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# Asset -Liability
# Management - Part I
ALM -driven investors, Types of Liabilities, ALM techniques
> Fernando Forcada, CFA
> Selected Topics, January 2025
# 1ALM Definition
>
Broad definition : Asset -Liability Management (ALM) consists of
considering both assets and liabilities in the investment decision -
making process
>
ALM strategies became popular in the 1970 s, following the surge in oil
prices and inflation, which led to episodes of high interest rate volatility .
Before, managers often made asset and liability decisions independently,
leading to unexpected gaps between them
>
Special cases of ALM :
Liability -driven investing (LDI), when the liabilities are given, and assets are
managed (i .e. insurance company, DB pension fund )
Asset -driven liabilities (ADL), when the assets are given, and debt liabilities are
structured in accordance with the interest rate characteristics of the assets (i .e.
leasing company)
>
We will focus on LDI and we will use the term ALM as equivalent to
Liability -driven Investing (LDI), that is, the management of assets taking
into account the investors liabilities
>
The traditional primary objective of ALM is the management of assets so
that their (interest rate) risk matches, or is as similar as possible, to that
of the liabilities
# 2ALM -driven Investors
ALM strategies are based on the concept that investors incorporate both
rate -sensitive assets and liabilities into the portfolio decision -making
process
ALM is about managing the relative market movements of assets and
liabilities . Therefore, it is key to understand the liability
representation and pro -actively manage/reduce unrewarded risks (i .e.
mismatch risks) to help free up risk capital
Liability -driven investors focus on meeting their future obligations
and maximizing the surplus (A -L) given an acceptable level of risk
In contrast, Asset -only investors focus on earning the highest level of return
for a given level of risk without considering any liability modeling
# 3ALM -driven Investors
Who are the main investors that apply ALM strategies?
Insurance companies provide financial protection and play a key role in a
countrys economic growth and development . The insurance business creates
both assets and liabilities : premiums are earned today, but claims are paid
later, often years later . The insurance industry can be divided into three broad
product categories : life insurance, health insurance, and property and liability
insurance, but for purposes of considering ALM, it is sufficient to narrow the
categories to life and non -life insurance companies :
Life Insurance sell many different insurance policies, such as whole life, term life,
universal life, annuities, or variable life (unit linked products) . Life liabilities are
complex and challenging : they are sensitive to interest rate shifts, are normally quite
long and may have embedded options to the policyholders . The net interest spread
(the difference between interest earned from investments and interest credited to
policyholders) is a key performance indicator . Liabilities are relatively certain in value
but uncertain in timing
Non -life Insurance (General Insurance - GI) includes health, property (fire, theft,
home, earthquake), motor (automobile insurance), marine (ships, cargo), surety
(coverage the failure of 3rd party obligations) or legal liability (civil law or criminal
law) . Non -life liabilities do not have guaranteed interest rates, do not normally have
embedded options, and durations tend to be shorter . Both liabilities value and timing
are uncertain 4ALM -driven Investors
Who are the main investors that apply ALM strategies?
Pension Funds contain assets that are set aside to support a promise of
retirement income . Generally, that promise is made by some enterprise or
organization (plan sponsor)
Defined -benefit Pension Plan (pay -as -you -go) specifies the plan sponsors
obligations in terms of the benefit to plan participants . They are promises made by a
plan sponsor that generate a future financial obligation or pension liability
and, thus, the plan sponsor bears the investment risk . Defined -benefit Plan have
promised to provide a retirement income to their members . To achieve this, Plans need
to ensure that they have enough assets to cover these liabilities over the life of the
scheme . ALM strategies are mainly implemented here
Defined -contribution Pension Plan (fully -funded) specifies the sponsors
obligations in terms of contributions to the pension fund . The contribution is made into
an account for each individual participant . The plan sponsor recognizes no financial
liability because the benefit is not promised, and the plan participants bear the
risk of investing (the sponsor must offer a menu of investment options that allows
participants to construct suitable investment portfolios)
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# ALM -driven Investors
Who are the main investors that apply ALM strategies?
Commercial Banks are financial intermediaries involved in taking deposits
and lending money to businesses and consumers . Traditionally, the objective of
banks has been earning a profitable spread between the lending and borrowing
rates, while trying to match the risk of assets to liabilities
Banks risk objectives are dominated by ALM considerations that focus on funding
liabilities . They must not assume a level of risk that jeopardizes their ability to meet
their liabilities to depositors and other entities
Banks typically face a balance sheet mismatch , given the nature of their business,
with short liabilities (bank accounts and deposits) and mid/long assets (loans,
mortgages)
Any individual investor with a future specific liability to fund (goals -
based approach) : university tuition, retirement plan (annuity), committed
payments to repay a loan or to fund an investment
# 6Liabilities
Liabilities are financial obligations or commitments derived from
routine underlying businesses and financial management decisions of
institutions such as banks, insurance companies, and pension funds
Examples : payouts on life insurance policies and pension benefits
Understanding Liabilities : To manage liability risks an investor must
understand three things :
HOW liabilities are valued (projecting future payments and valuing those
future payments in todays money)
THE FACTORS that change liability values (interest rates, inflation,
longevity) . For example, most pension plans have liabilities linked to inflation
HOW TO HEDGE against the impact of those factors (bonds, derivatives,
longevity swaps/bonds* )
# 7
(*) A longevity swap transfers the risk of pension plan members/policyholders living longer than expected to an
insurer. On the other hand, the payout on longevity bonds depends on the longevity experience of a given
population (the payment is related to the number of survivors). Basically, it would pay out more as the proportion
of survivors rises. 8Liabilities Classification
Liabilities can be classified according to the certainty/uncertainty of the
value and timing of their cash flows :
Type I: plain -vanilla bond with fixed coupons and no embedded options (A) ;
guaranteed investment contract or GIC (L)
Type II : fixed -coupon bonds with embedded options, i.e. callable/puttable bonds (A) ;
term life insurance policy (L) because the timing of the insureds death is unknown
Type III : floating -rate note (FRN) or inflation -indexed bonds (A) ; variable interest
rate loans (L)
Type IV : convertible bonds or a callable FRN (A) ; property and casualty insurance
claims, such as damages from catastrophic weather events or a defined benefit
pension plan (L)
# 9Fabozzi (2013) Liabilities Modeling
Building a model for the liabilities : We encounter model risk in
financial modeling 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 :
Lapses (withdraws, surrenders) Renewals and New Business hypothesis are
key assumptions to model liabilities
What yield curve (*) should be used to discount liabilities to find their PV?
Risk -free rates? Risk -free rates plus some spread/premium ?
A life insurance company holding a large portfolio of policies can benefit
from the law of large numbers . This means that the insurance
company can use actuarial science (mortality tables, lapses) to predict, on
average, the amount of total liabilities due for each year
Data quality is critical, otherwise the model will suffer from the
garbage in, garbage out issue
# 10 (*) For instance, in the United States, government regulators and the accounting authorities allow high -
> quality corporate bonds to be used to discount the future liabilities.
# Liabilities Modeling
>
Simple liabilities can be represented with cash flows and discounted with the
appropriate interest rate, while complex liabilities that have option -
liked behaviors can be represented with a combination of cash flows and
derivatives and valued using more advanced valuation models
>
Deterministic vs Stochastic :
Deterministic estimation generates only one scenario based on single estimates
(Best Estimate)
Stochastic estimation (i .e. Monte Carlo simulations) generates a probabilistic
forecast with a range of possibilities for the future based on multiple random
scenarios
>
Theoretical replicating portfolios may be used to capture the
sensitivities of the liabilities to market factors consistently with the assets .
Theoretical financial instruments, such as zero -coupon bonds but also
derivatives (swaptions, IR swaps ) are used to replicate the pattern of cash
flows and behavior of liabilities
>
It is strongly recommended that the Investment Department of an insurance
company, bank, or pension fund gets involved in the design of any new
(financial) product that the company may want to launch, particularly, if
the new product implies dealing with complex liabilities (surrender
option, additional premium option, minimum guaranteed rate, profit
sharing )
At the end of the day, it will be the investment team who will have to manage the
financial risks associated with any new product 11 Liabilities Modeling Examples
Example 1: A retail savings product :
The company offers a guaranteed interest rate that is reset every 6 months for 10
years . However, there is a floor (minimum rate) that is guaranteed during the whole
life of the product (10 yrs)
The client can surrender (withdraw) at any time at the prevailing market prices .
Therefore, an estimation of lapses is needed
The client can make new investments on a monthly basis . These periodical
premiums are set in the contract in advance, but they are not compulsory, and
extraordinary ones are also permitted . Thus, an estimation of these inflows is
needed
Every 6 months , when the interest rate is updated and reset for the next 6-month
period, the product is open for new business (that is, new clients can also buy the
product) . Therefore, an estimation of the expected inflows & outflows from new
business is needed from the actuarial/commercial department
Example 2: A traditional life savings insurance product :
The company offers a guaranteed interest rate with profit sharing
The company offers the option to surrender at the mathematical reserve (accredited
cash balance) regardless of the market value
The client can make new investments on a monthly basis
The product (life insurance) ends when the client passes away . In other words, the
product does not have an explicit maturity , and the actuarial team should estimate
the outflows 12 Liabilities Modeling Examples
Example 3: Defined -Benefit Pension Plan :
A good example of Type IV liabilities , for which both the amounts and dates
are uncertain
If a plan is not fully funded , the plan sponsor has an obligation to make
contributions to the plan
Note : Fully funded plan : the ratio of plan assets to plan liabilities is 100 % or greater
A representative employee covered by the pension plan has worked for G years ,
is expected to work for another T years (early retirement?) and then to retire
and live for Z years (mortality tables?)
Timeline Assumptions :
The retired employee receives a fixed lifetime annuity based on her/his wage at
the time of retirement (salary growth projection?)
The pension plan faces longevity risk , which is the risk that employees live
longer in their retirement years than assumed in the models (>Z years)
In recent years, some plans have become under -funded and have had to increase assets
because regulators required that they recognize longer life expectancies
# 13 ALM Techniques - CFM
ALM strategies are mainly designed to reduce or eliminate any sensitivity
mismatch between assets and liabilities associated with a change in
market interest rates (ALM/Market risk, interest -rate risk) together with
liquidity and reinvestment risk
However, other aspects, like credit risk (default risk, credit spread risk, rating
migration risk), are not covered and should not be overlooked
The main ALM Techniques are the following :
Cash flow matching (or dedicated bond portfolio) : it may be the simplest
(conceptually) and the most intuitive way to match a liability stream . This
approach attempts to ensure that all future liability payouts are
matched precisely by cash flows from bonds (or from fixed -income
derivatives, such as interest rate futures, options, or swaps)
This classic strategy requires building a dedicated high -quality bond portfolio that, as
closely as possible, matches the amount, currency, and timing of the scheduled
cash outflows, with no features (such as optionality) that would invalidate an
assumption of perfect effectiveness
A concern when implementing this strategy is the cash -in -advance constraint,
which means that securities are not sold to meet obligations ; instead, sufficient funds
must be available on or before each liability payment date to meet the obligation
If a perfect CFM is achieved, bonds are held to maturity, the effect of interest rate
changes on price are irrelevant and there are no interim cash flows to reinvest 14 ALM Techniques - CFM
Main advantages and disadvantages of Cash Flow Matching (CFM) :
(+) High reduction of risk (market risk, reinvestment risk and liquidity risk)
(+) Passive management (more certain returns with lower fees)
(+) Simple asset allocation (100 % bonds/fixed income derivatives, and cash)
(-) Difficulty of perfect implementation . In theory, CFM may be the most
intuitive way to match a stream of liability cash flows . However, in practice,
perfect matching of cash flows is very difficult to achieve
(-) Requirement for an accurate projection of liability cash flows
(-) Bond portfolio construction under CFM might be quite expensive (lower yield)
Note : The use of high -yield bonds (default risk) or callable bonds and
mortgages/MBS (prepayment risk) in CFM should be reduced or avoided .
Also, structured tailored -made assets (asset swaps / SPVs) with low
liquidity could be a problem when rebalancing the portfolio
# 15 ALM Techniques Dur Matching
Duration matching (or interest rate immunization ) is a hedging
strategy which objective is that, ideally, the liabilities and the portfolio of
assets should be affected similarly by a change in interest rates (i .e.,
an interest rate risk hedging strategy)
The asset portfolio is built and managed to offset the market value
movements from the liabilities based on three main variables :
Duration ,
Present Value (PV),
and Cash Flows Dispersion
As we refine and improve a Duration Matching, we are, indeed, getting closer
to a CFM . A non -perfect CFM can also be seen as a kind of Duration
Matching approach
Note : Watch out! Focusing just on duration may be misleading
Some practitioners just pay attention to the first two variables (duration and market
value) or even to just the first one (duration), dismissing HOW the asset portfolio
actually matches the liabilities cash flows
By doing this, they might end up having a portfolio apparently well matched in
terms of duration but horribly matched in terms of cash flows . And this might have
bad consequences in terms of reinvestment risk, liquidity risk, and even interest
rate ((yield -curve) risk 16 ALM Techniques Dur Matching
Depending on the level of sophistication/complexity applied in this
strategy, we can distinguish between three levels or approaches :
1st Level (wrong) : In this approach, we only focus on Duration : Assets
duration should be equal to Liabilities duration, that is, we should try to match
the asset portfolio Macaulay/Effective/Modified duration with the investment
horizon defined by the liabilities . However, this approach is too simplistic
and may still leave the company with significant ALM risks
2nd Level (partially wrong) : We need to consider the Present Value (PV) of
both assets and liabilities together with their Durations . To do so, we will
use the concept of Money Duration (often called Dollar Duration in the US),
which is the portfolio modified duration multiplied by the market value : Assets
Money Dur should match Liabilities Money Dur . With this, we make sure
that the market value sensitivity of both (A) and (L) is matched against parallel
yield curve movements, but that is not enough
3rd Level (correct) : This is the most sophisticated way to apply
Duration matching . We need to complement the 2nd approach with the
Dispersion of cash flows (which is frequently overlooked) and include the
concept of Convexity . It considers that interest shifts are not necessarily
parallel movements . The dispersion of the assets cash flows should
closely match the dispersion of the liabilities cash flows
# 17 ALM Techniques Dur Matching
Main advantages and disadvantages of Duration Matching :
(+) More flexibility in case of portfolio rebalancing
(+) The requirement of an accurate projection of liability cash flows is not so
restrictive
(+) The cost of constructing the bond portfolio is lower than in the case of CFM
(-) If it is designed properly, interest rate risk (from parallel shifts) may be hedged,
but other risks appear :
Reinvestment risk , the uncertainty of not knowing at which yield assets can be reinvested
or even the availability and nature of the future assets
Liquidity risk , given the need to fund outflows with the sale of assets
Yield -curve (Structural) risk : convexity and non -parallel movements should also be
considered
(-) Additionally, the design and monitoring of Duration Matching can be complex
and requires more frequent rebalancing (which implies higher trading
costs ), as market conditions change . The need to rebalance makes liquidity
considerations important
Note : equally, the use of callable bonds/mortgages/MBS (prepayment risk) or
illiquid assets (given the higher need of rebalancing) should be limited
# 18
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Others ALM strategies are :
Contingent immunization : A hybrid approach that combines
immunization with an active management approach when the asset
portfolios value exceeds the present value of the liability portfolio . The portfolio
manager is allowed to actively manage the asset portfolio, or some portion of the
asset portfolio, as long as the value of the actively managed portfolio exceeds a
specified value (threshold)
Horizon matching : Another hybrid approach that combines cash flow and
duration matching approaches . Normally, liabilities up to about four or five
years are covered by a cash flow matching approach, whereas the long -term
liabilities are covered by a duration matching approach, combining desirable
features of both approaches : a portfolio manager has more flexibility over the
less certain, longer horizon and can still meet more certain, shorter -term
obligations
# 21 References
>
The Handbook of Fixed Income Securities , 7th Edition . Frank J. Fabozzi ,
PhD, CFA, CPA, 2005
>
Liability -Driven and Index -Based Strategies . James F. Adams, PhD, CFA,
and Donald J. Smith, PhD . CFA Institute, 2017
>
The Evolution of Asset/Liability Management . Ronald J. Ryan, CFA . The
Research Foundation of CFA Institute, 2013
>
Managing Investment Portfolios : A Dynamic Process , 3rd Edition . John L.
Maginn , CFA, Donald L. Tuttle, PhD, CFA, Jerald E. Pinto, PhD, CFA, and
Dennis W. McLeavey , CFA, 2007
>
Understanding Fixed Income Risk and Return . James F. Adams, PhD,
CFA, and Donald J. Smith, PhD . CFA Institute, 2013
>
Longevity risk transfer markets : market structure, growth drivers and
impediments, and potential risks . Basel Committee on Banking Supervision .
Joint Forum . BIS, December 2013
>
www .investopedia .com
# 22 Annex Duration & Convexity
(Macaulay / Modified / Effective) Duration is a
useful risk measure, that is commonly used in the
financial markets around the world . It measures
the sensitivity of the bonds price to changes in
interest rates, providing a linear estimate of
the price change . However, it also presents some
important limitations for assessing market value
sensitivities accurately, which are :
The relationship between prices and yields is NOT
linear
The yield curve movements are, quite often, NOT
parallel
# 23
Convexity (together with duration) allows
for a better approximation of the change in
market value given a change in yields
because :
It assesses the curvature of the price -yield
relationship of assets and liabilities
It captures the non -linear relationship between
prices and yields
It measures the change in duration for a given
change in yield Annex Structural Risk
>
Structural risk arises from portfolio design, particularly the choice of the
portfolio allocations . The risk to the immunization strategy is the potential
for non -parallel shifts and twists to the yield curve , which may lead to
changes in the market value of the asset portfolio that differ from changes in
the debt liabilities
>
This risk is minimized by selecting the portfolio with the lower
convexity and dispersion of cash flows . That is, structural risk is
reduced by minimizing the dispersion of the bond positions, going from a
barbell design to more of a portfolio that concentrates the component bonds
coupons and principals on the liabilities cash flows . At the limit, a zero -
coupon bond that matches the date of the single obligation (or a portfolio of
zero -coupon bonds that provide a perfect CFM in the case of multiple
liabilities) has, by design, no structural risk
>
Remember the general principle that, for equal durations, a more convex
portfolio generally outperforms a less convex portfolio (higher gains if yields
fall, lower losses if yields rise) . However, the dispersion of the assets
should be as low as possible subject to being greater than or equal to the
dispersion of the liabilities to mitigate the effect of non -parallel shifts in
the yield curve
# 24 Annex ABO and PBO
There are two general measures of the retirement obligations for a
Defined Benefit Plan :
The Accumulated Benefit Obligation (ABO) calculates the liability
based on the years worked so far, and the current annual wage , even
though the annuity paid in retirement will be based on the projected final
wage at retirement and the total expected working years
The use of the current annual wage and the number of years worked is because
the ABO represents the legal liability today of the plan sponsor if the plan
were to be closed or converted to another type of plan, such as a DC plan
The Projected Benefit Obligation (PBO) is the liability reported in
financial statements and used to assess the plans funding status
The PBO liability measure also calculates the liability based on the years
worked so far, but it uses the projected final wage at retirement instead of
the current wage
# 25 Asset -Liability
# Management Part II
ALM techniques, Types of Liabilities, (Surplus) Change Analysis
> Fernando Forcada, CFA
> Selected Topics, January 2025
# 1A-L / Pension Surplus
Asset -Liability Surplus (or Deficit) is the difference between both
invested assets and liabilities at market/fair value
The A-L Surplus is the preferred term for insurance companies and Banks
Pension Surplus (or Deficit) equals pension plan assets at market
value minus the present value of pension plan liabilities
Fully funded plan : the ratio of plan assets to plan liabilities is 100 % or
greater
Underfunded plan : the ratio of plan assets to plan liabilities is less than 100 %
# 2ALM/Market Risk and Risk
# Measures
ALM/Market Risk can be defined as the risk that our investments
become insufficient to pay our liabilities due to adverse changes
in capital markets . ALM/Market risk assesses the risk that the market
value of assets minus liabilities will decline due to financial scenarios .
ALM/Market risk can be split into different risk categories : Equity / Real
estate / Interest rate / Credit / FX / Specific risk
# 3
In this example, if investments
were to underperform by little more
than 10 % of the value of the
insurance liabilities, shareholders
equity (capital) would be wiped out .
This level of shareholder
leverage makes ALM critical in
insurance investment management ALM/Market Risk
ALM/Market risk can be typically measured with the following market
risk figures (apart from assessing asset allocation and concentration risks) :
VaR : Value at Risk (VaR) measures the minimum loss that is expected
to be suffered over a holding period with a given probability . A 5%
VaR is often expressed as its complement a 95 % level of confidence .
Examples :
The loss from a 1-in -2000 (years) event (0.05 %) is defined as the Value at
Risk with a 99 .95 % level of confidence in one -year horizon
The 5% VaR of a portfolio is USD 4.2 million over a one -month period,
which can be read as :
5% of the time, losses would be at least USD 4.2 million (preferred interpretation)
We would expect a loss of no more than USD 4.2 million 95 % of the time (do not confuse
with maximum loss)
Other VaR metrics, such as Component VaR (proportion of the diversified
portfolio VaR that can be attributed to each of the individual components) or
Credit VaR (based on counterparty defaults) may be useful calculations to
include in the analysis
# 4 Expected Shortfall (ES) or Conditional VaR is derived by taking a
weighted average of the losses in the tail of the distribution of
possible returns, beyond the VaR cutoff point
It quantifies the amount of tail risk an investment portfolio has
Example : the 99 % Expected Shortfall measures the average loss of events with
a probability lower than 1%. In order to determine the 99 % ES one needs to find
the VaR point that splits the distribution as follows : 1% to the left and 99 % to
the right and then take the average loss in the left 1% tail . The average (or
expected) loss corresponds to the cases within the worst 1% of the distribution
# 5
Normal Prob VaR VaR (%/Surplus) Expected
Shortfall
> 99,000% 114.352.907 31,67%
> 99,250% 119.564.928 33,11%
> 99,500% 126.616.304 35,07%
> 99,900% 151.902.066 42,07%
> 99,950% 161.747.648 44,80%
> 99,999% 209.643.048 58,06%
Surplus Tail VaR (99%)
> 147.304.483
# ALM/Market Risk ALM/Market Risk and Risk
# Measures
ES( 99 %) measures
the average loss of
events with a
probability lower
than 1%
VaR (99 %) measures
the loss that is
expected to be
exceeded with a
probability of 1%
# 6ALM/Market Risk
Both VaR and ES can be estimated using two main approaches :
Parametric VaR method : It is based on variance -covariance model (also
known as delta -normal method) . The advantages of this method include its
speed and simplicity, but it is a linear approximation that assumes the returns
of the market variables are multivariate normally distributed with mean return
zero . Also, it measures inadequately the risk of nonlinear instruments, such as
options or mortgages
Simulation VaR method : It is more appropriate when the portfolio to
measure has a high optionality component . It is calculated with Monte Carlo
simulations that revalue assets and liabilities under many thousands of market
scenarios with statistical properties that are consistent with longer term
market history
Warning : Periods of low volatility may understate the potential for
risk events to occur and the magnitude . Risk may be further
understated using normal distribution probabilities, which rarely account
for extreme or tail events
# 7 Let us assume we have three
asset classes : Government
bonds, Equities and Credit
On the other hand, we have
liabilities that are interest -rate
sensitive
We run 20 simulations resulting
in different scenarios for
Interest Rate, Credit Spread
and Equity Market movements
Now, we have 20 scenarios, and
we calculate the ES( 90 %), that
is the average loss of the worst
10 % of scenarios in this
example, which equals two
scenarios
# 8
# Diversification
# Benefit Govt Equities Credit Assets Liabilities Net A-L
Simulation 1 42 11 54 107 -84 23
Simulation 2 42 14 55 111 -84 27
Simulation 3 40 16 57 113 -80 33
Simulation 4 39 5 46 90 -78 12
Simulation 5 37 11 50 98 -74 24
Simulation 6 44 12 57 113 -88 25
Simulation 7 40 14 54 108 -80 28
Simulation 8 36 13 49 98 -72 26
Simulation 9 41 11 57 109 -82 27
Simulation 10 41 7 54 102 -82 20
Simulation 11 40 8 52 100 -80 20
Simulation 12 45 15 54 114 -90 24
Simulation 13 42 14 52 108 -84 24
Simulation 14 42 6 49 97 -84 13
Simulation 15 43 3 52 98 -86 12
Simulation 16 44 12 53 109 -88 21
Simulation 17 40 11 53 104 -80 24
Simulation 18 38 12 47 97 -76 21
Simulation 19 41 10 55 106 -82 24
Simulation 20 40 11 53 104 -80 24
Stand Alone Risk
(ES90%) 4,35 6,80 6,15 10,80 -8,70 10,60
1) Total non-diversified market risk 17,30 5) Total market risk 10,60
(4.35 + 6.80 + 6.15) relative to liabilities (ES90%)
2) Total asset-diversified market risk 10,80
3) Asset diversification benefit 6,50 4) Market risk of liabilities 8,70
(17.30 - 10.80)
6) Diversification benefit relative to liabilities 0,20
(10.80 - 10.60)
Example of diversification benefit
Govt Bonds Equities Credit Bonds Assets Liabilities Net A-L
Initial Portfolio
(Market Value) 40 10 50 100 -80 20 ALM/Market Risk and Risk
# Measures
Stress Test/Sensitivity Analysis are a good complement to VaR /ES
metrics because it may consider low -frequent events (tail events) or specific
scenarios (i .e. predefined worst -case scenarios ) for each portfolio
Examples of Scenarios/What If Analysis for ALM analysis :
# 9
Scenario 1: Parallel shift +200bp
Scenario 2: Parallel shift -200bp
Scenario 5: Steepening curve -100bp/+100bp
Scenario 6: Flattening curve +100bp/-100bp
Scenario 7: Credit Spread widening +100pb
Scenario 8: Combination of Scenarios 4 & 7
Scenario 3: Parallel shift +200bp & EQ -20%
Scenario 4: Parallel shift -200bp & EQ -20%
WHAT IF ANALYSIS ALM/Market Risk
Main interest rate sensitivities :
Macaulay / Modified / Effective Duration
Convexity (together with duration) allows for a better approximation of the change
in value given a change in yields because :
It assesses the curvature of the price -yield relationship of assets and liabilities
It captures the non -linear relationship between prices and yields
It measures the change in duration for a given change in yield
Money Duration : it measures how much a bond's price changes in currency units
when its yield -to -maturity changes by 1% (100 bps)
DV 10 : The monetary price impact on a bond of a 10 -basis point parallel shift of the
yield curve .
Net DV 10 : If we look at both assets and liabilities, we can calculate the Net DV 10 by taking
the difference between the Asset DV 10 and Liability DV 10 .
DV 01 can also be used (the impact of a 1-basis point parallel shift)
Key Rate Durations (KRDs) : they are an additional, slightly more advanced
sensitivity . Unlike DV 10 , Key Rate Durations measure the price sensitivity of
assets and liabilities to non -parallel up/down moves in the yield curve . They
measure the price sensitivity of assets and liabilities to a change in yield for a given
term (maturity bucket)
Credit Spread Duration (CS Dur) / Credit Spread Money Duration (CS 10 or
CS 01 ): Sensitivity to changes of the credit spread . Only Assets are impacted
# 10 ALM/Market Risk
>
Should we assign a Duration metric for the equity and/or
alternative investments of our portfolio?
>
The conservative answer is NO , because
>
there is no stable and predictable relationship between valuations
on those asset classes (equity and alternatives) and market interest rates
Only fixed -income securities have a well -defined connection between market
values and the market yield curve
>
However, assuming zero duration does not imply that equity and
alternatives have no interest rate risk
>
The effect on equity and alternatives depends on why the nominal
interest rate changes :
A change in expected inflation?, a change in monetary policy? or a change in
macroeconomic conditions ?
# 11 Accounting vs. Economic View
>
Under an Accounting/Regulatory Balance Sheet , liabilities are typically
not represented at fair value and, therefore, are not affected by market
movements . On the other hand, invested assets (Equities, Fixed Income, Real
Estate, Mortgages ) might not be fully represented at fair/market value and
are just partially affected by market shocks
>
Regulators set solvency and other requirements (Solvency II, Basel
III ) that must be met in all circumstances . The objective of solvency
requirements is to ensure that banks/insurers/pension funds hold enough
assets to pay -out all claims/liabilities at all times
>
This accounting/regulatory approach is limited but complements the
economic ALM and helps determine the required regulatory capital that the
company needs to hold to run its business . Without this approach, the
economic ALM by itself might lead to wrong decisions , because it may
overlook regulatory constraints when making investment decisions
>
Economic ALM Approach : Under this approach, both Assets and
Liabilities are valued at market value . To do so, an Economic B/S is built .
The difference between both assets and liabilities at fair value is called the
Economic Capital or A-L Surplus of the company 12 A-L Surplus (Deficit) Management
The accounting/ regulatory ALM is
a constraint that needs to be
considered carefully before making
ALM decisions and optimizing SAA .
Obviously, as more regulators
adapt an economic (market/fair
value) approach to determine
the required regulatory capital
(Risk Based Capital models) the
dichotomy between accounting and
economic ALM will reduce
What if Equities suffer a market
shock of -40 % (6 x -40 % = -2.4)? The
Regulatory Capital (3) would be
about to disappear, while the
economic surplus would still be fine
# 13
Accounting/Regulatory ALM vs. Economic ALM
Assets Liabilities
Current Assets Current Liabilities
Fixed Assets Statutory Capital&Reserves
/ Economic Surplus
Invested Assets Long-term Liabilities
Other Assets Other Liabilities
Balance Sheet at Book Value / Market Value
Book Value Market Value
Invested Assets 76 100
Fixed Income 68 92
Equity 6 6
Cash&Short-Term 2 2
Book Value Market Value
Technical Provisions 73 85
Book Value Market Value
Capital / Economic Surplus 3 15 Analysis of Change ALM Walk
In the case of ALM -driven investment strategies, liabilities should be the
benchmark against which the performance of the portfolio manager can
be measured
The change in market value (of Assets, Liabilities, and above all,
Surplus) from one period to another can be split into different factors
in order to help identify/analyze the sources of change :
Interest rate movements (both assets and liabilities) : Shifts in the
benchmark yield curve that is used to calculate the PV of Assets and Liabilities
(marked -to -model)
Credit spreads : tightening or widening of spreads only affect Assets (marked -
to -model)
Market prices of Equity/Real Estate/Mutual Fund or any other marked -to -
market (MtM ) asset
FX rate : in case some Assets or Liabilities are denominated in different
currencies
Change in cash flows (inflows/outflows) : sales, purchases, coupons, tax
payments, dividend payments, liabilities payments, premiums collection
Change in Liabilities assumptions : Actuarial team may change/update the
hypothesis behind Liabilities cash flows (mortality tables, costs, renewals )
# 14 15
ASSETS MV LIABILITIES MV SURPLUS
31/12/2017 6.525 -5.990 535
31/03/2018 7.100 -6.975 125
YTD Change 575 -985 -410
Figures in USD thousands Portfolio ABC
YTD as of 31/03/2018
A. Interest rate shifts: Effect on Assets 269
A.1 Change in Interest rates 190
A.2 Change in value date 79
B. Interest rate shifts: Effect on Liabilities -448
B.1 Change in Interest rates -380
B.2 Change in value date -68
C. Credit Spread effect on Assets -175
D. Equity (change in market price) 25
E. Real Estate (change in market price) 36
F. Cash Flows: Assets -195
F.1. Equity 0
F.2. Real Estate 0
F.3. Fixed Income -195
G. Cash Flows: Liabilities 148
H. Change in Liability Assumptions -70
TOTAL EFFECTS -410
## ALM WALK
Example of an Analysis of
Change or ALM Walk : the
change in the economic
surplus of this portfolio (-410 )
is decomposed into
different factors that can be
analyzed in order to better
understand the reasons
behind the significant drop in
the surplus
# ALM Walk Executive Summary (Parts I&II)
ALM definition and ALM -driven investors
Different ALM techniques : Cash Flow Matching and Duration
Matching . Main advantages and disadvantages
ALM/Market Risk : definition, VaR / ES / Scenario Analysis
Key Interest Rate Metrics : Concept of Money Duration
Analysis of Change ALM Walk to identify sources of Surplus
change
Review of ALM Exercises (Excel attachment)
# 16 References
>
The Handbook of Fixed Income Securities , 7th Edition . Frank J.
Fabozzi , PhD, CFA, CPA, 2005
>
Liability -Driven and Index -Based Strategies . James F. Adams,
PhD, CFA, and Donald J. Smith, PhD . CFA Institute, 2017
>
The Evolution of Asset/Liability Management . Ronald J. Ryan,
CFA . The Research Foundation of CFA Institute, 2013
>
Managing Investment Portfolios : A Dynamic Process , 3rd
Edition . John L. Maginn , CFA, Donald L. Tuttle, PhD, CFA, Jerald
E. Pinto, PhD, CFA, and Dennis W. McLeavey , CFA, 2007
>
Understanding Fixed Income Risk and Return . James F.
Adams, PhD, CFA, and Donald J. Smith, PhD . CFA Institute, 2013
>
www .investopedia .com
# 17 Annex Convexity and Dispersion
>
The portfolio dispersion and convexity statistics are used to assess the
structural risk to the interest rate immunization strategy (Duration matching) .
Structural risk arises from the potential for shifts and twists to the yield curve
>
There is an interesting connection among the portfolio convexity, Macaulay
duration, dispersion, and cash flow yield :
>
This Equation indicates that minimizing portfolio dispersion is the same as
minimizing the portfolio convexity for a given Macaulay duration and cash
flow yield . Equally, higher dispersion implies higher convexity when the Macaulay
durations and cash flow yields are equal
Note : Whereas Macaulay duration is the weighted average of the times to
receipt of cash flow, dispersion is the weighted variance . It measures
the extent to which the payments are spread out around the duration .
# 18 Annex Example I
>
An institutional client asks a fixed -income investment adviser to recommend a
portfolio to immunize a single 10 -year liability . It is understood that the chosen
portfolio will need to be rebalanced over time to maintain its target duration .
The adviser proposes two portfolios of coupon -bearing government bonds because
zero -coupon bonds are not available . The portfolios have the same market value
>
The institutional clients objective is to minimize the variance in the
realized rate of return over the 10 -year horizon . The two portfolios have
the following risk and return statistics :
>
These statistics are based on aggregating the interest and principal cash flows
for the bonds that constitute the portfolios ; they are not market value weighted
averages of the yields, durations, and convexities of the individual bonds . The
cash flow yield is stated on a semi -annual bond basis, meaning an annual
percentage rate having a periodicity of two ; the Macaulay durations and
convexities are annualized
>
Indicate the portfolio that the investment adviser should recommend
and explain the reasoning 19 Annex Example I
Solution :
The adviser should recommend Portfolio A. First, notice that the cash flow yields of
both portfolios are virtually the same and that both portfolios have Macaulay
durations very close to 10 , the horizon for the liability . In practical terms, a
difference of 1 bp in yield is not likely to be significant, nor is the difference of 0.03 in
annual duration
Given the fact that the portfolio yields, and durations are essentially the same, the
choice depends on the difference in convexity . The difference between 129 .43
and 107 .88 , however, is meaningful . In general, convexity is a desirable property of
fixed -income bonds . All else being equal (meaning the same yield and duration), a
more convex bond gains more if the yield goes down and loses less if the yield goes up
than a less convex bond
The clients objective, however, is to minimize the variance in the realized
rate of return over the 10 -year horizon . That objective indicates a conservative
immunization strategy achieved by building the duration matching portfolio and
minimizing the portfolio convexity . Such an approach minimizes the dispersion
of cash flows around the Macaulay duration and makes the portfolio closer to the
zero -coupon bond that would provide perfect immunization
The structural risk to the immunization strategy is the potential for non -parallel
shifts and twists to the yield curve, which lead to changes in the cash flow yield that
do not track the change in the yield on the zero -coupon bond . This risk is
minimized by selecting the portfolio with the lower convexity (and
dispersion of cash flows) 20 Annex Example II
# 21
>
In the aftermath of prolonged financial turmoil and a recession, a large pan -
European life insurance company believes that corporate debt securities and
asset -backed securities are now very attractive relative to more -liquid
government securities . The yield spreads more than compensate for default
and credit downgrade risk . Interest rates for government securities are near
cyclical lows . The insurance company is concerned that rates may rise and
that, as a result, many outstanding annuities might be surrendered . The insurer
believes the probability of a large, adverse move in interest rates is much higher
than is currently reflected by the implied volatility of traded options on
government securities in the eurozone . The insurers regulatory capital and
reserves are deemed to be healthy
1) What are the consequences of lowering allocations to government
securities and raising allocations to corporate and asset -backed
securities?
2) Are there steps that the insurer should take on the liability side? Annex Example II
# 22
Solution to 1:
>
These proposed asset reallocations have several implications :
>
First, corporate debt securities have higher yields and thus shorter durations
than government securities of similar maturity . Asset -backed securities tend to
have lower effective durations than corporate and government bonds . Thus, the
proposed rebalancing would likely lower the overall duration of the
investment portfolio , which is consistent with the insurers concerns about
rising interest rates and the expected consequences
>
Second, the change in portfolio allocation would likely lower the companys
overall liquidity and lower regulatory risk -based capital measures ,
because the new securities are treated less favorably for regulatory purposes
(less liquid, higher credit risk corporate debt and asset -backed securities require
a higher equity charge than liquid, low credit risk government securities, so
regulatory equity to risky assets is reduced) . Thus, the proposed portfolio
moves make sense only if the regulatory capital position of the insurer is
already ample and if the existing liquidity elsewhere in the portfolio is enough
to fund an uptick of annuity surrenders in the case of rising interest rates
>
Finally, the reallocation would increase expected earnings (from higher
interest income) and set the stage for price gains if credit spreads versus
government securities contract to more normal levels .Annex Example II
# 23
Solution to 2:
>
Because overall interest rates are low, the company must also deal with an
asymmetric risk separate and apart from the reallocation of its investment portfolio .
In other words, the insurer must alter its liability profile in order to minimize
potential adverse changes in its common equity capitalization . A spike up in interest
rates could result in a rise in surrenders of annuities during a time when asset
values are coming under pressure . Because the company is more concerned about
higher interest rate volatility than is reflected in current option prices, the insurer
might consider purchasing out -of -the -money puts on government securities
and/or purchasing swaptions with the right to be a fixed -payer/floating -
receiver . Sharp rises in rates would make both positions profitable(*) and offset
some of the burden of premature annuity surrenders . If time passes without any
substantial rise in interest rates, the cost of purchasing option protection would
detract from the incremental benefits from the proposed switch into higher yielding
securities
(*) A put option becomes valuable to the holder if prices of the underlying asset fall . A
swaption with the right to enter a swap paying fixed and receiving floating is
economically analogous to a put option on a bond . If rates rise, the swaption owner
has the right to receive a rising stream of floating payments in exchange for what will
have then become a stream of reasonably low fixed payments . The swaption contract
will have gained in value Annex Example III
# 24
>
Serena Soto is a risk management specialist with
Liability Protection Advisors . Trey Hudgens, CFO of
Kiest Manufacturing, enlists Sotos help him immunize a
$20 million portfolio of liabilities . The liabilities range
from 3.00 years to 8.50 years with a Macaulay duration
of 5.34 years, cash flow yield of 3.25 %, portfolio convexity
of 33 .05 , and basis point value (BPV/DV 01 ) of $10 ,505 .
Soto suggested employing a duration -matching strategy
using one of the three AAA rated bond portfolios
presented in Exhibit 1
>
Soto explains to Hudgens that the underlying duration -
matching strategy is based on the following three
assumptions :
> 1.
Yield curve shifts in the future will be parallel
> 2.
Bond types and quality will closely match those of
the liabilities
> 3.
The portfolio will be rebalanced by buying or
selling bonds rather than using derivatives Annex Example III
# 25
Exhibit 1: Possible AAA Rated Duration -Matching Annex Example III
# 26
1 Based on Exhibit 1, the portfolio with the greatest structural risk is :
A Portfolio A
B Portfolio B
C Portfolio C
2 Based on Exhibit 1, relative to Portfolio C, Portfolio B:
A has higher cash flow reinvestment risk
B is a more desirable portfolio for liquidity management
C provides less protection from yield curve shifts and twists
3 Sotos three assumptions regarding the duration -matching strategy indicate the
presence of :
A model risk
B spread risk
C counterparty credit risk Annex Example III
# 27
Solution to 1:
>
C is correct . Structural risk arises from the design of the duration -matching
portfolio . It is reduced by minimizing the dispersion of the bond positions .
With bond maturities of 1.5 and 11 .5 years, Portfolio C has a definite barbell
structure compared with those of Portfolios A and B, and it is thus subject to a
greater degree of risk from yield curve twists and non -parallel shifts . In
addition, Portfolio C has the highest level of convexity , which increases a
portfolios structural risk
Solution to 2:
>
B is correct . Portfolio B is a laddered portfolio with maturities spread more or
less evenly over the yield curve . A desirable aspect of a laddered portfolio is
liquidity management . Because there is always a bond close to redemption, the
soon -to -mature bond can provide emergency liquidity needs . Barbell portfolios,
such as Portfolio C, have maturities only at the short -term and long -term ends
and thus are much less desirable for liquidity management Annex Example III
# 28
Solution to 3:
>
A is correct . Soto believes that any shift in the yield curve will be parallel .
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 . A
non -parallel yield curve shift could occur, resulting in a mismatch of the
duration of the immunizing portfolio versus the liability