous?

Lesson summary
  1. 1Corporate bonds add default risk: the issuer might not pay.
  2. 2Default means a missed promised interest or principal payment.
  3. 3Ratings summarize credit quality but are opinions, not guarantees.
  4. 4Investment grade and non-investment grade differ by perceived credit quality.
  5. 5Lower-rated bonds usually require higher promised yields.
  6. 6Corporate spreads contain default risk, liquidity, taxes, systematic risk, and other components — not just default probability.
  7. 7Promised YTM is not the same as expected YTM.
  8. 8Default premium equals promised YTM minus expected YTM.
  9. 9Risk premium equals expected YTM minus risk-free yield.
  10. 10Securitization can repackage risk, but it relies on diversification, accurate measurement, normal markets, and sophisticated investors.
  11. 11Senior structured claims can still lose value when correlations, liquidity, and model assumptions change.