Session 7 - Fixed Income (I) Flashcards
Inflation protection on Inflation-linked bond
- both principal and coupons are protected from inflation
Inflation protection on Floating-coupon bonds
- only coupons are protected from inflation
Inflation protection on Fixed-coupon bonds
- principal and coupons are not protected from inflation
Cash flow matching
- have an asset that matures with the same amount and at the time the liability is due
- no need for reinvestment
- difficult to do/find in real life
- defaults & optionality (explicit & implicit) will create mismatches
- only rebalance (not required) to lower costs
Duration Matching
- match the duration AND the present value of the asset and liabilities so they both fluctuate by the same amount with interest rate changes
- protects only against parallel shifts in the yield curve
- only immunized for a period of time as yields and market conditions change, need to be rebalanced
- defaults & credit downgrades cause issues
Contingent immunization
- hybrid of immunization and active management
- MVA – MVL = surplus
- the PM can pursue active investment strategies, as if operating under a total return mandate, as long as the surplus is above a designated threshold
- if performance is poor & surplus evaporates, mandate reverts
to a purely passive strategy
Role of Fixed Income
- diversification benefits - low correlation with equities
- generally less volatile than any other major asset classes
- benefits of regular cash flows - better planning to meet future liabilities
- inflation hedging potential
Liability-Based Mandates
- managed to match or cover expected liability payments with future projected cash inflows (structured mandates, asset/liability management - ALM, liability-driven investments - LDI)
- banks, pensions, insurance
4 types of Liability-Based Mandates
- Cash-flow matching
- Duration Matching
- Contingent immunization
- Horizon matching
Horizon matching
- combines cash-flow & duration matching
- ST liabilities are covered by CF matching while LT
- liabilities are covered by duration matching
3 Types of Total Return Mandates
- Pure indexing
- Enhanced indexing
- Active Management
Pure indexing
- attempts to replicate a bond index as closely as possible (target RA & 𝝈𝑹𝑨 are both zero)
- rebalance the same as the index
- full replication approach ⇒ produce a portfolio that is a perfect match to the index (very difficult & costly)
- many issues are illiquid/infrequently traded
- sampling approach ⇒ select a sample of issues while matching risk factor exposures of the benchmark (duration, credit/sector/call/prepayment risk)
Enhanced Indexing
– attempts to match the benchmark’s Primary risk factors and generate modest outperformance
- allows for minor risk factor mismatches (target 𝝈𝑹𝑨 < 50 bps/yr.)
Active Management
– allows for larger risk factor mismatches relative to the benchmark, most notably duration
- highest portfolio turnover, highest fees
Bond Market Specific Liquidity
- most bonds have less active secondary markets (vs. equities) (many do not trade on a given day)
- bonds are very heterogeneous
- bond markets are typically OTC dealer markets (search cost, price discovery)
- liquidity is highest right after issuance (supply not yet bought up by buy-and-hold investors)
- liquidity affects bond yields – illiquidity premiums
- compensate for exit costs prior to maturity
- premium depends on the issuer, issue size, date of maturity
Liquidity among Bond Market Subsectors
- subsectors can be categorized by issuer type, credit quality, issue size, maturity
- issuers: - sovereign government bonds, non-sovereign gov’t. bonds, gov’t. related bonds, corporate bonds (a.k.a. credits) - securitized bonds
Sovereigns vs. Corporates Bond Market Subsectors
- Sovereigns/ – typically more liquid, larger issuance size, use as benchmark bonds, acceptance as collateral in the repo market, well-recognized issuers
- high credit quality issuers more liquid than lower credit quality issuers
- Corporates/ many more issuers, smaller issue size, a wide range of credit quality (IG → HY)
- low credit quality issues, may be difficult to even find a dealer with inventory (or even willing to take them into inventory)
- small issues typically excluded from bond indexes with minimum issue size requirements
- liquidity varies across other dimensions (issue size, maturity)
Effects of Liquidity on Fixed-Income Port. Mgmt./
1) Pricing – many issues may have stale prices or prices that are often estimated (recent transaction prices may not be valid) so matrix pricing can be used
2) Portfolio Construction
- trade-off between yield & liquidity
- buy-and-hold investor will prefer illiquid bonds for the higher yield (illiquidity premium)(longer maturities, small issues, private placements)
- illiquid bonds will also have wider bid-ask spreads (dealer risk – likely to remain in inventory longer)
3) Alternatives to Direct Investment in Bonds
- fixed-income derivatives are often more liquid than
their underlying bonds (futures, options on futures, interest rate swaps, credit default swaps)
- fixed-income ETFs & mutual funds
Yield Income
coupon payments + reinvestment income (current yield)
Rolldown Yield
⇒ change in price by the passage of time (pulled to par)
– amortization of premium/discount
- assumes an unchanging yield curve
Rolling yield
Yield income + Rolldown Return
E(credit losses)
= PD × LGD (prob. of def. × loss given def.)
Leverage formula
[𝒓𝑰𝑽𝑬 + 𝑽𝑩(𝒓𝑰 − 𝒓𝑩)] / 𝑽𝑬
Methods of Leverage
1) Futures Contract
2) Swap Agreements
3) Structured Financial Instruments - inverse floaters
4) Repurchase Agreements
5) Securities lending
Repurchase Agreements
- a sale & a repurchase (basically a collateralized loan)
- difference between the sale & repurchase price called the repo rate (= interest)
- typically overnight → few days (maybe longer)
- repo may be:
– cash-driven – borrow cash to buy assets
– security-driven – borrow particular securities - protection against default provided by collateral
high quality → 97% - 99% borrowing capacity – called the ‘haircut’ - lower quality/higher volatility → lower capacity
Securities lending
– like repos, except that cash is required as collateral (or high-quality bonds)
- when bonds are used as collateral, income earned flows back to borrower Rebate rate = coupon – lending rate
– if the borrowed securities are difficult to borrow, the lending rate may be greater than the coupon
income of collateral
- typically open-ended agreements
Risks of Leverage
– magnified losses, higher risk, forced liquidations
Equity Duration Formula
(𝑫𝑨𝑨 − 𝑫𝑳𝑳) / E
Difference between Type 2 and Type 3 Liabilities
Type 2 - Cash Flow is known, timing not known (life insurance payout)
Type 3 - Cash Flow unknown, timing is known (floating rate annuity payout)
Immunization - Single Liability
- construct a portfolio that minimizes the variance in the realized rate of return
- matching a future liability with an equal term zero-coupon bond settles it (no risk ~ cash flow matching)
- if we must deal with bonds with incoming cash flows,
we have price and Re-investment Risk exposure
1. set duration of portfolio = investment horizon
(minimum condition) (or Liability duration)
2. initial PV of portfolio CFs ≥ PV of future liability
3. Portfolio Convexity is minimized
For something to be immunized means…
- price risk & reinvestment risk are offset which is achieved through mgmt. of duration
- immunization is essentially an interest rate hedging strategy
- market yield will fluctuate over the investment horizon
- portfolio duration will change as both market yields change and time passes
- as time passes, the portfolio must be rebalanced so that its duration (not avg) is readjusted to the duration of the liability
- essentially a ‘zero-replication’ strategy
i. e. immunizing with coupon paying bonds entails continuously matching the portfolio MacDur with the MacDur of a zero over time as the yield curve shifts
Zero-Coupon Bond Immunization Strategy
- no risk immunization strategy
- Zero variance in ROR
- variance results from the volatility of future interest rates
Bullet portfolio Immunization Strategy
– portfolio CFs concentrated around the horizon date
- low variance in ROR
- variance results from the volatility of future interest rates
Barbell Portfolio Immunization Strategy
– portfolio’s CFs dispersed
- High variance in ROR
- variance results from the volatility of future interest rates
Structural Risk
– risk that yield curve twists and non-parallel shifts cause MacDurp ≠ MacDurz (or L)
- reduced by minimizing the dispersion of the bond positions - min. dispersion is the same as min. Convexity
Cash Flow Matching for Multiple Liabilities
- can improve the company’s credit rating (dedicated assets reduce liability risk)
- may be able to use ‘accounting defeasance’ – ability to remove both the asset & liability from the B.S.
- cash-in-advance constraint ⇒ bonds are not sold to meet obligations, they mature ⇒ maturity timing mismatches mean funds must be available before each liability pmt.
- may lead to large cash holdings
Duration Matching for Multiple Liabilities
1) PVassets ≥ PVliabilities
2) Dollar Duration of portfolio = DDL
3) distribution of individual portfolio assets must have a wider range than the distribution of the liabilities (higher dispersion, ∴ higher convexity)
i.e. must have an asset with ModDur ≤ shortest-duration liability & an asset with ModDur ≥ longest-duration liability
but: wider the range, more reinvestment risk
- DDp will drift from DDL – twists & non-parallel
shifts in the yield curve
- must balance transaction costs against duration drift
Why for equal durations, a more convex portfolio outperforms a less convex portfolio
higher gains if yields fall, lower losses if yields rise
Derivatives Overlay for Multiple Liabilities
- long an interest rate futures contract increases a portfolio’s sensitivity to interest rates (increase duration) - short → decreases sensitivity (decrease duration)
- traded on both short-term (T-Bills, Eurodollars) and long-term (Treasury Notes, Bonds)
- duration of the futures contract is the duration of the CTD
CTD – cheapest-to-deliver
→ the seller determines which actual bond to deliver
Conversion Factor
- based on the price a deliverable bond would sell for at the beginning of the delivery month if it were to yield 6%
Number of future contracts needed to hedge (Nf) Formula
𝑵𝒇 = 𝑩𝑷𝑽𝑳 − 𝑩𝑷𝑽𝑨/ 𝑩𝑷𝑽𝑭
𝑩𝑷𝑽𝑨 + 𝑵𝒇𝑩𝑷𝑽𝑭 = 𝑩𝑷𝑽𝑳
𝑩𝑷𝑽𝑳 = 𝑫𝑫𝑳 ×. 𝟎𝟎𝟎𝟏
𝑩𝑷𝑽𝑭 Formula
𝑩𝑷𝑽𝑪𝑻𝑫/𝑪𝑭𝑪𝑻𝑫
≈ (𝑫𝑪𝑻𝑫𝑽𝑪𝑻𝑫 ×. 𝟎𝟎𝟎𝟏) / 𝑪𝑭𝑪𝑻𝑫
Interest Rate Swaps
- pay floating, receive fixed ~ long a fixed + short a
- adding a swap (pay fl., rec. fx.) increases BPVA ~ BPVfix
𝑩𝑷𝑽𝒔𝒘𝒂𝒑 = 𝑩𝑷𝑽𝒇𝒊𝒙 − 𝑩𝑷𝑽𝒇𝒍𝒐𝒂𝒕
− 𝑩𝑷𝑽𝒇𝒊𝒙 mainly determines 𝑩𝑷𝑽𝒔𝒘𝒂𝒑 since 𝑩𝑷𝑽𝒇𝒍𝒐𝒂𝒕 is typically small - pay fixed, receive floating ~ long a floating + short a fixed
- adding a swap (pay fx., rec. fl.) decreases BPVA ~ BPVfix
𝑩𝑷𝑽𝒔𝒘𝒂𝒑 = 𝑩𝑷𝑽𝒇𝒍𝒐𝒂𝒕 − 𝑩𝑷𝑽𝒇𝒊𝒙
Interest Rate Options/Swaption
a) receiver swaption pay fl.rate, receive fixed
- pay premium (known cost)
-exercise if fixed swap rate is below exercise rate
b) payer swaption– pay fx. - receive fl.
- receive a premium ( not known)
- when the receiver and payer combined = swaption
collar
Interest rate anticipation strategies - Rates expected to decrease
- receive fixed, enter the receiver swaption
- increase duration
- buy future contracts
- long interest rate options
- if BPVA > BPVL – do nothing
Interest rate anticipation strategies - Rates expected to increase
- pay fixed, enter the payer swaption
- decrease duration
- short future contracts
- short interest rate options
- if BPVA < BPVL – do nothing
Hedge Ratio
– the extent of interest rate risk management
- 0% – no hedging 100% – full hedging
- partial hedge – between 0% - 100%
𝑩𝑷𝑽𝑨 × 𝚫𝒚𝒊𝒆𝒍𝒅𝒔𝑨 + 𝑩𝑷𝑽𝑯 × 𝚫𝒚𝒊𝒆𝒍𝒅𝒔𝑯 ≈ 𝑩𝑷𝑽𝑳 × 𝚫𝒚𝒊𝒆𝒍𝒅𝒔𝑳
Model Risk
– whenever assumptions are made about future events
& approximations are used to measure key parameters
(BPVA, BPVL)
Measurement error
– approximating portfolio duration using the weighted average of the individual durations of the component bonds instead of the cash flow yield (BPVA)
- also, BPVH ⇒ an approximation is used (𝑩𝑷𝑽𝑪𝑻𝑫/𝑪𝑭)
The implicit assumption that Δyields are equal for A, H & L
- source of risk if assets, derivatives and liabilities are positioned at varying points along the curve and at varying spreads
(𝜟yield for A & L refer to various classes of corporate bonds) L = IG, A may have HY
Spread risk
– underlying of BPVH are Treasuries, BPVL are typically corporate obligations (𝝆HL < 1)
(IG corporate yields less volatile than Treasuries)
- less volatility in the corporate/swap spread than the corporate/Treasury spread
Counterparty credit risk
when not collateralized
Collateralization risk
– the risk that available collateral becomes exhausted
Benchmarking to a Bond Index
- no specific rate of return (ROR) is guaranteed
- objective: relative performance (match/exceed ROR of the benchmark)
- known as investing on a benchmark relative basis
• lower fees, greater diversification, avoiding the downside risk of active mgmt.
Challenges of Benchmarking in the Bond Market
1) fixed income markets are much larger & broader
- # of outstanding securities much larger
- much more heterogeneous
2) fixed income is a dealer market
- most bonds have a less active secondary market
- many do not trade on a given day
- stale prices or prices that are estimated using matrix pricing (creates variation between portfolios and the index)
3) limited size of many issues – often completely
owned by buy-and-hold investors
4) index composition tends to change frequently – maturities, callability, new issues
- typically recreated monthly ⇒ as composition changes, risk profiles may change
6 Risk Factors (primary)
1/ portfolio modified adjusted duration – EffDur.
- option-adjusted duration, convexity
2/ key rate duration - captures the effect of shifts at key points on the yield curve
- matching key rate Dur. instead of only EffDur. will reduce tracking risk
3/ sector and quality percent - match the %’ age weight in the various sectors & qualities of the index
(further away, greater the tracking risk)
4/ sector and quality spread duration - match the sector & quality duration exposure
5/ sector/coupon/maturity cell weights – match the optionality exposure of sectors
6/ issuer exposure – match the issuer-event risk
Passive Approach
- assumes bond market expectations are correct, so set the portfolio’s risk profile identical to the benchmark index’s risk profile
Strategies of Passive Approach
1/ pure bond indexing (full replication) 2/ enhanced indexing (sampling) 3/ fixed-income mutual funds 4/ ETFs - greater liquidity vs. MF 5/ Total return swap (OTC) - exchange of CFs between 2 parties
Pure bond indexing (full replication) Strategy
- produce a portfolio that is a perfect match to
the index (own all the bonds in the same %’age as the index) - very difficult & costly (many issues are illiquid/infrequently traded, esp. non-Treasuries) - full replication rarely attempted in fixed-income
Enhanced indexing (sampling)
– attempt to match the Primary risk factors and reach a higher return versus full replication
- done by stratified sampling
- reduces construction & maintenance costs
- larger tracking error vs. full replication
Enhanced indexing strategies
1/ lower cost enhancements 2/ issue selection enhancements 3/ yield curve enhancements 4/ sector/quality enhancements 5/ call exposure enhancements
Fixed-income mutual funds/
- lower investment requirement without sacrificing diversification
- redemption at NAV rather than a need to sell positions
Total return swap (OTC)
- smaller initial outlay
- lower swap bid-ask spreads
- total return receiver pays LIBOR + spread and depreciation of the index
- total return payer pays Index CFs+ Appreciation
Qualities of an index:
1) Unambiguous – the identities & weights of the benchmark components are clearly defined (clear, transparent rules for security inclusion and weighting)
2) Investable
3) Measurable – benchmark returns are readily calculable on a reasonably frequent basis
- bond index risk characteristics will reflect bond issuers preferences
- cap-weighted bond indices give more weight to issuers that borrow the most (the bums)
- maybe more likely to be downgraded in the future and experience lower returns
Laddered Bond Portfolios
- better protection from shifts/twists in the yield curve
- cash flows diversified across time
- balances cash flow reinvestment & market price risk
- similar to dollar-cost averaging
- bonds mature each year and are reinvested at the longer end of
the ladder (portfolio duration is constant) - liquidity – always a bond that is
close to redemption – low duration, stable price
Lower cost enhancements (one of Enhanced indexing strategy)
- tight controls on trading costs and management fees (limit # of securities chosen)
Issue selection enhancements (one of Enhanced indexing strategy)
- identify & select undervalued securities, select ‘possible credit upgrade’ issues, avoid ‘possible credit downgrade’ issues
Yield curve enhancements (one of Enhanced indexing strategy)
- overweight the undervalued areas of the curve, underweight the overvalued areas
Sector/quality enhancements (one of Enhanced indexing strategy)
- periodic over/underweighting of sectors/qualities across the business cycle
e. g. overweight Treasuries when spreads are expected to widen
Call exposure enhancements (one of Enhanced indexing strategy)
- underweight callable bonds if rates are expected to drop
e. g./ a drop in rates may cause a callable bond to shift from being priced on a YTM basis to a yield-to-call basis (negative convexity)
