Fixed Income Flashcards
Inflation linked bonds
Floating rate bond
Par value adjustmed on both coupon and notional principle.
Floating rate bond is an adjustment to coupon ONLY. “Floupon only”
Spread duration define
Duration time spread =
Spread duration is portfolio percentage sensitivity to a 1% change in credit spreads. More useful for IG bonds. HY bonds focus credit default loss.
Duration time spread = Spread duration x bond credit spread
Total return Swap
One party (total return receiver) pays interest rate plus a spread in return for the total return on a reference bond portfolio.
What is a repo and what are they used for?
Repos are used to gain leverage by borrowing against a security.
Sell and repurchase later on for cash.
Futures contracts margin requirements
Futures require little initial margin deposit.
Leverage = (notional value of contract - margin amount) / margin amount
What is a Swap Agreement and who benefits in falling interest rate?
Receive fixed, pay floating.
Fixed rate receiver benefits in falling interest rate environment.
What is matrix pricing is used for?
Matrix pricing is used for illiquid bonds and does not require sophisticated modelling of term structures.
Three conditions to Immunize a single liability.
It aims to lock in which yield YTM or Cash flow yield?
3 conditions
Three conditions for MULTIPLE liability immunization
Cash flow matching
Upward shift in yield curve effect for a immunized portfolio. Coupon reinvestment risk and price risk?
Single liability immunization
1.Macaulay duration matches liability due
2. Initial MV of portfolio > PV of liability
3. Minimize portfolio convexity.
Immunisation aims to lock in the IRR/Cash flow yield (NOT the weighted avg YTM). You would immunise a single liability by matching portfolio Macaulay duration to that liability.
Multiple liability immunization
1. MVA > MVL
2. Money duration of BPV of A ‘equal to’ Money duration of BPV of L.
3. Convexity & Dispersion of CF’s of Assets greater than Convexity & Dispersion of CF’s of Liabilities.
Cash flow matching is a type of immunization where a zero coupon bond is used to match a simple known liability.
Upward shifts sees price effect cancelling out coupon reinvestment effect.
Contingent Immunization
PVA exceeds PVL. Suplus can be managed in a way which adds value.
Structural risk
What to look for?
Structural risk = HIGHEST Convexity. Where yield curve changes impact cash flow and yield. Structural risk is the risk that the immunization strategy does not work due to non-parallel shifts and twists of the yield curve. Structural risk is directly related to the convexity of the immunizing portfolio when its convexity is higher than the convexity of the liabilities being immunized.
Enhanced Indexing
Tracking error aka Active Return =
1.25%
Active Risk =
Enhanced Indexing matches all primary ‘risk exposures’ but not all holdings.
Tracking error = Pr - Br
1.25% would mean that on 68% of occasions within a normal distribution returns would lie within 1.25% of the index.
Active risk = SD of active returns
How do you reduce portfolio duration using swaps?
Enter a Pay fixed/Receive floating interest rate swap.
How do you increase duration with futures?
How do you decrease duration with futures?
How to close the duration gap (Asset BPV «_space;Liability BPV)
Increase duration = BUY futures
Decrease duration = Sell futures
How to close the duration gap (Asset BPV «_space;Liability BPV) = Buy Futures or enter into Receive Fixed IRS.
What type of duration does an Option Embedded Bond use?
Option embedded bonds require Effective Duration
Asset Liability Management
Liability Driven Investing
Asset-driven Liabilities
Would you use Asset Liability Management or Liability driven investing when:
Commercial bank managing interest rate exposure?
Asset Manager Immunizing corporate debt obligations
Asset Liability Management - 2 types LDI and ADL
Liability Driven Investing - Takes liabilities as a given and assets are structured and managed for interest rte risk (use of derivatives in DB plans 2022 where derivative margin calls created stress)
Asset-driven Liabilities - Takes assets as a given and liabilities are structured to manage interest rate risk. Cyclical businesses with revenues linked to the business cycle use ADL.
Commercial bank managing interest rate exposure? Asset Liability Management
Asset Manager Immunizing corporate debt obligations?
Liability driven investing
Which bond to pick when given:
A stated single liability?
Concerns of structural risk?
For immunization of a single liability Macaulay Duration of an asset should match as closely as possible to the liability. PVA should equal or exceed PVL. Convexity of the asset should slightly exceed the convexity of the liabilities.
Structural risk is reduced by choosing low convexity bonds.
IMMUNIZEMACD
STRUCTURALOWCONVEX
Stratified Sampling techniques
- Lower cost enhancement - buy less bonds
- Yield curve enhancement - Overweight (underweight), maturities deemed undervalued (overvalued)
- Issue selection enhancement - Overweight bond issues which look better value.
Positive butterfly twist?
What is an increasing butterfly spread?
Positive butterfly twist? Short and long yields go up. Mid yield goes down
What is an increasing butterfly spread? Where medium term yields rise relative to short term yields.
High or low convexity bonds perform better during increased volatilty?
Bonds with higher convexity outperform bonds with lower convexity in periods of high interest rate volatility.
Barbells provide better protection from yield curve shifts and twists as they have higher convexity.
Repo carry trade
Borrow at cheaper short term rates to invest at long term rates.
Receive fixed, pay floating affect on duration?
Receive Fixed INCREASE duration.
Higher convexity bonds Barbell,Bullet, Ladder?
Portfolio value effects can be most easily reduced from non parallel shifts in yield curve by increasing or decreasing convexity?
Higher convexity = means higher duration change when yields change. Preferred when immunizing multiple liabilities. Barbell highest convexity with most protection of yield curve twists and shifts.
Portfolio effects can be minimized with non-parallel shifts in yield curve by minimizing convexity. Higher convexity fall less when yields rise and rise more when yields fall.
NONPARALOWCONVEX
Payer Swaption =
Receiver Swaption =
Swaptions collar =
Payer Swaption = Pay fixed swap. More valuable as rates rise which decreases duration and convexity. Decreases duration and convexity.
Receiver Swaption = Right to receive fixed-rate swap. Increases duration and convexity. Upfront prmeium paid.
Swaption collar = A long receiver swaption and write a payer swaption (zero cost swaption)
Key rate duration
Measures aggregate sensitivity of a portfolio to movement in key maturity rates while others remain constant. Identifies where portfolios has the most sensitivity and exposure to non-parrallel shifts in yield curve slope/curvature.
Change in portfolio value / (Portfolio value x change in Key rate)
Covered Interest rate parity
Higher interest rate will be at a forward rate DISCOUNT.
Eur interest at 1%, USD interest at 3%.
Sell EUR at a 2% premium
Buy USD at a 2% discount
When does a barbell perform best on a yield curve strategy?
Convexity highest to lowest?
Barbell
Bullet
Laddered (Benefits include?)
Barbells perform best on a flattening yield curve.
Bullet - Lowest convexity (Highest reinvestment risk)
Barbell - Highest convexity (Lowest reinvestment risk)
Laddered - High convexity but less than a bullet. Protects most against yield curve twists and shifts compared to both others. Favourable in stable yield curve upward sloping environments where short dated bonds are replaced with higher yielding longer dated bonds. Preferable from a liquidity perspective.
Higher convexity benefits more from interest rate changes
Check errata
How to decrease convexity when yield curve is expected to be stable?
How to add convexity with options?
increase duration with options?
decrease duration
Buy MBS,
Sell Calls
Sell Puts
Add convexity by buying calls and buying puts.
Increase duration = Buy calls, Sell puts
Decrease duration = Sell Calls, Buy Puts
i-spread
Asset swap spread
z-spread
option adjsuted spread =
i spread =
i-spread = YTM - interpolated swap fixed rate
Asset swap spread = Coupon - i-spread
z-spread = when used discounts a bond above a risk free rate to a current Market Value. Roughly a CDS spread. credit exposure vs SPOT curve
option adjusted spread = remove the impact of options on an interest rate tree. credit exposure vs YTM curve.
I-spread = swap rates
VaR
Paramentric Method (positives and negatives)
Historical Simulation (positives and negatives)
VaR = minimum loss with specified probability. $7m at 1% daily VaR means there is a 1% chance a portoflio will lose AT LEAST $7m on any given day.
Paramentric Method = uses parameters such as mean and SD. + Easy to apply, - ignores normal distribution
Historical Simulation = Movements (historically) of key risk factors such as rates/spreads. + can use non-normal returns. - Historical data is not a guide to future performance.
Conditional VaR
Incremental VaR
Relative VaR
Conditional VaR = A measure of average loss in the tail
Incremental VaR = Change in VaR from adding or removing a position in a portfolio
Relative VaR = VaR of a portfolio relative to a benchmark. tested by switching out a position.
EM considerations
Institutional considerations
Economic profile
Exchange rate regime
Institutional considerations = Enforcement of property rights, contract law, level of political stability + ESG factors.
Economic profile = Tax revenues from economic activity plus level of debt. Annual deficit as a % of GDP.
Exchange rate regime = Fixed FX regimes limit the effectiveness of monetary policy. Higher foreign debt to GDP implies more stress.
Three major fixed income Analystical tools.
Inputs
User defined Parameters
Outputs
Inputs = includes position, market data (yields/FX) credit and ESG ratings.
User defined Parameters = Model for term structure (VaR), scenario analysis. Time horizon for investor.
Outputs = Summary of portfolio positions, risk exposures vs benchmark, position selection and portfolio construction tools.
MBS type of options
MBS have inherent call options from early repayment of mortgages. They become more valuable when interest rate volatility DECREASES due to borrowers extending mortgages during periods of stress known as extension risk.
Analytical duration for LOW quality securities vs Emperical duration
Analytical duration is found from general inputs.
Emperical data is regressed against historical data and may highlight how flight to safety will cause high yield and IG bonds to behave differently than expected in certain scenarios.
Analytical duration is HIGHER than Empirical duration for LOW quality securities A > E LOW(HY)
Macaulay duration
Modified Duration
Effective duration
Weighted average time to receive cash flows, where weights are the present value of the cash flows. At that point price risk and reinvestment risk cancel eachother out regardless of shifts in the yield curve..
MD = Macaulay duration divided by one plus the periodic yield of the bond Macaulay duration divided by one plus the periodic yield of the bond. Approximate expected percentage change in bond price for a 1% change in yield. For example, a bond with a modified duration of 7 is expected to fall by approximately 7% when yields rise by 1%.
ED = Sensitivity of a bond’s price to a parallel shift change in a benchmark yield curve. Effective duration is used for complex bonds where cash flows are not certain and may be contingent on interest rate changes, such as bonds with embedded options.
Money Duration
Price value of a basis point (PVBP)
Money Duration = modified duration × market value.
A measure of the monetary gain or loss expected due to a 1% change in yield, which is calculated as
Price value of a basis point (PVBP) = Money duration × 0.0001 It measures the absolute change in portfolio value (in currency terms) when yields change by 1 basis point
Laddered vs direct bond portfolio. Effect of convexity.
With a laddered portfolio, the investor is diversified between price and reinvestment risk. The more distributed cash flows of the ladder compared to the bullet will provide greater convexity benefiting performance for large changes in rates
Pure Indexing
Enhanced Indexing
Active Management
Pure Indexing - Low turnover, no devation from benchmark. No outperformance.
Enhanced Indexing - Slightly higher turnover, modest outperformance 20-30bps tracking error less than 50bps.
Active Management - Much higher turnover, higher outperformance.
Dispersion
Measures the ‘variance of time’ to receive cash flows from fixed-income securities.
Highest liquidity bond
Lowest liqudity bond
Highest = recently issued on the run sovereign
Lowest = lower credit quality corporates issued further back in time.
Carry trade can be achieved with long off the run, short on the run. (Off the run = secondary issue)
Note - lower credit quality will demand a liquidity premium
Methods to add leverage to fixed income.
Difference between the main ones?
- Repos (sale of treasuries) and repurchase
- Securities lending (lower quality veriosn of repos). Sale of bonds and repurchase. They are open ended and callable any time.
- Swap agreements
- Futures contracts
- Structured finance agreements.
How to increase duration when bullish.
Swap
Futures
Repo
Swap - Receive fixed, pay floating
Futures - Buy a long futures contract
Repo - Buy a repo
Bond A Overvalued with £1m gain
Bond B Undervalued with £1m loss
Taxable and Tax exempt investor sells which?
Taxable investor sells bond B for Tax Loss Harvesting
Tax exempt investor sells Bond A which is deemed over valued.
Liability type I
Liability type II
Liability type III
Liability type IV
Liability type I Known Amount of cash outlay Known Timing of cash outlay = Government bonds
Liability type II Known Amount of cash outlay Uncertain Timing of cash outlay = Government bonds = Demand and time deposits as depositor can redeem prior to maturity. Callable and Putable bonds
Liability type III Uncertain Amount of cash outlay Known Timing of cash outlay. FRNs and Inflation protected securities.
Liability type IV Uncertain Amount of cash outlay Uncertain Timing of cash outlay = Uncertain Timing of cash outlay = Contingent convertibles and Residential mortgages due to call option by home owner. Property and casualty insurers.
How to mitigate the risk of non-parralell shifts in yield curve?
A cashflow matching strategy will mitigate the risk of non-parallel shifts in yield curve. Errors associated with interest rate changes may adversely affect the bond portfolio. Parallel shifts in yield curve is a sufficient but not a necessary condition to achieve the desired outcome.
Difference between Accumulated Benefit Obligation and Projected Benefit Obligation for Liability driven investing of DB pension schemes.
ABO is based on current wages. Legal liability today if a plan were to be closed or transferred to another type. ABo =Always Lower ABO.
DBO is based on expected future earnings and is always higher than ABO
Nf = BPVL - BPVA / BPVctd
When do you overhedge?
When do you underhedge?
Given rising or falling yields
Under hedge when yields are expected to rise if you are long futures (BPVliabilities more than BPVassets)
Over hedge when yields are expected to fall If you are long futures
Under hedge when yields are expected to fall if you are short futures (BPVliabilities less than BPVassets)
Over hedge when yields are expected to rise If you are short futures
Model risk
Spread risk
Counterparty credit risk
Model risk arises when many approximations are used to measure key paramenters ie the CTD bond value could change. Assumptions are made such as future events and approximations ie yield curve shifts will be parallel, bond quality willl remain the same and no use of derivatives. Minimized with a flat yield curve or cash flows concentrated on flat section of the yield curve
Spread risk is apparent in derivatives overlay of LDI strategies. Comparing corporate bonds with hedging by using a 10 year treasury used in the CTD formula creates risk that spreads will change differently. Oddly corporate bond yields are more stable than treasuries due to liquidity.
Counterparty credit risk is a concern faced by interest rate swaps if they are uncollateralized. Credit Support Annex requires collateral. It can be managed by careful consideration of the derivative chosen. (collateralized preferred).
Synthetic Fixed Income Strategies. Total return swaps. Cost and availability?
Use of derivatives to create an index is usually lower cost than full replication. Derivatives are OTC for access to less liquid developing markets and high yield. Useful for smaller portfolios, less inital outflow than mutual funds but brings in counter party risk.
Index requirements
Which index is less suseptible to low credit quality? Value or equal weighted indexes?
Clear transparent rules
Daily valuation
Availability of past returns and turnover
Value weighted indices will overweight more indebted companies debt. An equal weighted index should be chosen.
Which duration minimizes tracking error due to
a) parallel shifts in yield curve
b) non parallel shifts in yield curve
a) parallel shifts in yield curve - Matching modified duration minimizes tracking error due to parallel shifts in the yield curve.
b) non parallel shifts in yield curve - Matching key rate durations minimizes tracking error due to nonparallel twists in the yield curve.
Z DM vs DM vs QM For recovery or downturn?
FRN FV greater than PV discount or premium?
Z DM > DM > QM in a Downturn FRN is at a discount.
Z DM less than DM in a recovery.
FRN FV greater than PV shows it is trading at a discount.
