FIXED INCOME — CFA LEVEL II CHEAT SHEET

TERM STRUCTURE OF INTEREST RATES

Core Relationships

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Bootstrapping Process

Extract z₁ from 1-year par bond

Use z₁ to extract z₂ from 2-year par bond: PV(coupons at z₁) + PV(par+final coupon at z₂) = $100

Repeat sequentially to longer maturities

Yield Curve Theories

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Key LPT Insight: Forward Rate = Expected Future Spot + Liquidity Premium ∴ Expected Spot = Forward Rate − Liquidity Premium

Swap Rates & Spreads

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CREDIT ANALYSIS & MODELING

Default Risk Components

Expected Loss = PD × LGD = PD × (1 − Recovery Rate)

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Structural (Merton) Model

Framework: Equity = Call option on firm assets

• Equity Value = Max(V_A − D, 0)

• Debt Value = Min(V_A, D) = V_A − Max(V_A − D, 0)

Where: V_A = asset value; D = debt face value

Credit Risk Drivers:

• ↑ Asset volatility → ↑ PD (equity call option more valuable; assets swing wider)

• ↓ Equity value / ↑ D → ↑ PD (less cushion before default)

• ↓ Time to maturity → ↓ PD (less time for V_A to fall below D)

Reduced-Form Models

Alternative to structural models; observable inputs:

• PD modeled as hazard rate (instantaneous default probability)

• Credit Spread calibrated from market bond prices

• No explicit asset dynamics; focus on empirical default correlations

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FIXED INCOME VALUATION & SPREADS

Credit Spread Components

Credit Spread = Expected Loss + Risk Premium for Uncertainty

$$\text{Credit Spread} ≈ \text{PD} × \text{LGD} + \text{Risk Premium}$$

Factors widening spreads (↑ credit risk):

• ↑ Default probability or ↓ recovery expectations

• ↑ Credit risk aversion (risk-on → risk-off)

• ↓ Liquidity in credit market

• ↑ Correlation among defaults (systematic risk)

Rating Categories & Typical Spreads (vs. Treasuries)

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bps = basis points (0.01%)

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DECISION RULES & EXAM CUES

Yield Curve Interpretation

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Concept	Definition	Formula
Spot Rate (z_T)	Yield on zero-coupon bond, maturity T	Discount rate for single cash flow at T
Forward Rate f(j,k)	Rate for loan beginning year j, ending year k	(1+z_k)^k = (1+z_j)^j × (1+f(j,k))^(k-j)
Par Rate	Coupon rate pricing bond at par	Derived from spot curve via bootstrapping
No-Arbitrage Rule	Links all three curves	f(j,k) = [(1+z_k)^k / (1+z_j)^j]^(1/(k-j)) − 1
Theory	Explanation	Curve Shape Driver	Key Assumption
Pure Expectations (PET)	Forward rates = unbiased predictors of future spot rates	Only rate expectations	No risk premium
Liquidity Preference (LPT)	Forward rates include liquidity premium for duration risk	Rate expectations + liquidity premium	Investors demand premium for longer bonds
Market Segmentation	Different maturities dominated by different institutions	Supply/demand in maturity segments	Institutions prefer specific maturities
Preferred Habitat	Hybrid: institutions have preferences but move if yield premium sufficient	Expectations + premiums + institutional flows	Blend of above theories
Term	Definition	Use
Swap Rate Curve	Fixed rates paid in interest rate swaps (vs. SOFR floating)	Corporate bond pricing benchmark; reflects true funding costs
Swap Spread	Swap Rate − Government Bond Yield (same maturity)	Positive = credit risk premium; widens in financial stress; negative under QE
Component	Definition	Range
PD (Probability of Default)	% chance issuer fails to pay	0–100%
LGD (Loss Given Default)	% of principal lost if default occurs	Inverse of recovery rate
Recovery Rate	% of principal recovered post-default	60–70% seniors; 20–40% subordinated
Model Type	Strength	Weakness
Structural (Merton)	Links equity & credit; forward-looking	Hard to calibrate; V_A not directly observable
Reduced-Form	Uses market data directly; simpler	Black-box; less intuitive link to fundamentals
Rating	Risk Level	Typical Spread
AAA/AA	Investment Grade (IG), minimal credit risk	10–50 bps
A	IG, moderate risk	50–150 bps
BBB	IG floor; elevated risk	150–300 bps
BB & below	High Yield (HY); significant default risk	300 bps–10%+
If curve is...	Implies (under PET)...	Action cues
Steep upward	↑ rates expected	Long bonds → relative value; guard duration risk
Flat	Uncertain