9. Fixed Income

Question 1

Dominance Effect

Answer 1

Payoff Today ≠ Payoff Future

Question 2

Aditividade

Answer 2

Soma do Todo = Soma das Partes

Question 3

Derive Spot from Par (Method)

Answer 3

Par 1y = 4% / S1 =4%
Par 2y = 5%

Spot 2y:
0.05/1+S1
+0.05/(1+S2)^2

Solve for S2

Question 4

Interest Rate Models (Types)

Answer 4

Arbitrage Free: Less Parameters. Forces PV of the model into Real Prices.

Equilibrium: More Parameters.

Question 5

Interest Rate Models (Names)

Answer 5

a. Arb Free: Ho-Lee and KWF (Asia & Germany)
b. Equilibrium: Vasicek & CIR (Russia desequilibrada)

Acronyms = No Negative Rates

Question 6

Arbitrage Free Models

Answer 6

1) Ho-Lee: No Mean Revert. Calibrate with Fwd Rates

2) KWF: Uses log. May be used with options

Question 7

Equilibrium Models

Answer 7

1) Vasicek: Vol Constante. Drift Mean Revert.

2) CIR: Vol Drift projeta menos variação em juros de low leves, o que evita juros negativos.

Question 8

Z-Spread (Concept)

Answer 8

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)

Question 9

OAS Spread (Concept)

Answer 9

Z-Spread - Option Cost

Put: add value to bondholder (less spread)
Call: remove value to bondholder (more spread)

Question 10

TED Spread

Answer 10

TED Spread = LIBOR - T-Bill
TED Spread = Bancos v. Governo

Concept: Sums up credit + liquidity (overall)

Question 11

LIBOR-OIS Spread

Answer 11

Money Market Spread (< 1 year bonds)

LIBOR = Unsecured
OIS: Credit risk free swap overnight (curtinho)

Question 12

Swap Spread

Answer 12

Swap Spread = Swap - Government Bond on the run

Measures counterparty risk

Question 13

Term Structure Theories

Answer 13

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.

Question 14

Portfolio Choices (Types)

Answer 14

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).

Question 15

Duration (Types)

Answer 15

Effective Duration Option Bonds ≤ Option Free
One-sided Duration: Option bonds will be less sensible
Σ Key Rate Duration = Effective Dur

Question 16

Conversion Ratio (Formula)

Answer 16

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

Question 17

Conversion Value (Formula)

Answer 17

CV = (CP * Po Stock)

-
Onde:
CV = Multiplica

Question 18

Market Conversion Price (Formula)

Answer 18

MCP = (PV Bond Conversível / CR fixo)

Question 19

CoCo Bond Value (Formula)

Answer 19

CoCo Value = Higher (CV, Mkt Value Bond)

Question 20

Credit Risk (Formula)

Answer 20

PE = PD * LGD

LGD = EAD * (1 - RR)

Question 21

Credit Valuation Adjustment Formula

Answer 21

CVA = Σ PV Expected Loss (PE)

PV Expected Loss = PD * [EAD*(1-RR)] / (1 + Rf)ˆt

Question 22

Credit Bond Valuation (Steps)

Answer 22

1. Valuate Bond @ Risk Free

2. Discount CVA (Σ PVPE)

Question 23

Defaulted Bonds Valuation (Steps)

Answer 23

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

Question 24

Downgrade Matrix Formula

Answer 24

Δ% Price = (-ModDur)*(New Spread - Old Spread)

Question 25

Credit Models (List)

Answer 25

1. Structural: Asset < Liabilities. Default is endogenous. Option pricing.
2. Reduced Form: When, not why. Default is not endogenous. It is random (e.g.: 2008).

Question 26

CDS (Dynamic)

Answer 26

1. Buyer pays PMT series to seller based in a notional
2. Seller pays notional if default
3. CDS ~ 1-5% for Investment Grade - High Yield

Question 27

CDS Legs

Answer 27

Protection Leg = Buyer devia pagar credit spread ao Seller

Premium Leg = Buyer tá pagando PMT fixa

Question 28

Upfront PMT CDS (Formula)

Answer 28

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)

Question 29

CDS Settlement

Answer 29

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)