Fixed Income

Question 1

♦FIX INC♦ Forward Calculation

Answer 1

[1 + s(5)]⁵ = [1 + s(3)]³ * [1 + F(3,2)]²

Question 2

♦FIX INC♦ YTM

Answer 2

Weighted avg of spot rate

Question 3

♦FIX INC♦ Par rate

Answer 3

YTM para cada vencimento

DESCONTAR SEMPRE PELO SPOT

Bootstrapping - Você vai descobrindo passo a passo.

Primeiro o spot 1, depois 2…

100 =

100 * %par3 / (1 + spot1)¹ +

100 * %par3 / (1 + spot2)² +

100 * (1 + %par3) / (1 + spot3)³

Question 4

♦FIX INC♦ Swap spreads

Answer 4

Swap spread = Swap rate - gvt rate (alguns paises que não tem uma curva spot liquida, usam o swap spread no lugar)

I-spread = Interpolated spread caso o vencimento não esteja disponível

z-spread = valor que você soma a cada spot para pegar o risco do bond (não usar para bonds com opção)

TED spread = Libor - Tbill Libor

OIS = Libor - Overnight spread

Question 5

♦FIX INC♦ Interest rate theories

Answer 5

1. Pure expectations: Foward = future spot

2. Local expect: short term tudo =, depois mat risk premium

3. Liquidity preference: 1 com bias de liquidez

4. Segmented mkt: Participants have a permitted maturity to invest

5. Preferred Habitat: Preference, but willing to move if compelling

Question 6

♦FIX INC♦ Modern Term Structure Models

Answer 6

Equilibrium:

1. Cox-Ingersoll-Ross - Single factor, mean reverting, short term, volatility increases with higher interest rate
2. Vasicek - constant vol with higher int rate

Arbitrage Free:

1. Ho-lee - não justifica se a atual curva esta certa ou errada, apenas assume ela como definida e precifica os próximos nós

Question 7

♦FIX INC♦ Effective duration

Answer 7

(PV_Δ- - PV_Δ+) / (2* Δ * PV₀)

Question 8

♦FIX INC♦ Effective convexity

Answer 8

(PV_Δ- + PV^_Δ+ — 2*PV₀) / (Δ² * PV₀)

Question 9

♦FIX INC♦ Bond with option

Answer 9

V_callable = V_straight - V_call (no máx 100 - issuer the right to call back the bond)

V_putable = V_straight - V_put (no mín 100 - holder is allowed to sell (put) the bond back to the issuer - VENCIMENTO ANTECIPADO)

Interest rate ^ bond v call v put ^ (quem vai vencer antes o bond para emitir mais caro no caso da call)

Question 10

♦FIX INC♦ European | American | Bermuda Options

Answer 10

Single date | Anytime | Several dates

Question 11

♦FIX INC♦ OAS

Answer 11

Option adjusted spread - goal seek que explica o spread de risco de um bond corp

Como é calculada depois de ajustar o preço pela opção, quando a volatilidade sobe o OAS cai (pensa que ele é o inexplicado, então se eu consigo alocar uma parte maior do preço na opção, ele deve cair mesmo)

Question 12

♦FIX INC♦ Expected Loss

Answer 12

Expected Loss = Probability of Default * Loss given default

Loss given default = 100% - Recovery Rate

Question 13

♦FIX INC♦ Present Value of Expected Loss

Answer 13

PV exp loss - exp loss = risk premium - TVM dicount

Question 14

♦FIX INC♦ Option analogy

Answer 14

Stock = Max ( 0 , Assets - Dívida) _ call option Dívida = Min ( Assets , Dívida) _ rf + european put

Question 15

♦FIX INC♦ Asset Backed Securities

Answer 15

Do not default

Question 16

♦FIX INC♦ Credit rating vs Structural Model vs Reduced Form model

Answer 16

Credit Rating - least accurate, but tend to be stable Structural model impose assets to be traded (theorical) Reduced form só tem restrição no output, mas é mais mundo real, usa dados históricos e é randomico

Question 17

♦FIX INC♦ CDS buyer and seller

Answer 17

CDS buyer = long protection = short credit quality

Buyer receives protection leg and pays premium leg

Question 18

♦FIX INC♦ CDS upfront payment

Answer 18

(CDS spread - CDS coupon) * duration

Question 19

♦FIX INC♦ CDS settlement

Answer 19

1. Physical - Sell your bond to the CDS seller
2. Cash settlement - payout ratio = 1 - recovery rate

Payout amount (payoff) = payout * notional

Always choose the Cheapest to Deliver, sendo que as vezes dá mais dinheiro você pegar o cash settlement, pq tem um bond tradando a um valor menor que o seu com relação a par

Question 20

♦FIX INC♦ Hazard rate & expected loss

Answer 20

Hazard rate = (1 - %) * (1 - %) …

Expected loss = hazard rate * loss given default