Section 3 - Fixed Income Flashcards
Types of Liabilities
AMOUNT / TIMING (AT)
Type 1: KK
Type 2: KU
TYPE 3: UK
TYPE 4: UU
ZCB Immunization Advantages
NO reinvestment risk
NO price risk (Held to Maturity)
Immunization For 1 Liability (How To Implement)
- MacDur Asset = Inv Horizon Liability
- Initial PV CF ≥ PV Liability
- Portfolio Convexity ≥ Convexity Liabilities BUT minimized after it
Extra: ZCB is really good
Zero Coupon Bond Portfolio (characteristics)
- No Price Risk
- No Reinvestment Risk
- No Variace of RoR
Bullet Porfolio
- CFs concentrated @ horizon of investment
- Low Variance of RoR
- Small risk of reinvestment because there may be a longer bond after maturity
- BETTER for STEEPENING Curve
Barbell Porfolio
- CFs are dispersed
- More convexity
- More variance of RoR
- BETTER for FLATTENING Curve
Immunized Convexity Porfolio (Formula)
Immunized Convexity Porfolio = [MacDur² + MacDur + Dispersion)] / (1 + CFYield per period)²
Duration Matching Multiple Liabilities (How To)
- MVasset ≥ MVliability
- DDa = DDpassivo OU BPVa = BPVpassivo
- Dispersão Ativo > Dispersão Passivo (convexity) BUT minimized after it to reduce structural risk
Laddered Portfolio (Advantage)
Good to manage liquidity risk since there is always a bond maturing
Convexity Differences per Porfolio Strategy GIVEN
- Same Duration
- Same CF Yield
- Barbell: (++) Convexity
- Laddered: (+) Convexity
- Bullet (=) Convexity
BPV Formula
BPV Formula = MVa * ModDur * 0.0001
Immunization w/ Derivatives Overlay
- BPV a = BPVliability
- If BPV a > BPV liab, sell duration
Buy Futures = Buy Duration
Sell Futures = Sell Duration
Nf = (BPVliability - BPV asset) / BPVFutures
Nf (Fórmula)
Nf = (BPVliability - BPV asset) / BPVFutures
BPV Future = BPV CTD / Conversion Factor
Contingent Immunization (Concept)
If MVa > MVpassivo by a considerable amount, one may pursue active strategy to earn better returns
Interest Rate Swaps Immunization (Condition Formula)
BPVa + BPVswap/100par = BPV liability
Receiver Swaption
Asset: Fixed
Liability: Float
Dur = (+)
Buy: LONG Duration
Sell: SHORT Duration
Payer Swaption
Asset: Float
Liability: Fixed
Dur = (-)
Buy: SHORT Duration
Sell: LONG Duration
Level of Certainty of Interest Rates Movements and Which Strategy to Use
High Confidence: SWAP (afunda direto)
Low Confidence: SWAPTION (if i > ou < strike)
Medium Confidence: Collar (combinação de ambos)
When to do NOTHING if ↑i increases
If BPV asset < BPV liabilities
Because Prices will Drop ↓
When to do NOTHING if ↓i drops
If BPV asset > BPV liabilities
Because Prices will Increase ↑
What to do with DURATION if ↑i increases
Sell Duration in Assets
What to do with DURATION if ↓i increases
Buy Duration in Assets
Strategy for 100% Hedge (Condition Formula)
[(BPVa*ΔYTMa)+(BPVh+ΔYTMh)] ~ [(BPVliab * ΔYTMliab)]
Put and Call Option (Duration Signal)
Call Option = (+) Duration
Put Option = (-) Duration
Liability-Driven Risks
- Model Risk: Assumptions
- Measurement Error = Approximations, Weighted Avgs for Portfolio Measuring instead of BPV (even for Type 1 Liabilities)
- Spread Risk = Assets are hedged w/ TSY (more vol) and Liabilities are Corp Bonds (less vol) If spread between both changes, there is a risk.
- Counterparty Risk = when OTC derivatives are used. Includes collateral exhaustion risk.
- Assumption that ΔYTMa = ΔYTMliab in interest rate movements
Portfolio Dispersion (Rationale)
(+) Disperse = (+) Convexity
