Session 7 - Fixed Income (I) Flashcards

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1
Q

Inflation protection on Inflation-linked bond

A
  • both principal and coupons are protected from inflation
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2
Q

Inflation protection on Floating-coupon bonds

A
  • only coupons are protected from inflation
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3
Q

Inflation protection on Fixed-coupon bonds

A
  • principal and coupons are not protected from inflation
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4
Q

Cash flow matching

A
  • 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
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5
Q

Duration Matching

A
  • 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
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6
Q

Contingent immunization

A
  • 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
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7
Q

Role of Fixed Income

A
  • 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
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8
Q

Liability-Based Mandates

A
  • 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
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9
Q

4 types of Liability-Based Mandates

A
  1. Cash-flow matching
  2. Duration Matching
  3. Contingent immunization
  4. Horizon matching
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10
Q

Horizon matching

A
  • combines cash-flow & duration matching
    • ST liabilities are covered by CF matching while LT
  • liabilities are covered by duration matching
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11
Q

3 Types of Total Return Mandates

A
  1. Pure indexing
  2. Enhanced indexing
  3. Active Management
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12
Q

Pure indexing

A
  • 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)
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13
Q

Enhanced Indexing

A

– attempts to match the benchmark’s Primary risk factors and generate modest outperformance
- allows for minor risk factor mismatches (target 𝝈𝑹𝑨 < 50 bps/yr.)

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14
Q

Active Management

A

– allows for larger risk factor mismatches relative to the benchmark, most notably duration
- highest portfolio turnover, highest fees

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15
Q

Bond Market Specific Liquidity

A
  • 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
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16
Q

Liquidity among Bond Market Subsectors

A
  • 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
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17
Q

Sovereigns vs. Corporates Bond Market Subsectors

A
  • 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)
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18
Q

Effects of Liquidity on Fixed-Income Port. Mgmt./

A

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

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19
Q

Yield Income

A

coupon payments + reinvestment income (current yield)

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20
Q

Rolldown Yield

A

⇒ change in price by the passage of time (pulled to par)
– amortization of premium/discount
- assumes an unchanging yield curve

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21
Q

Rolling yield

A

Yield income + Rolldown Return

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22
Q

E(credit losses)

A

= PD × LGD (prob. of def. × loss given def.)

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23
Q

Leverage formula

A

[𝒓𝑰𝑽𝑬 + 𝑽𝑩(𝒓𝑰 − 𝒓𝑩)] / 𝑽𝑬

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24
Q

Methods of Leverage

A

1) Futures Contract
2) Swap Agreements
3) Structured Financial Instruments - inverse floaters
4) Repurchase Agreements
5) Securities lending

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25
Q

Repurchase Agreements

A
  • 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
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26
Q

Securities lending

A

– 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

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27
Q

Risks of Leverage

A

– magnified losses, higher risk, forced liquidations

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28
Q

Equity Duration Formula

A

(𝑫𝑨𝑨 − 𝑫𝑳𝑳) / E

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29
Q

Difference between Type 2 and Type 3 Liabilities

A

Type 2 - Cash Flow is known, timing not known (life insurance payout)
Type 3 - Cash Flow unknown, timing is known (floating rate annuity payout)

30
Q

Immunization - Single Liability

A
  • 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
31
Q

For something to be immunized means…

A
  • 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
32
Q

Zero-Coupon Bond Immunization Strategy

A
  • no risk immunization strategy
  • Zero variance in ROR
  • variance results from the volatility of future interest rates
33
Q

Bullet portfolio Immunization Strategy

A

– portfolio CFs concentrated around the horizon date

  • low variance in ROR
  • variance results from the volatility of future interest rates
34
Q

Barbell Portfolio Immunization Strategy

A

– portfolio’s CFs dispersed

  • High variance in ROR
  • variance results from the volatility of future interest rates
35
Q

Structural Risk

A

– 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

36
Q

Cash Flow Matching for Multiple Liabilities

A
  • 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
37
Q

Duration Matching for Multiple Liabilities

A

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

38
Q

Why for equal durations, a more convex portfolio outperforms a less convex portfolio

A

higher gains if yields fall, lower losses if yields rise

39
Q

Derivatives Overlay for Multiple Liabilities

A
  • 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
40
Q

CTD – cheapest-to-deliver

A

→ the seller determines which actual bond to deliver

41
Q

Conversion Factor

A
  • based on the price a deliverable bond would sell for at the beginning of the delivery month if it were to yield 6%
42
Q

Number of future contracts needed to hedge (Nf) Formula

A

𝑵𝒇 = 𝑩𝑷𝑽𝑳 − 𝑩𝑷𝑽𝑨/ 𝑩𝑷𝑽𝑭
𝑩𝑷𝑽𝑨 + 𝑵𝒇𝑩𝑷𝑽𝑭 = 𝑩𝑷𝑽𝑳
𝑩𝑷𝑽𝑳 = 𝑫𝑫𝑳 ×. 𝟎𝟎𝟎𝟏

43
Q

𝑩𝑷𝑽𝑭 Formula

A

𝑩𝑷𝑽𝑪𝑻𝑫/𝑪𝑭𝑪𝑻𝑫

≈ (𝑫𝑪𝑻𝑫𝑽𝑪𝑻𝑫 ×. 𝟎𝟎𝟎𝟏) / 𝑪𝑭𝑪𝑻𝑫

44
Q

Interest Rate Swaps

A
  1. 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
  2. pay fixed, receive floating ~ long a floating + short a fixed
    - adding a swap (pay fx., rec. fl.) decreases BPVA ~ BPVfix
    𝑩𝑷𝑽𝒔𝒘𝒂𝒑 = 𝑩𝑷𝑽𝒇𝒍𝒐𝒂𝒕 − 𝑩𝑷𝑽𝒇𝒊𝒙
45
Q

Interest Rate Options/Swaption

A

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

46
Q

Interest rate anticipation strategies - Rates expected to decrease

A
  • receive fixed, enter the receiver swaption
  • increase duration
  • buy future contracts
  • long interest rate options
  • if BPVA > BPVL – do nothing
47
Q

Interest rate anticipation strategies - Rates expected to increase

A
  • pay fixed, enter the payer swaption
  • decrease duration
  • short future contracts
  • short interest rate options
  • if BPVA < BPVL – do nothing
48
Q

Hedge Ratio

A

– the extent of interest rate risk management
- 0% – no hedging 100% – full hedging
- partial hedge – between 0% - 100%
𝑩𝑷𝑽𝑨 × 𝚫𝒚𝒊𝒆𝒍𝒅𝒔𝑨 + 𝑩𝑷𝑽𝑯 × 𝚫𝒚𝒊𝒆𝒍𝒅𝒔𝑯 ≈ 𝑩𝑷𝑽𝑳 × 𝚫𝒚𝒊𝒆𝒍𝒅𝒔𝑳

49
Q

Model Risk

A

– whenever assumptions are made about future events
& approximations are used to measure key parameters
(BPVA, BPVL)

50
Q

Measurement error

A

– 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)

51
Q

The implicit assumption that Δyields are equal for A, H & L

A
  • 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
52
Q

Spread risk

A

– 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

53
Q

Counterparty credit risk

A

when not collateralized

54
Q

Collateralization risk

A

– the risk that available collateral becomes exhausted

55
Q

Benchmarking to a Bond Index

A
  • 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.
56
Q

Challenges of Benchmarking in the Bond Market

A

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

57
Q

6 Risk Factors (primary)

A

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

58
Q

Passive Approach

A
  • assumes bond market expectations are correct, so set the portfolio’s risk profile identical to the benchmark index’s risk profile
59
Q

Strategies of Passive Approach

A
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
60
Q

Pure bond indexing (full replication) Strategy

A
  • 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
61
Q

Enhanced indexing (sampling)

A

– 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
62
Q

Enhanced indexing strategies

A
1/ lower cost enhancements 
2/ issue selection enhancements
3/ yield curve enhancements 
4/ sector/quality enhancements
5/ call exposure enhancements
63
Q

Fixed-income mutual funds/

A
  • lower investment requirement without sacrificing diversification
  • redemption at NAV rather than a need to sell positions
64
Q

Total return swap (OTC)

A
  • 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
65
Q

Qualities of an index:

A

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

66
Q

Laddered Bond Portfolios

A
  • 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
67
Q

Lower cost enhancements (one of Enhanced indexing strategy)

A
  • tight controls on trading costs and management fees (limit # of securities chosen)
68
Q

Issue selection enhancements (one of Enhanced indexing strategy)

A
  • identify & select undervalued securities, select ‘possible credit upgrade’ issues, avoid ‘possible credit downgrade’ issues
69
Q

Yield curve enhancements (one of Enhanced indexing strategy)

A
  • overweight the undervalued areas of the curve, underweight the overvalued areas
70
Q

Sector/quality enhancements (one of Enhanced indexing strategy)

A
  • periodic over/underweighting of sectors/qualities across the business cycle
    e. g. overweight Treasuries when spreads are expected to widen
71
Q

Call exposure enhancements (one of Enhanced indexing strategy)

A
  • 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)