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)
