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19-1 liability-driven and index-based strategies (3 interest rate …
19-1 liability-driven and index-based strategies
1 introduction
passive - active: based on manager's particular view on interest rate and credit mareket conditions
asset-liability management ALM: based on incorporate both rate-sensitive asset and liabilities into decision process
liablity-driven investing LDI: liabilities given and asset managed
to ensure adequate funding for
index-based investment strategy: to gain broader exposure to fixed-income markets
2 liability-driven
investing
the frame of reference - a balance sheet of rate-sensitive assets and liabilities
asset-liability committees ALCOs:
to monitor and manage the maturity gaps and set rates in a coordinated manner
→use of derivatives such as interest rate swaps to manage maturity gaps through synthetic ALM strategies
asset-driven liabilities - ADL
-special cases of ALM:
asset given and liabilities structured to manage interest rate risk
aiming to match maturities of assets and liabilities to min risk
liability-driven
investing - LDI
-special cases
of ALM:
liabilities given and assets managed
start with analyzing size and timing of entity's liabilities
liability
type
1 amount know - timing know
financial contracts specify certain amounts due on scheduled future dates
yield duration statistics can used to measure interest rate sensitivity of liabilities
2 know - uncertain
callable and putable bonds / a term life insurance policy
effective duration
3 uncertain - know
floating-rate note / structured notes
effective duration
4 uncertain - uncertain
propery and casualty insurance company
effective duration
3 interest rate
immunization -
managing the
interest rate
risk of a
single liability
immunization: the process of
structuring and managing fixed-income bond fortfolio
to min variance in realized rate of return over know time horizon
the most obvious way to immunize interest rate risk on single liability - zero-coupon that matures on obligation's due date
the two effects
of yield curve
change
the price effect:
value change - money duration = modified duration * price
pulled to par as maturity dates
the coupon reinvestmetn effect:
the point the two effects cancel each other - Macaulay duration
Macaulay
duration
-weighted average of times to receipt of cash flow -
weighted by share of total market value for each date
the yield curve is not flat - the difference of cash flow yield and market value weighted average yield
annualized by dividing by periodicity of bonds
first-order effect
structural
risk
the portfolio
dispersion statistic
annualized by dividing by the periodicity squared
the weighted variance - extent to payments spread out around the duration
the porfolio
convexity
second-order effect
Convexity = Macaulay duration^2 + Macaulay duration +
Dispersion / (1+Cash flow yield)^2
a desirable property -
more convex gains more if yield goes down
and loses less if yield goes up
→ min dispersion and convexity:
a barbell design to more of a bullet that
concenttrates durations around investment horizon
*to interest rate immunization arise from potential for shifts and twists to yield curve
essentially zero replication - interest rate hedging
as yield rise and fall - unrealized losses and gains
immunizing
with
coupon-
bearing
bonds
continuously matching Macalay duraton
with zero-coupon as yield curve shifts
portfolio initial market value has to
match or exceed PV of zero-coupon
key assumption: any ensuring change in cash flow yield equal to change in the yield to marturity on zero-coupon
the difference - twists to yield curve /
some non-parallel shifts
characteristics of bond portfolio structured to immunize a single liability
initial market value >= PV of liability
portfolio MD matches liability's due date
min portfolio convexity statistic
4 interest rate
immunization -
managing the interest rate
risk of a multiple liability
cash flow
matching
to build a dedicted asset portfolio of high-quality fixed-income bonds that matches amount and timing of scheduled cash outflows -
held-to-maturity
buyback strategy difficult and costly to implement
a corporate
finance
motivation
to improve company's credit rating
the process of accounting defeasance:
remove both dedicated asset and
bebt liabilities from balance sheet
the cash-
in-advance
constraint
sufficient funds must available on or befor each liability payment date to meet the obligation
duration
matching
money duration / dollar duration: modified * market value
modified duraion = macaulay duratoin / ( 1 + cash flow yield)
the basis point value ( BPV) = money duration * 1bp
for equal duration, more convex generally outperform - higher gains if yield fall and lower losses if yield rise
immunization of multiple liabilities -
essentially an interest rate risk hedging strategy
source of loss - steeping twist
comparable gain - flattening twist
→ rebalance:
wati until mismatch large enough / use interest rate derivatives
derivatives
overlay
yields and duration inversely related
a derivatives overlay transforms some aspect of underlying portfolio:
exchange derivatives - currency
credit default swap contracts - credit risk profile
interest rate derivatives - interest rate risk profile
the required number of futures contract:
Asset portfolio BPV + (N_f × Futures BPV)
= Liability portfolio BPV
//N_f positive - buy / long
//Futures_BPV ≈ BPV_CTD / CF_CTD
the term synthetic: created with derivatives
contingent
immunization
a hybrid
passive-active
strategy
the surplus:
the difference between
the market value of asset
and liabilities
the objective - to gain
on actively managed funds
a natural setting - in fixed-income
derivatives overlay strategy
over-hedged - yield expected to fall
under-hedge - yield expected to rise
5 liabillity-driven investing - an examples of a defined benefit pension plan
6 risks in liability-driven investing
7 bond indexes and the challenges of matching a fixed-income portfolio to an index
8 alternative methods for establishing passive bond market exposure
9 benchmark selection
10 laddered bond portfolio