13.1 Corporate Bonds

Corporate Bonds

FMP–17 is the corporate credit market reading that sits between vanilla rates (FMP–16) and securitized products (FMP–18). FRM candidates must know how corporates are traded and quoted, what legal documents constrain issuers, how high-yield structures differ from investment-grade, how to separate default risk from spread risk, and how expected returns decompose into risk-free, spread, and expected-loss pieces.

Trading and Yields

Corporate bonds trade primarily in the over-the-counter (OTC) dealer market, not on a continuous exchange like listed equities. Bid–ask spreads widen for smaller issues, lower ratings, and stressed markets. Quotes are typically clean prices (flat prices) as a percent of par. The cash amount paid at settlement is the dirty (full) price:

Dirty price = Clean price + Accrued interest

Accrued interest for corporates usually follows a 30/360 day-count (exact conventions vary by market). Yield measures include:

Worked accrued-interest and dirty-price example

A 6% semiannual corporate (pays $3 per $100 par every six months) last paid a coupon 60 days ago under 30/360. Accrued = 3 × (60/180) = $1.00 per 100 par. If the clean quote is 98.50, dirty price = 98.50 + 1.00 = 99.50. The buyer pays 99.50 and receives the full next coupon; the seller is compensated for the fraction of the coupon earned while holding the bond.

Worked YTM sketch

Par 100, annual coupon 5, maturity 2 years, clean price 98 (ignore accrued for a simple annual model). Solve 98 = 5/(1+y) + 105/(1+y)^2. Try y = 6%: PV = 5/1.06 + 105/1.06^2 = 4.717 + 93.449 = 98.17. That PV sits above the 98 market price, and price falls as yield rises, so the YTM must be a little above 6% ⇒ YTM ≈ 6.1%. On the exam, set up the IRR equation carefully and interpolate if needed.

Indenture and Trustee

The bond indenture is the legal contract between issuer and bondholders. It specifies coupon, maturity, covenants, collateral, subordination, events of default, and early-retirement provisions. A trustee (often a bank) represents bondholders, monitors covenant compliance, and acts in default. Key covenant types:

Investment-grade indentures are often lighter; high-yield indentures are denser because creditors demand contractual protection when ratings are weak.

High-Yield Features

High-yield (junk) bonds are rated below BBB−/Baa3. Structural features that appear frequently:

• Deferred-interest / zero-coupon / PIK (payment-in-kind) bonds that pay in additional notes instead of cash early in the life
• Step-up coupons that rise if ratings fall or after a deferral period
• Callable structures with declining call premiums (issuers refinance when spreads tighten)
• Reset and floating-rate notes that reprice periodically
• Equity kickers (warrants) or convertible features in some deals
• Senior secured vs senior unsecured vs subordinated waterfall positioning

High-yield investors earn higher promised yields but face higher default probabilities, lower recovery in many capital structures, and greater event risk.

Credit Default Risk vs Credit Spread Risk

Distinguish two related but different risks:

A BBB bond can lose substantial mark-to-market value when its OAS widens 100 bp even though coupons are current. Risk managers who only track expected default losses miss spread VaR. Conversely, holding to maturity with no default still leaves reinvestment and mark-to-market noise along the way if the position is marked.

Worked spread-duration loss

Approximate ΔP/P ≈ −spread duration × Δspread. If spread duration = 5 and spreads widen 0.80% (80 bp), price change ≈ −5 × 0.008 = −4.0%. On a $10 million position, mark-to-market loss ≈ $400,000 with no credit event.

Event Risk

Event risk is the risk that a discrete corporate action suddenly worsens credit quality: leveraged buyouts, debt-funded acquisitions, spin-offs that strand debt, large shareholder distributions, or fraud revelations. Rating agencies may downgrade after the event; spreads gap wider overnight. Covenant packages (change-of-control puts, leverage tests) partially mitigate but do not eliminate event risk—especially for legacy investment-grade issues written when covenants were loose.

Classification: Issuer, Maturity, Rate, Collateral

Corporate bonds are classified along several axes FRM questions love to cross:

Equipment trust certificates and mortgage bonds have specific collateral; debentures rely on general credit. In bankruptcy, absolute priority is the starting point, but negotiated reorganizations often deviate.

Early Retirement Mechanisms

Issuers retire bonds before final maturity through several channels:

Callable bonds have negative convexity near the call region: when rates fall, price appreciation is capped near the call price. Investors demand a call premium in yield (lower price / higher YTM versus otherwise identical bullets).

Worked call decision (issuer view)

Outstanding 7% bond callable at 103; refinancing rate for a similar new issue is 5%. Ignoring frictions, the issuer compares the present value of calling (pay 103, issue 5% debt) versus continuing to pay 7%. If the interest savings exceed transaction costs and the call premium amortization, the issuer calls. Bondholders face reinvestment risk: they must reinvest at lower yields.

Recovery Rates and Default Rates

Default rate = fraction of issuers (or dollar amount) that default over a horizon. Recovery rate = fraction of par (or of claim) recovered after default, often measured as the post-default market price of the bond or ultimate recovery in bankruptcy. Loss given default (LGD) = 1 − recovery rate.

Empirical patterns (stylized for FRM):

• Senior secured recovers more than senior unsecured, which recovers more than subordinated
• Recoveries are procyclical: lower in deep recessions when asset values fall and defaults cluster
• Industry and capital-structure thickness matter as much as rating alone

Worked expected loss

One-year PD = 2.0%, expected recovery = 40% (LGD = 60%). Expected loss ≈ PD × LGD = 0.02 × 0.60 = 1.2% of exposure. If the credit spread is 180 bp and other premia are small, a rough comparison asks whether 1.80% promised spread compensates 1.20% expected loss plus risk premia and liquidity—exam vignettes often stop at PD × LGD.

Expected Return Components

A useful decomposition of a corporate bond’s expected return (promised yield view):

Expected return ≈ Treasury (or SOFR) baseline + credit spread − expected default loss + (±) other effects

More explicitly, the promised YTM embeds compensation for:

1. Risk-free term structure
2. Expected loss from default (PD × LGD, with timing)
3. Credit risk premium (compensation for systematic default/spread risk)
4. Liquidity premium
5. Tax and embedded-option adjustments (call, put, convert)

Mark-to-market return over a short horizon is dominated by spread changes and rate changes, not by realized defaults. Holding-period return ≈ carry (coupon/pull-to-par) − duration × Δy − spread duration × Δs + convexity terms.

Worked holding-period sketch

Bond YTM 5.5%, modified duration 6, spread duration 5. Over one year, if the benchmark yield rises 20 bp and the spread tightens 10 bp, approximate price return ≈ −6 × 0.0020 − 5 × (−0.0010) = −0.012 + 0.005 = −0.7%, plus coupon carry ~5.5%, for a rough total near 4.8% before convexity and defaults.

Exam Synthesis

When a vignette describes a high-yield issuer, map seniority, covenants, and call features before computing yields. When P&L is discussed without a bankruptcy headline, think spread risk. When comparing bonds, align collateral and maturity, then compare spreads after adjusting for embedded options. Expected-loss arithmetic (PD × LGD) is the bridge from credit analysis to the promised spread.