Understand credit ratings and default risk — Stock-Market notes

WHAT is being measured?

WHY it exists: Investors can't personally audit every company. Rating agencies do the analysis once and publish a comparable grade, reducing information cost for the whole market.

The rating ladder (WHAT the letters mean)

HOW to read it: Higher letter = lower default probability = lower spread = lower yield. "D" means already in default.

Figure — Understand credit ratings and default risk

HOW default risk turns into price (derive the spread)

We derive why a risky bond must pay more, from first principles — no formula dump.

Setup. You can either:

Buy a risk-free bond returning $r_f$ for certain, OR
Buy a risky bond promising yield $y$ , but with default probability $p$ (over the period), and if it defaults you recover a fraction $R$ (the recovery rate) of what you were owed.

Step 1 — What must be true for you to bother? Why this step? A rational investor only takes on default risk if the expected return at least matches the safe return. So set expected payoffs equal.

Invest $1. Risk-free gives $(1+r_f)$ . Risky bond: with probability $(1-p)$ you get full $(1+y)$ ; with probability $p$ you recover only $R(1+y)$ .

Step 2 — Write the expected payoff of the risky bond. $\mathbb{E}[\text{payoff}] = (1-p)(1+y) + p\,R(1+y) = (1+y)\big[(1-p) + pR\big]$ Why this step? We weight each outcome by its probability — that's the definition of expectation.

Step 3 — Set expectations equal (no-arbitrage / risk-neutral pricing). $(1+y)\big[1 - p(1-R)\big] = 1 + r_f$ Why this step? If the risky bond's expected value were higher, everyone buys it, its price rises, its yield falls until equality. Markets push toward this balance.

Step 4 — Solve for the yield $y$ . $1+y = \frac{1+r_f}{1 - p(1-R)} \;\;\Rightarrow\;\; y = \frac{1+r_f}{1 - p(1-R)} - 1$

Step 5 — Read off the spread. $\boxed{\;\text{spread} = y - r_f = \frac{(1+r_f)\,p(1-R)}{1 - p(1-R)}\;}$ Why this step? Subtract the safe rate. The spread grows with ==default probability $p$ == and with loss given default $(1-R)$ . If $p=0$ , spread $=0$ — a certain bond is priced like the risk-free one.

Worked examples

Common mistakes (Steel-manned)

Active recall

Recall Quick self-test (hide answers first)

Where is the investment-grade / junk boundary? → between BBB and BB.
What two things drive the spread? → ==default probability $p$ and loss given default $(1-R)$ ==.
If $p=0$ , what is the spread? → zero.
Price and yield move…? → in opposite directions.

Recall Feynman: explain to a 12-year-old

Imagine you lend your lunch money to friends. Aisha always pays back — you'll lend to her for almost nothing. Rahul sometimes forgets — you'll only lend to him if he promises to pay back a bit extra to make it worth the risk. A credit rating is just the teacher's public sticker saying "Aisha = A+ payer, Rahul = risky payer." The riskier the sticker, the more extra you charge. And even if Rahul doesn't pay, maybe he gives back half his snack — that "half back" is the recovery rate, so you charge less extra than if you'd get nothing.

Connections

Bond Yields and Prices — spread adds on top of the risk-free yield.
Yield Curve and Interest Rates — $r_f$ comes from the government yield curve.
Duration and Interest-Rate Risk — different risk from default risk.
Diversification and Portfolio Risk — spreading default risk across issuers.
Risk and Return Tradeoff — spread is the price of bearing risk.

What is default risk?

The probability an issuer fails to make a promised coupon/principal payment, combined with the loss if it happens.

What is a credit rating?

An agency's graded opinion (AAA…D) of an issuer's/bond's likelihood of default.

Name the three big rating agencies.

Moody's, S&P, and Fitch.

Where is the line between investment grade and junk?

Between BBB (lowest investment grade) and BB (highest speculative/junk).

What is the credit spread?

The extra yield a risky bond pays over a risk-free government bond of equal maturity.

Formula for spread in terms of p and R?

spread = (1+r_f)·p(1-R) / [1 - p(1-R)].

What is loss given default (LGD)?

1 minus the recovery rate R; the fraction of value lost when default occurs.

Why do two bonds with equal default probability have different spreads?

Different recovery rates R (seniority/collateral) → different LGD.

If default probability is zero, what is the spread?

Zero — the bond is priced like the risk-free asset.

What happens to a bond's price when it is downgraded?

Its required yield rises, so its price falls (yield and price move oppositely).

Does high yield mean a better investment?

No — it is compensation for higher default risk, not free extra return.

Does a downgrade cause a default?

No, it reflects worsening fundamentals; it is a signal, not the cause.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, credit rating ek report-card jaisa hai jo batata hai ki koi company ya government apna udhaar (bond) time pe wapas karegi ya nahi. Rating agencies — Moody's, S&P, Fitch — har issuer ko ek letter grade deti hain: AAA sabse safe, aur neeche jaate jaate D yaani already default. Ek badi line hoti hai BBB aur BB ke beech — upar wale "investment grade" (safe), neeche wale "junk / high-yield" (risky).

Ab default risk ka matlab hai — kitni probability hai ki paisa doobega. Jitni zyada risk, utna zyada extra interest investor maangega. Is extra interest ko credit spread kehte hain — yeh risk-free government bond ke upar ka bonus yield hai. Formula humne first principles se nikala: expected return safe return ke barabar hona chahiye, tabhi koi risky bond khareedega. Isse aata hai spread ≈ $p \times (1-R)$ ka effect — yaani default probability $p$ aur loss given default $(1-R)$ dono important hain.

Ek zaroori point: sirf "default hoga ya nahi" mat dekho, recovery rate $R$ bhi dekho. Do bonds ki default probability same ho sakti hai, par agar ek secured/senior hai (zyada paisa wapas milega), to uska spread kam hoga. Aur yaad rakho — high yield hamesha achha nahi hota; woh extra yield risk ka compensation hai, muft ka paisa nahi.

Practical baat: jab bond downgrade hota hai (rating gir jaati hai), market zyada yield maangta hai, isliye purane bond ka price gir jaata hai (price aur yield ulte chalte hain). Isliye rating changes market me bade moves laate hain — investors ko pata chal jaata hai ki risk badh gaya.

Test yourself — Equity & Fixed Income

Connections