FI 18-21 Flashcards
diversification benefit of FI
- Investment grade bond has low correlation with equities, US high yield bond and EM bonds
- less volatile
- correlation between T bond and equity decrease during recession while correlation between junk and equity increase
inflation hedge potential
bond with floating rate coupon protect interest income from inflation
because the reference should adjust for inflation
floating rate bonds only adjust coupon risk
inflation linked bonds
hedge both coupon and principle risk.
include real return + additional component that is tied directly to inflation rate.
std is lower than conventional bonds and equity because it depends on real interest rate.
result in superior risk adjusted real portfolios returns
result in superior mean-efficient frontier.
fixed coupon bond
no protection for either coupon or principle risk
liability based mandates
managed to match to lower exp. liability pmt with future projected cash inflows
structured mandate
ALM
liability driven LDI
liability based mandate approach
- cash flow match
- duration match
lowest initial funding
higher expected return - continent immunization
highest expected return
highest initial funding
(hybrid of cf and duration) - horizon matching
(hybrid of cf and nearer-term and duration matching LT liability)
low initial funding
less expected return
immunization = zero replication
~ liability BPV * change in liability yields
characteristics of a bond portfolio structured to immunize a single liability are that it
(1) mv(A)>=mv(L)
(2) has a portfolio Macaulay duration that matches the liability’s due date, and
(3) minimizes the portfolio convexity statistic.
process of structuring and managing FI portfolio to minimize the variance in the realized rate of return over a known time horizon
match CF yield
- variance arises from volatility of future interest rate
- immunize the int. rate on a single liability is to buy a zero-coupon bond that futures on the obligation’s due date
par matches the liability amount
imitation:
- may not be enough bonds available to match all liabilities
- protects against only a parallel change in the yield curve
- rebalancing and the need to liquidate position can result in high portfolio turnover
- a potfolio is an immunized portflio only at a given point in time
- need to rebalance makes liquidity consideration important
- assume bond issuer do not default, and do not protect against issuer-or bond-specific interest rate change such credit quality change.
- can accommodate bonds with embedded option to the extend a bond’s duration is replaced by its effective duration as an input to the methodology
duration matching
lowest initial cost
high expected return
require reinvestment risk and price risk to offset.
multiple liability:
matching money duration is useful because the market value and cash flow yield of asset and liabilities are not necessarily equal
interest rate increase, high reinvestment income offset the decrease in bond prices
interest rate decrease, reduce reinvestment income is offset by an increase in a bond prices
- MV(A)>=MV(L)
- BPVa = BPVl
- convexityA > Convexity liabilities
- rebalance required as time and yield change
zero-coupon bond designed to match liability CF
compare duration vs. cf matching
no yield curve assumption
duration:
parallel yield curve shift risk of shortfall in cf is minimized by matching duration and pv of liability steam
cf: bond portfolio cf match liability
basic principle duration:
duration: cf for coupon and principle pmt offset liability cost
cf: coupons, principle of bond portfolio offset liability cf
more complexity than cf matching method
contigent immunization
MOST COSTLY
Highest return
active management requires surplus
v(A) > v(l) a surplus
if asset earn more than initially available immunization rate, the surplus will grow and eventually be returned to the investor
overhedge the duration gap
if yields are expected to fall
and underhedge the duration gap
if yields are expected to rise.
concerns:
vulnerable to liquidity risk
- if surplus declines, assets must be quickly liquidated without further loss and converted to an immunizing portfolio before the surplus become negative
- even if only the surplus amount is active managed, liquidity issues can still be a problem.
- IF short option contracts were used, the downside risk is unlimited for calls an very large for puts. Likewise the potential losses on futures contract are very large and could exceeds the portfolio surplus.
Liquidity is an important consideration in a contingent immunization strategy because positions may need to be unwound as the surplus is eliminated due to losses.
horizon matching
ST liability (4-5 yr) covered by cf matching LT liability covered by a date matching approach
Horizon matching is another hybrid approach, combining cash-flow and duration matching to fund multiple future liabilities. Shorter-term liabilities are cash-flow matched, and longer-term liabilities are duration matched. The horizon matching should cost less than pure cash-flow matching, with minimal additional risk.
total return mandates
pure index
enhanced index active risk <=50bps
active management outperformance >=50bps
bond market liquidity
most recent issued (on the run) DM gov’t bond are likely to be quite liquid.
search cost
liquidity is highest right after insurance
liquidity affects bond yield, require increase yield for invest in iliquid securities
high yield/cost include opportunity cost associate with delays in finding trading counter-parties
bid-ask spread
liquidity premium various depending on issuer, issue size, date of maturity.
bond with higher liquidity
higher credit worthy govt’ issue
greater price transparency
lower search cost
liquidity, search cost, and price transparency are closely related to the type of issuer an its credit quality.
liquidity varies across sub-sectors, categorized by key features, such as issuer type, issue size, credit quality, and maturity.
increase for Sovereign g-bond
high credit
larger size
near-term maturity
effect of liquidity on FI portfolio management
- pricing is less transparent but improving
benefit: not sophisticated
disadvantage: some value relevent features b/w diff bonds maybe ignored
- portfolio construction:
trade off between yield and liquidity
- illiquid bond have higher yield, buy and hold investor prefer high yield over liquidity
- bid-ask spread is affect by the liquidity of dealer’s inventory
Bid is a function of bond’s complexity, liquidity directly increase bid ask spread
alternatives to direct invest in bonds
fixed income derivative on OTC
bond futures, inflation swap, total return swap, credit swap
ETFs inkinds AP & redem
E(R) =
yield income \+roll-down return = roll-down yield \+E(change implied based on invests view of yield and yield spread) -E(credit losses) \+E(currency g/l)
yield income
coupon / current bond price
roll down return
P1/P0-1
E(change in price from view)
(-MD*change in yield)
+1/2(convexity * (change in yield)^2))
used ED for bond with embedded option
Exp credit losses
POD*LGD
Limitation of expected return decomposition
- only downward convexity are used to summarize the price-yield relationship
- assume all intermediate cf are reinvested at YTM
- ignores local richness/cheapess effects
- ignores potential financial advantages to certain maturity segments in the repo market
FI leverage
rp return on levered portfolio
increase return
rp = portfolio return/ portfolio equity
= ri + VB/VE*(ri-rb)
vb Value of borrowed
ri return on investment return
rb cost of borrwing
methods for leveraging FI portfolio
- futures contract
- structured financial instruments
- Repos
- Securities lending
structured financial instruments
designed to repackage and redistribute risks
inverse floating-rate not/floater
coupon has an inverse relationship to LIBOR
REPOs
source of ST financing for FC security dealer
A repurchase agreement (repo) is a form of short-term borrowing for dealers in government securities. In the case of a repo, a dealer sells government securities to investors, usually on an overnight basis, and buys them back the following day at a slightly higher price.
reverse repos: collateralized loans
repo rate = selling price- repurchase price
Dollor interest: principle amount * repo rate * (term of repo in days/360)
cash driven: own bonds & want to borrow cash -tri-party repo
security-driven: lender seeks a particular security for hedging/arbirage/speculation - bilateral report
FI futures contract
leverage futures = notional value / margin -1
interest rate swap long short bond portfolio
Short FI bond: fixed rate payer
long FI bond, floating rate receiver
Duration = D(fixed) - D(floaters) >0 , yield decrease, value increase
securities lending
short sale, borrow securities to sell
- financing/collaterilized borrow, owner lends for cash
rebate rate: collateral range rate - security leading rate
difficult to borrow <0
Risk of leverage
- heavily levered portfolio may incur significant losses
- can lead to forced liquidation
- leverage investor may be forced to reduce their investment exposure at exactly the worst time
FI taxation
- taxes on interest income and capital g/l
- tax is payable on ly on CGt can interest income that have actually been received
realize loss to offset gain from selective tax loss harvest
extend holding period to realized LT capital gain
extend holding period to defer taxes
consider the trade off between capital gain and income for tax purpose
Tax exempt: high yield
taxable investors need also to consider the effects of taxes on both expected and realized net investment returns.
ALM asset liability mgmt
take the assets as a given and manages or adjusts the liabilities in relation to those asset
It is appropriate when both the present value (PV) of the assets and liabilities change with changing interest rates.
liability-drive investing LDI
take the liabilities a given and manages the assets to meet those future liabilities value.
used when there are definable future liability, it’s classified as passive total return
Pension DB Type II liability with known cash flow unknown timing
face longevity risk:
risk employees live longer in their retirement years than assumed in the models
increase PBO and ABO
Time horizon increase, decrease liability
ED= (PV- -PV+)/ (2change in yieldPV0)
Liabiltiy type I
option free fixed rate
KNOWN cash outlay and timing
Measurement error for Asset BPV can arise even in the classic passive immunization strategy for Type I cash flows, which have set amounts and dates.
Liability type ii
callable/putable bonds
known cash outlay
unknown thing of outlay
Liability type iii
fioating rate TIPs
unknown cash outlay
known timing of outlay
liability type IV
property and casualty
DB
UNCERTAIN cash outlay and timing
coupon bearing fixed income bond
upward shift
decrease in bond value offset increase in reinvestment income
downward shift
increase in bond value offset decrease in investment income
investment horizon = Macaulay duration is effectively protected or immunized from int. rate risk and coupon reinvestment effects offset for either higher or lower rates
Macaulay duration
is the weighted average term to maturity of the cash flows from a bond.
more appropriate measure of the time for some immunization techniques
investor inv. horizon < Macaulay duration
price risk dominates over reinvestment risk.
inv. horizon >Macaulay duration
then reinvestment risk dominates over price risk.
modified duration
macaulay duration / (1+R)
more accurate measure of immediate price change
dispersion
weighted variance
convexity
macauley duration^2 + macaulay duration + dispersion
/ (1+ cf yield)^2
inverse with yield
If yields rise, a portfolio of a given duration with higher convexity will experience less of a price decrease than a similar- duration, lower-convexity portfolio.
structural risk
assess with dispersion and convexity
arises from potential shifts and twists to yield curve
- use lowest convexity portfolio to immunize
goal of immunized portfolio
to earth the initial portfolio IRR, not the avg YTD to the bonds
Earning the iRR means the portfolio will grow to a sufficient fv to fund the liability
key assumption: “any ensuring change in the cf yield on bond portfolio is equal to the change in ytm on the zero coupon bond.”
change in CF Yield = change in YTD
characteristic of bond portfolio structured to immunize a single liability:
- mv0 > pv(l)
- macaulay duration matches liability due date
- minimize the convexity statistics
interest rate immunization
mgmt the interest rate of multiple liability
- money duration BPVsA= BPVs L
- convexity A >= Convexity L but lowest
the convexity of the immunizing portfolio should be minimized in order to minimize dispersion and reduce structural risk.
cash flow matching
safest approach
simple:
1. no yield curve assumption required
2. rebalancing not required
3. complexity is low
4. CF of asset align with cf of liability portfolio
eliminate the int rate risk arising from multiple liabilities is to build a dedicated HTM bonds asset portfolio of high-quality FI bonds that as close as possible matches the amount and timing of the scheduled cash outflows
Mitigate risk from non-parallel shift in yield curve
no yield curve assumption
concern: cash-in-advance constraint
securities are not sold to meet obligations, instead sufficient funds must be available on or before each liability pmt date to meet the obligation
Why not use the cash to buy back and retrieve the liability
buyback is difficult and costly to implement if the bonds are widely held by buy-and-hold institutional and retail investors
MONEY DURATION
= modified duration * market value
=MD * MV
BPV
= MD * MV /10,000 = Dollar duration /10,000
duration gap = BPVL-BPVA
Derivative overlay
reduce duration gap
int. rate derivative can be cost-effective method to rebalance the immunizing portfolio to keep it on its target duration as yield curve shift and twists as time pass
buy low int rate futures contract to rebalance most cost efficient
interest rate swap
use to close the duration gap while keep the underlying portfolio unchanged
BPVL= BPVA + Nf * BPVf Nf = (BPVL - BPVA)/BPVF
BPFV= BPVCTD/CFCTD Nf = (BPVT - BPVA)/( BPVCTD/CFCTD)
managing duration gap Derivative overlay
- futures contract
use treasury bond contract to eliminate gap
Nf= BPVL-BPVA / BPVf
hedging with futures contract creates operational and practical risks.
Margin must be posted and adjusted daily means all g/l on the contract are posted in daily cash.
if hedge s successful, g/l is an offset to change in value of the liability, but those changes in unrealized value, not cf that must be posted in the margin account.
In practice, these issues make 100% hedge rare in such situation.
Partial hedge to reduces the duration gap are more common.
interest rate and duration 反比
increase interest rate pay fixed receive float
decrease duration
decrease interest rate pay float receive fixed
increase duration
managing duration gap Derivative overlay
- interest rate swap
receive fixed swap = buy more bond, increase duration
pay fixed swap = reduce bond, duration decrease
先算fixed /float side bpvv = market value * md /10,000
diff= net swap bps
Np = BPVL-BPVA/ (net swap bpv/100)
SFR respecified swap rate
= swaption strike rate
cost is limited to the initial premium paid
at time passes, compare the SFR for new swaps to the SFR of the swaption determines if the swaption has value
SFR new > strike, payer swaption should pay strike
swaption is valuable and should be exercised
option strategies 3
- enter a receive fixed swap vs. pay libor
- buy a receiver swaption
- enter a zero-cost collar composed of buying the receiver swaption and selling a payer swaption
If duration gap exist:
is at risk if interest rate fall, because asset increase less than liability increase,
surplus fall
receiver swaption hedge swap
has the option to enter a swap to receive fixed and pay float
risk in LDI
- hedge amount based on assumed duration and ignored convexity
- duration assumes parallell shift
- structure risk
- model risk
- spread risk
- counterparts credit risk
- collateral exhaustion risk
- liquidity risk
bond market index provides
low cost diversification and an alternative to achieve fixed income mgmt.
The goal is to minimize tracking error.
pure indexing
full replication
aides to replicate an existing market index by providing all the securities in the index to minimize tracking error.
- neither feasible or cost efficient
Enhanced indexing
purchase few securities in the index but match primary risk factor
cost efficient with less diversification
active mgmt
investor takes positions in primary risk factor that deviate from the index in order to generate excess return
alternate duration
pure indexer/enhanced indexer would keep the duration matches to index.
FI risk factors
parallel shift/ rate change
call risk
- key rate duration
garage the index’s sensitivity to non-parallel yield curve shifts
can be used in duration matching strategy; matching key rate durations of the assets to liabilities will better control risk than only matching total duration.
can be used in continent immunization as an active management tool seeking to add value by identifying points on the yield curve that expected to show the greatest value decline in yields, resulting in relative price gain.
change in specific maturity along the yield curve
matching key rate duration between portfolio and underlying index can significantly reduce the portfolio’s exposure to change in yield curve
- sector and quality spread duration contribution PM match the amount of index duration associated with the issuer sectors and credit quality
- issuer exposure
concentration of issuers within a portfolio exposes that asset manager to issuer-specific event risk. Seek to match portfolio duration effect from holding in each issuer.
spread duration SD= Y high yield - y gov’t
refers to the change in a non-treasury security’s price given a widening or narrowing of the spread compared with the benchmark
lower credit rating implies lower SD.
measure for determine a portfolio’s sensitivity to change credit spread
- provide the approximate % increase in bond price expected for 1% decrease in credit spread
- non-callable fixed rate corp bonds, spread duation is generally close to md
- more significant/substantial, spread duration diff for floating/floaters
change in price = -SD * P* S
alternative method to establish passive market bond exposure
strafed sampling/cell approach to index
enhanced indexing
- first each cell or significant index portfolio characteristic is identified and mapped to the current index
- position in each cell and adjust over time given change to the underlying index vs. existing portfolio position
alternative method to establish passive market bond exposure
ESG
lower tracing error associated with expenses and transition cost:
lower cost enhancement issue selective enhancements yield curve enhancement sector/quality enhancement call exposure enhancements
alternative method to establish passive market bond exposure
mutual funds
open-ended, buy/sell at nav
alternative method to establish passive market bond exposure
ETF
AP
creation units
liquidity
alternative method to establish passive market bond exposure
total return swap (OTC derivative strategy)
TRS
cheapest, lowest initial cash outlay, lower bid-offer costs
OTC customized arrangement between two counterparties that reference an underlying market price or index.
synthetic long poistion interest rate swap + credit derivatives
- PROVIDE exchange of CF during life of contract
based on reference obligations that is an underlying equity, commodity, or bond index
total return receiver receives both the cf from the underlying index as well as any appreciation in the index over the period in exchange for paying libor + pre-determined spread
total return payer pay the reference obligation f and return to the receiver but will also be compensated by receiver for any depreciation in the index or default losses
OTC based on ISPA master agreement
synthetic secured financing transaction in which the investor benefits from more-advantageous funding term faced by a dealer offering to facilitate the transitions
disadvantage to not direct invest:
- do not directly own underlying security
- normally short term, has roll over risk if cannot be renewed
- the specific return can be for a subset of bond market or a sector where transaction and liquidity issues make direct investment impractical
- structural and regulatory changes have been increase the cost and decrease the flexibility to TRS
Benchmark selection
last step of the asset allocation process
- consider inplicit/explicit duration preformed when choosing benchmark
- factor in broad range of issuers and characteristics available in FI market
bums pro.
greater allocation to more levered borrower
-which arises as a result of a market-cap-weighted portfolio increasing the weight of a particular issuer or sector that has increasing borrowings.
the desired duration profile may be considered the portfolio “BETA” with the target duration = to an invite’s preferred duration exposure
ladder bond portfolio
spread evenly along the yield curve
adv:
1. protection from shifts and twists
cf are essentially diversified across time spectrum
2. convexity is the middle of three
3. provide better liquidity mgmt
limitation:
1. using mutual funds is required
2. actual bonds entail much higher cost or acquisitions
yield curve strategies
designed to capitalize on expectations regarding the level, slope, and shape of yield curve.
yield curve strategies
butterly spread
-(ST yield) + (2* medium term yield) - LT yield
takes on larger position values when yield curve has more curvature
increase spread, increase curvature
profit from decrease in curvature of yield cure
= long barbell + short bullet
enhance portfolio yield
- maturity extension if curve is upswing (riding the curve)
2. buy lower-credit securities
active strategy with stable yield curve
extend duration to add yield
- buy & hold
- roll down/ride the yield curve (buy longer maturity anticipate coupon income and price appreciation)
- sell convexity add duration
buy bond
sell call/put option to earn premium
buy MBS (with negative convexity)
- carry trade
buy security and finance it at a lower rate than yield of the security
active strategy with yield curve movements of LSC
%P = -D * CHANGE IN YIELD
- duration management
alter duration with derivative
reduce by selling securities and hold cash
increase duration sell short-duration securities and simultaneously buy 10-yr duration securities
%change in value = -D * change in yield curve 2. buy convexity buy call/put option sell MBS sell bond with short option
of option needed= PVBSbond/PVBS option * MV bond
cash outflow reduce yield
- use bullet and barbell structure
carry trade
needs
- perfect capital mobility
- the fx rate between countries fixed (2 market share one yield curve)
require high average
no fx risk
may or may not involve maturity mis-matches.
on a flattening curve, borrow LT invest in ST
on a steeping curve, borrow ST invest in LT.
3 ways to implement:
- buy a bond and finance in repo market
- received fixed and pay floating on an interest rate swap
- replicate the cf associated with such an asset an a liability - take a long position in a bond/note futures contract
inter market carry trades
UICP does not hold
- depends on more than one yield curve
- the investor must either accept or hedge currency risk
accept currency exposure: borrow low interest rate, lend high interest rate - duration mismatch
bullet
lowest convexity
steepen
less curve
make up of securities targeting a single segment of the curve
- offer protection against steeping curve
- have little or no exposure at maturities larger or shorter than the targeted segment of the curve
barbel
highest convexity
flattening curve
more curvature
combine short and long term maturity
- take advantage of flattening yield curve
- if long rate decrease more than short term, long duration securities will capital the benefit of the falling rates that the intermediate duration securities cannot
- if the curve flattens through rising ST rates, portfolio losses are limited by lower price sensitivity to the change y yield at the short end of the curve whereas non-barbell intermediate duration securities ids poorly.
barbell
highest convexity
flattening curve
more curvature
combine short and long term maturity
- take advantage of flattening yield curve
- if long rate decrease more than short term, long duration securities will capital the benefit of the falling rates that the intermediate duration securities cannot
- if the curve flattens through rising ST rates, portfolio losses are limited by lower price sensitivity to the change y yield at the short end of the curve whereas non-barbell intermediate duration securities ids poorly.
change in interest rate, direction uncertain
volatile interest rate increase
increase convexity
gain more on decrease rate and lose less in rising rates
long barbell + short bullet
volatility decrease
long bullet + short barbell
change in interest rate, direction uncertain
volatile interest rate increase
increase convexity
gain more on decrease rate and lose less in rising rates
long barbell + short bullet
volatility decrease
long bullet + short barbell
investment grade bond
higher credit rating
lower credit + default risk
have more exposure to interest rate risk
credit spread negatively corrected with rf interest rate due to economical growth default rates, and momentary policy usually have opposite effect on rf rates and spread
high yield bond
low credit rating
higher credit and default risk
usually have greater exposure to credit risk
because bid–offer spreads are larger for high-yield bonds than for investment-grade bonds of similar maturity. Therefore, turnover in high-yield bond portfolios is generally more costly than turnover in investment-grade portfolios. Notably, many high-yield bonds do not trade frequently and can be very difficult to buy or sell.
credit risk
- default risk
pro. borrower default or fail to meet obligation to make full and timely pmt of principal and payment - loss severity / LDG
amount of loss if default occur
expected loss = POD* LDG
credit migration risk an spread risk
determination in credit quality widen credit spread
yield =
default ref interest rate + spread (o for rislkless asset)
empirical duration
measure of interest rate sensitivity that is determined from market data
run regression analysis
is smaller than the theoretically based effective duration
- rf decrease, credit spread increase by more than the magnitude of rf change in interest rate
-default loses are low and credit spreads are tight
high yield behave like invest grade bond
benchmark spread
security yield - on-the-run gov’t bond
problem: maturity mismatch between credit security and benchmark bond
G-spread
yield spread over an interpolated government bond. The spread is higher for bearing higher credit, liquidity, and other risks relative to the government bond.
when maturity mismatch presented, a linear interpolation of the yield on 2-on-the-run government bonds is used as the benchmark rates, reduce maturity mismatch
adv: easy to calculated and understand
-indication a way to hedge credit securities’ interest rate risk
sell duration-weighted amount of the 2 benchmark government bonds
- useful for estimated yield and price change for fixed rate credit securities with no options
i-spread
interpolated spread between a bond yield and swap rate. Libor
used swap rates dominated in the same currency as the credit security
- smoother than gov’t bond yield curve
- gov’t bond yld comes are affected by S&D for specific bonds, especially on the run issues
- bmk rate is usually more helpful when it represents a credit rf rate
- credit investors hedge interest rate exposure using bak bonds
z spread and oas
yield spread that must be added to each point of the implied spot yield curve to make pv of bond cf= market value
z- spread
good measure for non option embedded bonds
oas
good measure for option embedded bond
Most widely accepted
MOST appropriate for a portfolio-level spread
Market value = face value * (price/100 + accrued interest)
portfolio OAS= weight a*OASa + weight b * OASb
shortcoming:
- depends on assumption regarding future interest rate volatility
- bond with embedded option is unlikely to realize the spread implied by OAS
duration time spread DTS
attempt to account for both average OAS and average spread duration
= duration * OAS
=SD * OAD
Excess return EXR ~
EXR = (s × t) – (∆s × SD) – (t × p × L)
where
s = Z-spread
t = Holding period
SD = Spread duration
p = Probability of default
L = Loss severity
SPREAD- change in spread * Spread duration - (t* p* l)
PL= exp annual credit loss
DERIVATIVES
adv:
- key rate duration can be controlled independently of credit spread curve exposures
- liquidity of interest rate derivatives market allows exposure to be easily exchanged
Disadvantage:
using it can be impractical for smaller portfolios/investors
Maturity management
adv: can be accomplished without use of derivative
disadvantage:
desired corp. bonds / zero coupon bond are not available in all maturities, it maybe difficult to match key rate duration closely
top-down approach
a sizable portfolio of credit returns can be attributed to macro factors
difficult to implement because expectation for interest rates economic cycles change
tail risk:
the chance of a loss occurring due to a rare event, as predicted by a probability distribution.
- returns experience more large declines than consistent with their STD
- difficult to model and virtually impossible to predict in advance
suggests that the distribution of returns is not normal, but skewed, and has fatter tails.
-there is a larger probability and anticipated that an investment will move beyond 3 std.
assessing tail risk
- extremely unusual events
scenario analysis
use historical and hypothetical scenario analysis
The primary purpose of scenario analysis is to test the portfolio’s performance under plausible but unusual circumstances.
managing tail risk through
portfolio diversification
adv:
may only have a modest incremental cost
limitation:
difficult to identify attractively valued investment opportunities that can protect against every tail risk that the investor foresees
tail risk hedge
using securities/derivatiew that act as “insurance” in tail event scenarios
CDs by CDs
options
drawback: cost reduce return
more expensive than when tail risk event seems most likely to occur
international credit portfolio
EM
- offer greater value opportunities
- concentrated in commodity and banking government ownership
- sovereign ceiling, corp issue subject to no higher rating than sovereign bond
- credit quality high yield and lower return of investment grade bond
- global difference in regulation and law
structure financial instruments MBS ABS CDO Covered bonds
securities backed by collateral, or pools of assets, and in turn repackage risk
benefit:
- potential for higher portfolio returns compare with traditional fixed income securities
- potential for relative value opportunities
- improve portfolio diversification
MBS
Government agency backed MBSs generally offer similar returns but better liquidity compared to high-quality corporate bonds.
provide liquidity
exposure to real estate
exposure to exp. change in interest rate volatility
low default risk because interest and principal pmt are guaranteed by US government agency
Primary risk:
- prepayment risk
cf from the MBS occur earlier than the scheduled CF as a result of interest rate decline
- extension risk
agency mBS
cf occur later than scheduled cf becauase of interest rate rise
- useful tool for investing based on view to credit cycle and real estate cycle
ABS
deal with Exposure to consumer credit
more liquid alternative to corp. bonds for expressing views on some sectors
Several types of non-mortgage assets are used as collateral for ABS, including auto loans and lease receivables, credit card receivables, student (or other personal) loans, bank loans, and accounts receivable. ABS may thus provide a way for investors to express views on consumer credit.
MBS
buy MBS increase liquidity
has negative convexity
provide liquidity
exposure to real estate
exposure to exp. change in interest rate volatility
low default risk because interest and principal pmt are guaranteed by US government agency
Primary risk:
- prepayment risk
uncertainty of timing of actual cf from the MBS will differ from and occur earlier than the scheduled CF as a result of interest rate decline
- extension risk
agency mBS
timing of actual cf differ from and occur later than scheduled cf becauase of interest rate rise
- useful tool for investing based on view to credit cycle and real estate cycle
covered bonds
dealt with
Lower-risk exposure to the financial sector
is a debt obligation usually issued by a bank and backed by a segregated pool of assets called a “cover pool”.
This dual recourse protection for creditors in the event of default against both the issuer and the cover pool lowers the credit risk of covered bonds relative to otherwise similar corporate bonds or ABS.
Investors typically view covered bonds as a lower-risk alternative to financial sector bonds. An investor who wants to reduce his portfolio’s risk to the financial sector may sell corporate debt issued by banks and buy covered bonds instead.
in event of default, bondholders have recourse right against both financial institutions and the assets in the cover pool
- dual protection
- lower credit risk and lower yield
Model risk
Model risk arises whenever assumptions are made about future events and approximations are used to measure key parameters. The risk is that those assumptions turn out to be wrong and the approximations are inaccurate.
如果expect paralle shift但是却发生了twist
Model risk
Model risk arises whenever assumptions are made about future events and approximations are used to measure key parameters. The risk is that those assumptions turn out to be wrong and the approxibmations are inaccurate.
如果expect paralle shift但是却发生了twist
full-repricing method
- The use of spot rates (zero-coupon curves)
- most accurate measure of price changes in securities.
it requires more data than the duration-based approach.
butterfly spread
= - short term +2*mid term yield - long term yield
z-spread
is the constant spread that makes the price of a security equal to the present value of its cash flows when added to the yield at each point on the spot rate Treasury curve where cash flow is received
implementation of a duration-neutral, currency-neutral intermarket carry trade
OPTIMAL:
sell long/buy short in the steepest market, and sell short/buy long in the flattest market.
using interest rate swaps
receive-fixed interest rate swap in the steepest market and into a pay-fixed interest rate swap in the flattest market.
With Treasury note futures
long the steepest market and a short the flattest market.
change in portfolio value =
−key rate PVBP Portfolio par amount × (curve shift in bps / 100)
Stratified sampling can accommodate the use of derivatives and socially responsible investing.
The use of stratified sampling limits the need for frequent rebalancing, as the index-tracking portfolio does not seek to replicate the underlying index exactly.
arithmetic weighting does not take into account the nonlinear nature of credit risk and is likely to
overestimate a portfolio’s credit quality (or underestimate a portfolio’s credit risk).
The investment-grade bond market
is both larger in total size
and more liquid than the high-yield market.
liquidity advantage of IG.
Regulations and decreased risk appetites among broker-dealers has caused dealers to hold smaller inventories of high-yield bonds and further reduces the relative liquidity of HY.
inter-market carry trade
do not, in general, break even if each yield curve goes to its forward rates unless the “first-period” rate is the same in the two markets.
trades should be assessed on the basis of returns hedged into a common currency.
Doing so ensures that they are comparable.
The primary driver of inter-market trades is anticipated changes in yield differentials.
most relevant for active bond management, the capital gains/losses arising from yield movements generally dominate the income component of return (i.e., carry) and rolling down the curve.
monitor liquidity in a portfolio
Trading volume
Spread sensitivity to fund outflows
Another measure used to evaluate liquidity is spread sensitivity to large withdrawals by investors from credit funds. A large withdrawal is likely to require a fund to sell assets.
Bid–ask spreads
Bid–ask spreads can also be used to assess liquidity in credit markets. Generally speaking, bid–ask data should be analyzed cautiously because such information is stable only when markets, in turn, are stable. More volatile market conditions often have a negative effect on bid–ask spreads. This effect is often temporary and suggests that bid–ask levels tend to stabilize after a brief period of volatility.
managing liquidity risk
- Holding cash
- Holding greater weights of liquid credit securities
- Making use of CDS index derivatives and ETFs
As a measure of interest rate sensitivity for high-yield bonds, empirical duration is superior to effective duration.
For all credit ratings, empirical duration is smaller than the theoretically based effective duration because credit spreads tend to be negatively correlated with risk-free interest rates. One important reason for this phenomenon is that key macro factors, such as economic growth, default rates, and monetary policy, usually have opposite effects on risk-free rates and spreads. As a result of the typically negative correlation between risk-free rates and credit spreads, changes in risk-free rates tend to generate smaller changes in corporate bond yields than theoretical measures of duration suggest. This reduced effect is even more pronounced for securities with high credit risk and large credit spreads.
Levered exposure to credit use CDO or CLO
Mezzanine and equity tranches of CLOs and CDOs provide a mechanism for investors to gain additional return if the underlying collateral has strong returns. Conversely, these tranches also face heightened risk of losses in an adverse credit environment. This risk–return trade-off of mezzanine and equity tranches of CLOs and CDOs thus provides leveraged exposure to the underlying collateral (e.g., loans and bonds).
Entering a pay fixed swap means that portfolio duration will decrease
Entering a received fixed swap means that portfolio duration will increase
Initial funding required (PVA) low to high
Comparison of Liability-Based Strategies
Duration matching
Horizon matching
Cash flow matching
Contingent immunization
Risk and complexity low to high
Comparison of Liability-Based Strategies
Cash flow matching
Horizon matching
Duration matching Lowest
Contingent immunization
Expected realized return if successful
Comparison of Liability-Based Strategies
Cash flow matching
Horizon matching
Duration matching Lowest
Contingent immunization
advantage of using portfolio convexity to measure the extent of structural risk
the portfolio convexity statistic can be approximately by the market value weighted average of the individual bonds’ convexity.
