Credit Risk and Spreads

Where the spread comes from

A 10-year US Treasury yields about 4.2%. A 10-year AT&T corporate bond yields about 5.5%. A 10-year B-rated junk bond yields about 9%. Why the differences?

Treasuries are essentially default-free in nominal terms (the US government can always print dollars to pay). Corporate bonds can default. The extra yield over Treasury is the credit spread, compensating investors for that risk:

$$y_{\text{corp}} = y_{\text{Treasury}} + \text{spread}.$$

A simple way to see why: if a bond defaults with probability $p$ and recovers fraction $\delta$ of face value, then the expected payment per dollar of promised payment is $1 \cdot (1 - p) + \delta \cdot p$. To get the same expected return as the risk-free rate, the promised yield must be high enough to compensate. Algebra gives (approximately, for small p):

$$\text{spread} \approx p \cdot (1 - \delta).$$

A bond with 2% annual default probability and 40% recovery rate needs a spread of about $0.02 \times 0.6 = 1.2\% = 120$ bps over Treasury to break even on expected return. Real-world spreads are typically higher than this; investors demand extra premium for bearing the risk (not just the expected loss).

Default probability p: 1.50%Recovery rate δ: 50.00%Treasury yield: 4.00%Reset

Break-even spread = p(1 − δ) = 75 bps. Fair corporate yield = 4.00% + 0.75% = 4.75%.

The line is the spread that just compensates for expected loss; its slope is (1 − δ), so dragging recovery down steepens it. Drag δ to 0 (lose everything in default) and the spread equals the default probability outright. Actual market spreads trade above this line: that gap is the risk premium for bearing default risk, not just expecting it. The Treasury-yield slider moves only the fair corporate yield in the readout (corporate = Treasury + spread); the spread curve is independent of the risk-free level.

Baseline: 1.5% default probability, 50% recovery, 4% Treasury, giving the 75 bps break-even spread and 4.75% fair yield worked below. Drag recovery to zero and the break-even spread equals the default probability outright.

Credit ratings

Three big rating agencies (S&P, Moody’s, Fitch) classify bonds on a letter-grade scale. Simplified:

Grade	S&P / Fitch	Moody’s	Default risk
Investment grade	AAA	Aaa	Very low
	AA	Aa	Very low
	A	A	Low
	BBB	Baa	Modest
Speculative (“high yield” / “junk”)	BB	Ba	Material
	B	B	High
	CCC	Caa	Distressed
	D	C	In default

Two bright lines matter:

1. Investment grade vs speculative, drawn between BBB- and BB+. Many institutions (pension funds, insurance companies) are legally barred from holding below-investment-grade bonds; a downgrade across this line forces selling and widens spreads sharply.
2. AAA: very few entities qualify. The US Treasury did not even carry universal AAA after S&P downgraded it in 2011.

Empirically, rating predicts default reasonably well over 1-5 year horizons; less well at very long horizons or in deep recessions.

What drives spreads

Three forces:

• Issuer-specific. Financial leverage, profitability, cash flow, industry. A heavily indebted firm in a cyclical industry trades wider than a cash-rich tech company.
• Macro. In recessions, default rates rise across the board and spreads widen for everyone, even firms whose individual risk hasn’t changed.
• Risk appetite. When investors are flush with capital and comfortable, spreads compress to almost nothing. In 2007 BBB spreads were under 100 bps; by late 2008 they were over 800.

FRED series to watch: BAMLC0A0CM (investment-grade corporate spread), BAMLH0A0HYM2 (high-yield spread), and T10Y3M (yield-curve slope). Together they tell you a lot about how financial markets are pricing risk.

The term structure of spreads

Spreads also depend on maturity. For investment-grade firms, the curve typically slopes upward (longer = more time for things to go wrong). For deeply distressed firms, it can slope downward. If a firm survives the near term, it has demonstrated some resilience; the unconditional default rate is concentrated in the short window.

A worked example

A 5-year corporate bond pays a 6% annual coupon on face value of $1,000. Treasury 5-year yields are 4%. Investors believe the bond defaults with 1.5% annual probability; recovery in default is expected to be 50 cents on the dollar.

Approximate fair spread: $0.015 \times (1 - 0.5) = 0.0075 = 75$ bps. So the fair YTM (under risk-neutral pricing) is about 4.75%. The market actually trades it at 6%, so there’s a 125 bps spread, of which roughly 75 bps compensates for expected loss and the remaining ~50 bps is the risk premium.

In recessions both pieces grow: expected default rate rises and the risk premium rises. That’s why high-yield spreads can swing from 250 bps in good times to 1,!000+ bps in crises.

What’s next

Unit 3 turns from pricing financial securities to valuing real projects and equity. The same TVM machinery applies; only the discount rate (now the cost of capital, not a bond yield) changes.