9. Fixed Income Flashcards
Dominance Effect
Payoff Today ≠ Payoff Future
Aditividade
Soma do Todo = Soma das Partes
Derive Spot from Par (Method)
Par 1y = 4% / S1 =4%
Par 2y = 5%
Spot 2y:
0.05/1+S1
+0.05/(1+S2)^2
Solve for S2
Interest Rate Models (Types)
Arbitrage Free: Less Parameters. Forces PV of the model into Real Prices.
Equilibrium: More Parameters.
Interest Rate Models (Names)
a. Arb Free: Ho-Lee and KWF (Asia & Germany)
b. Equilibrium: Vasicek & CIR (Russia desequilibrada)
Acronyms = No Negative Rates
Arbitrage Free Models
1) Ho-Lee: No Mean Revert. Calibrate with Fwd Rates
2) KWF: Uses log. May be used with options
Equilibrium Models
1) Vasicek: Vol Constante. Drift Mean Revert.
2) CIR: Vol Drift projeta menos variação em juros de low leves, o que evita juros negativos.
Z-Spread (Concept)
Fixed Value that should be added to Spot Rates so that PV = PMT / (1 +S2 + Z-Spread)ˆ2
Put: add value to bondholder (less spread)
Call: remove value to bondholder (add more spread)
OAS Spread (Concept)
Z-Spread - Option Cost
Put: add value to bondholder (less spread)
Call: remove value to bondholder (more spread)
TED Spread
TED Spread = LIBOR - T-Bill
TED Spread = Bancos v. Governo
Concept: Sums up credit + liquidity (overall)
LIBOR-OIS Spread
Money Market Spread (< 1 year bonds)
LIBOR = Unsecured
OIS: Credit risk free swap overnight (curtinho)
Swap Spread
Swap Spread = Swap - Government Bond on the run
Measures counterparty risk
Term Structure Theories
a. Expectations:
a1) Pure: No difference between bonds. Choose any
a2) Local: Rbonds is the same in the short run. In the long run, they differ
b. Liquidity Preference: Everybody loves short term. It generates a premium for long term which biases the fwd interest rates.
c. Segmented Theory: Each maturity is a different market
d. Preferred Habitat: Each investor makes a market for its favorite maturities.
Portfolio Choices (Types)
Bullet: Cobra tudo no dia do vencimento. Melhor opção quando a curva tá steepening (inclinando)
Barbell: Cobra repagamento ao longo da operação. Melhor quando a curva tá flattening (plana).
Duration (Types)
Effective Duration Option Bonds ≤ Option Free
One-sided Duration: Option bonds will be less sensible
Σ Key Rate Duration = Effective Dur
Conversion Ratio (Formula)
CR = (Par CoCo Bond / Qtd de Shares que dá direito) CR = (Par CoCo Bond / Conversion Price)
-
Onde:
CR = Divide Turma
CP = Conversion Price = # Ações que o bond dá direito
Conversion Value (Formula)
CV = (CP * Po Stock)
-
Onde:
CV = Multiplica
Market Conversion Price (Formula)
MCP = (PV Bond Conversível / CR fixo)
CoCo Bond Value (Formula)
CoCo Value = Higher (CV, Mkt Value Bond)
Credit Risk (Formula)
PE = PD * LGD
LGD = EAD * (1 - RR)
Credit Valuation Adjustment Formula
CVA = Σ PV Expected Loss (PE)
PV Expected Loss = PD * [EAD*(1-RR)] / (1 + Rf)ˆt
Credit Bond Valuation (Steps)
- Valuate Bond @ Risk Free
2. Discount CVA (Σ PVPE)
Defaulted Bonds Valuation (Steps)
Se quebrou em t = 1, calcule a IRR utilizando
PV = Investment CF outflow t = T of default time PMT = Received PMTs until default FV = Recovery Value
Find IRR
Downgrade Matrix Formula
Δ% Price = (-ModDur)*(New Spread - Old Spread)
Credit Models (List)
- Structural: Asset < Liabilities. Default is endogenous. Option pricing.
- Reduced Form: When, not why. Default is not endogenous. It is random (e.g.: 2008).
CDS (Dynamic)
- Buyer pays PMT series to seller based in a notional
- Seller pays notional if default
- CDS ~ 1-5% for Investment Grade - High Yield
CDS Legs
Protection Leg = Buyer devia pagar credit spread ao Seller
Premium Leg = Buyer tá pagando PMT fixa
Upfront PMT CDS (Formula)
Upfront PMT = (PV Protected - PV Premium)
Upfront PMT = [(Spread - PMT Coupon) * Dur] * Δ% Price
> 0, buyers pays additional spread
< 0, seller pays because spread is reducing (Brazil virando a Suíça - Aaa)
CDS Settlement
1) Financeiro: Seller paga cash [ (1 - RR) * Cheapest to Deliver]
2) Físico: Holder do CDS fica com o bond quebrado e o seller do CDS paga o Par Value p/ recomprar ($1000)
