Credit Risk and Corporate Bonds

Investment Theory

Lorenzo Naranjo

Fall 2026

Corporate Bonds

• Promised fixed payments, like Treasuries, but the issuer can default.
• A claim on the firm’s cash flows, senior to its stock.
• Ratings: Baa/BBB and above is investment grade; below is high yield.
• The yield spread: the corporate yield minus the Treasury yield of the same maturity.
• This chapter:
  • Promised yields and expected returns.
  • A century of spreads, and how much of them is default.
  • Corporate bond returns from transaction prices.

Promised Yields and Expected Returns

• A one-year zero with promised yield y, default probability \pi and recovery R of face value: \operatorname{E}(r) = (1 + y) \left( 1 - \pi (1 - R) \right) - 1 \approx y - \pi (1 - R).
• \pi (1 - R) is the expected default loss.
• The spread over Treasuries also pays for:
  • a risk premium, because defaults cluster in bad times,
  • a liquidity premium, because corporate bonds are costly to trade,
  • taxes, since states tax corporate interest but not Treasury interest.

Example 1 (How Much of the Spread Is Expected Loss?) With Treasuries at 4.5%, a Baa bond yielding 6% with a 0.25% default probability and 40% recovery has an expected return of 1.06 \times (1 - 0.0025 \times 0.6) - 1 = 5.84\%: the expected loss is 0.16 of its 1.5-point spread. A B bond yielding 8.5% with a 4% default probability expects 1.085 \times (1 - 0.04 \times 0.6) - 1 = 5.90\%: the expected loss is 2.6 of its 4-point spread.

Spreads over a Century

Moody’s Baa minus Aaa yields since 1919, and Baa minus the 10-year Treasury par yield since 1971, in percentage points.

• Baa-Aaa: mean 1.16, peak 5.64 in May 1932, 3.38 in December 2008, 0.59 at the end of 2025.

Spreads Are Not Default Forecasts

• Giesecke et al. (2011): U.S. corporate bond defaults, 1866 to 2008.
  • Railroad crisis of 1873 to 1875: defaults of 36% of the par value of the market.
  • Stock returns, volatility and GDP growth forecast defaults; credit spreads do not.
  • Spreads are about twice default losses: a credit risk premium of about 80 basis points.

How Much of the Spread Is Default?

• Elton et al. (2001), 10-year A-rated industrials:
  • Expected loss 17.8%, state and local taxes 36.1%, and a risk premium for the remaining 46%.
• Merton (1974): equity is a call on the assets; debt is a riskless bond minus a put.
• Huang and Huang (2012): structural models explain under 20% of investment-grade spreads, the credit spread puzzle.
• Chen et al. (2009): defaults and risk premia rise together in recessions, which shrinks the puzzle.

Evidence from Credit Default Swaps

• A credit default swap pays the loss on a bond if its issuer defaults, so its premium prices default alone.
• Longstaff et al. (2005): the default component of the spread over Treasuries is
  • 51% for AAA and AA, 56% for A, 71% for BBB, 83% for BB.
• The rest varies with the illiquidity of bonds and of the bond market.
• Default risk is the largest part of the spread, much larger than the expected default loss.

Example 2 (Debt as a Riskless Bond Minus a Put) A firm with assets of $100 million owes $80 million in one year, the risk-free rate is 5%, and a one-year put on the assets with a strike of $80 million is worth $3 million. The debt is worth 80/1.05 - 3 = \$73.19 million and the equity $26.81 million. The promised yield is 80/73.19 - 1 = 9.30\%, a spread of 4.30 points. More volatile assets raise the put’s value and the spread.

Corporate Bond Returns

	Mean (%)	Volatility (%)	Sharpe ratio	Worst month (%)
Investment grade	3.11	5.87	0.53	-6.08
High yield	4.98	7.87	0.63	-14.22
Stock market	10.37	15.18	0.68	-17.20

• Value-weighted portfolios from TRACE transaction prices (WRDS Bond Returns), September 2002 to December 2025, in excess of bills.
• Both had their worst month in March 2020, before the Fed announced it would buy corporate bonds.

What Risks Do They Carry?

	Alpha (%)	t(alpha)	MKT	TERM	R-squared
Investment grade	-0.45	-0.52	0.20	0.85	0.61
High yield	0.62	0.40	0.38	0.24	0.53

• Regressions on the stock market (MKT) and a 5-year Treasury (TERM).
• Investment grade: mostly Treasury risk; high yield: more equity-like, because default risk rises when stocks fall.
• No alpha is significant.

Factor Models for Bonds

• Fama and French (1993): a term factor and a default factor capture most of the variation in bond returns.
• Bai et al. (2019): downside, credit and liquidity risk factors, retracted in 2023.
  • Dickerson et al. (2023) found the result came from misaligned dates in the data.
  • With aligned data, the corporate bond market factor is hard to beat.
• A replication lesson: when returns are built from complex data, the alignment of dates is part of the result.

Spreads and the Economy

• Collin-Dufresne et al. (2001): leverage, volatility and interest rates explain little of the changes in spreads; a single common factor drives most of the rest.
• Gilchrist and Zakrajšek (2012): split spreads into expected defaults and an excess bond premium.
  • The excess bond premium rises when financial intermediaries lose capital.
  • It predicts declines in economic activity: a contraction in the supply of credit.

Reaching for Yield

• A higher promised yield is not a higher expected return if it comes with more default risk.
• Choi and Kronlund (2018): corporate bond funds that tilt toward higher-yield bonds
  • earn higher returns and attract more inflows, especially when rates are low,
  • but tend to have negative risk-adjusted returns,
  • and hold less cash and less liquid bonds.
• The right benchmark has the same exposure to default risk.

Takeaways

• A corporate yield is a promise; the expected return is lower by the expected default loss.
• For investment-grade bonds, expected losses are a small part of the spread; default risk, liquidity and taxes make up the rest.
• Spreads widen in crises and leave a long-run credit risk premium of about 80 basis points.
• Investment-grade returns are mostly Treasury risk; high-yield returns are more equity-like.
• Single-factor bond models are hard to beat, and data errors can create the appearance of more.

References

Bai, Jennie, Turan G. Bali, and Quan Wen. 2019. “Common Risk Factors in the Cross-Section of Corporate Bond Returns.” Journal of Financial Economics 131 (3): 619–42.

Chen, Long, Pierre Collin-Dufresne, and Robert S. Goldstein. 2009. “On the Relation Between the Credit Spread Puzzle and the Equity Premium Puzzle.” The Review of Financial Studies 22 (9): 3367–409.

Choi, Jaewon, and Mathias Kronlund. 2018. “Reaching for Yield in Corporate Bond Mutual Funds.” The Review of Financial Studies 31 (5): 1930–65.

Collin-Dufresne, Pierre, Robert S. Goldstein, and J. Spencer Martin. 2001. “The Determinants of Credit Spread Changes.” The Journal of Finance 56 (6): 2177–207.

Dickerson, Alexander, Philippe Mueller, and Cesare Robotti. 2023. “Priced Risk in Corporate Bonds.” Journal of Financial Economics 150: 103707.

Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann. 2001. “Explaining the Rate Spread on Corporate Bonds.” The Journal of Finance 56 (1): 247–77.

Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33 (1): 3–56.

Giesecke, Kay, Francis A. Longstaff, Stephen Schaefer, and Ilya Strebulaev. 2011. “Corporate Bond Default Risk: A 150-Year Perspective.” Journal of Financial Economics 102: 233–50.

Huang, Jing-Zhi, and Ming Huang. 2012. “How Much of the Corporate-Treasury Yield Spread Is Due to Credit Risk?” The Review of Asset Pricing Studies 2 (2): 153–202.

Longstaff, Francis A., Sanjay Mithal, and Eric Neis. 2005. “Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market.” The Journal of Finance 60 (5): 2213–53.

Merton, Robert C. 1974. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” The Journal of Finance 29 (2): 449–70.