Chapter 16: Asset-liability management

Question 1

What are the principles of investment?

Answer 1

The principles of investments state that:

 Investments should be chosen that are appropriate for liabilities (nature, term, currency and uncertainty) and reflect risk appetite of investor

 Investments should be chosen to maximise returns

Principles of investment

 A provider should select investments that are appropriate to the:

 nature

 term

 currency, and

 uncertainty

of the liabilities, and

 the provider’s appetite for risk

 Subject to the above, investments should be selected so as to maximise the overall return on assets, where overall return includes both income and capital

Question 2

What is the key decision providers of financial benefits will need to make about the interaction between assets and liabilities?

Answer 2

Interaction between assets and liabilities

 Providers of financial benefits will invest contributions received for those benefits in order to deliver benefits

 Key decision: whether to invest so that expected cashflows from assets held match those from liabilities and degree to which such matching should be applied

 Matched strategy ideal to remove risks of assets performing poorly relative to liabilities

 Matching may be required by regulator

 Decision to match must be considered taking into consideration need to maximize investment returns – these objectives might conflict

 Matched strategy expected to result in lower returns than unmatched strategy

 Matching may also not be practical or possible – depending on available assets

 If decision taken to match, then optimal matched position will need to be determined

 Given uncertainties in future cashflows of different liabilities and possible uncertainties associated with some assets – difficult exercise

 Optimal matched position – the matched position that satisfies provider’s required degree of certainty in meeting the liabilities for least cost, taking into account regulatory requirements and other investment objectives

 If decision taken not to match, then additional capital will need to be held to cover possibility of insufficient assets to meet liabilities when they fall due

 Determination of how much extra capital will be needed is not trivial

 Additional capital (free assets) provides cushion against adverse market movements

 If correctly determined how much extra capital needed – then should be sufficient assets to meet liabilities when they fall due despite fall in market value of the assets (for example)

Question 3

How are liability cashflows identified?

Answer 3

Liability cashflows – identification

 For insurance companies, positive cashflows (premiums) are received before negative cashflows (claims and expenses) arise

 These are available for investment and will generate investment income – which is another positive cashflow

 Premium paid by policyholder might be used to cover immediate costs associated with setting up the insurance policy and remainder invested

 Investment returns will be earned on premium until further expenses or claims payments are paid out

 Where there is uncertainty about the amount or timing of cashflows – actuarial technique is to assign probabilities to amount and existence of a cashflow

 Probability that payment will take place could be estimated by looking at past results

Question 4

What are the points that need to be made when looking at cashflow scenarios?

Answer 4

Examples of cashflow scenarios

 Have clear understanding of:

 from which party’s viewpoint you are examining the cashflows

 what the main cashflows are

 whether cashflow is:

• positive or negative
• fixed or real
• known or unknown in amount
• known or unknown in timing and term
• the form of payments i.e. lump sum or regular

Question 5

What is the cashflow scenario for an annuity and how are liabilities matched?

Answer 5

Example 1: An annuity

 An annuity provides a series of regular payments in return for a single premium

 Conditions under which annuity payments will made will be clearly specified

 For an immediate annuity, payments are made as long as annuitant is alive

 Often a guaranteed period – e.g. 5 years for which payments will continue to be made or be commuted into lump sum even if annuitant dies

 Cashflows for investor will be initially negative (for purchase of annuity) followed by series of smaller regular positive cashflows throughout the annuitant’s lifetime

 Annuities cannot normally be discontinued – unlikely to be discontinuance payment

 From the perspective of annuity provider – initial positive cashflow followed by unknown number of regular known negative cashflows

 If annuity payments are specified to increase in line with index – the amount of regular negative cashflows will be unknown in monetary terms

 Cashflows will comprise of annuity instalments and provider’s expenses in administering the contract

 Number of future negative cashflows depends on how long annuitant lives

 Provider likely to invest the initial positive cashflow in bond market (negative cashflow) and will receive in return number of interest and capital payments (positive) – expected to match outgoings on expenses and annuity payments and leave some surplus cash as profit

 Providers may invest in both government and corporate bonds:

 Fixed-interest bonds – used to match level annuities and annuities increasing by fixed amounts

 Index-linked bonds – used to match index-linked liabilities

 Other investments e.g. commercial mortgages and swaps

Question 6

What is the cashflow scenario for a repayment loan and how are liabilities matched?

Answer 6

Example 2: A repayment loan (or mortgage)

 Repayment loan is repayable by series of amounts – each includes partial repayment of loan capital in addition to interest payments

 If interest rate is fixed – payments will be of fixed equal amounts, paid at regular known times

 Cashflows are like those for an annuity except that the number of cashflows will usually be fixed (rather than related to survival)

 May be added complications if interest rate is allowed to vary or if loan can be repaid early

 Possible that regular repayments could be specified to increase or decrease with time

 Such changes could be smooth or discrete

 Breakdown of each payment into interest and capital changes significantly over the period of the loan:

 1st repayment will consist almost entirely of interest and will provide very small capital repayment

 Final repayment will consist almost entirely of capital and have small interest content

 Particularly relevant when interest and capital are taxed differently

 Amount of loan outstanding will reduce throughout term of loan

 At start of contract entire loan will be outstanding and so interest part of payment is large and capital part small

 At end of contract the amount of the loan outstanding will be small and so interest due will also be small

Question 7

What does the net liability outgo consist of and what does the actual liability outgo depend on?

Answer 7

Liability cashflows – categorisation by nature

 Net liability outgo consists of:

  benefit payments

+ expense outgo

• Premium/contribution income

 In practice, actual liability outgo in any year or month depends on:

• the monetary value of each of constituents, and
• the probability of it being received or paid out

Question 8

How are the liability cashflows categorised by nature looking at the benefit payment component?

Answer 8

Benefit payments

1. Guaranteed in money terms

 Consists of benefit payments where amount is specified in money terms

2. Guaranteed in terms of an index of prices, earnings or similar

 Consists of benefits whose amount is directly linked to an index

 Index may not be nationally published one

 For example, benefits accruing under benefit scheme may increase in line with pay awards granted by sponsoring company

 Many of the cashflows that fit under this category may not be truly guaranteed

3. Discretionary

 Consists of any payments that are payable at the discretion of the provider

 E.g. future bonus payments under with-profit contracts or pension increases in excess of guaranteed amounts

4. Investment-linked

 Consists of benefits where amount is directly determined by value of investments underlying contracts

 E.g. unit-linked fund where liabilities are directly linked to value of underlying investments, or defined contribution pension scheme

Question 9

How are the liability cashflows categorised by nature looking at the expense outgo component?

Answer 9

Expense outgo

 Expense payments tend to increase over time

 Natural rate of increase is likely to fall somewhere between price and earnings inflation

 There are exceptional items which might be expenditures or cost savings

 For investment purposes, it is adequate to treat expenses as being linked to prices or earnings

 Hence, they can be included with benefit payments guaranteed in terms of an index of prices or similar

 Administrative expenses may be broadly real but rarely guaranteed to move in line with an index

Question 10

How are the liability cashflows categorised by nature looking at the premium/contribution income component?

Answer 10

Premium/contribution income

• Premium/contribution payments may:

 be fixed in monetary terms…

 …and hence can be thought of as negative benefit payments guaranteed in money terms; or

 Increase in line with an index…

 …and hence can be thought of as negative benefit payments guaranteed in terms of an index

• Existence of contracts or transactions where the client can vary amount of premium each year does not invalidate this

Question 11

Summarise how the liability outgo can be split by nature.

Answer 11

Summary

• We can therefore split the liability outgo (by nature) into four categories:

 guaranteed in money terms i.e.
benefit payments specified in money terms
minus premium/contribution income that is fixed in money terms

 guaranteed in terms of a prices index or similar i.e.

benefit payments linked to an index

PLUS, expense outgo that is real in nature

MINUS premium/contribution income that is linked to an index

 discretionary benefit payments

 investment-linked benefit payments

Question 12

How are assets selected by nature of liabilities, when liabilities are guaranteed in money terms?

Answer 12

Guaranteed in money terms

Pure matching

 Provider will want to invest so as to ensure that it can meet guarantees

 This means investing in assets which produce a flow of asset proceeds to match the liability outgo

 Match needs to be in terms of both the timing and amount of the liability outgo

 Will involve taking into account the term of liability outgo and probability of the payments being made to indicate term of corresponding assets

Approximate matching

 Except for certain types of liability – probably impossible in practice to find assets with proceeds that exactly match expected liability outgo

 Terms of available fixed-interest securities may be much shorter than corresponding liabilities – particularly with very long-term pension liabilities

 Even if suitable assets are available their price may prove off-putting due to increased demand

 Existence of options in either liabilities or assets also means that full cashflow matching cannot realistically be achieved

 Best match achieved by investing in high quality fixed-interest bonds of term suitable to match expected term of liability outgo

 Derivatives could be used to produce asset flows that match liability outgo

 Generally expensive and exact matching may not always be possible

Question 13

How are assets selected by nature of liabilities, when liabilities are guaranteed in terms of a price index?

Answer 13

Guaranteed in terms of a prices index or similar

 Most suitable match is likely to be index-linked securities (where available) ideally chosen to match expected term of liability outgo

 In their absence, substitute would be assets that are expected to provide real return e.g. equity-type investments

Question 14

How are assets selected by nature of liabilities, when we have discretionary benefits?

Answer 14

Discretionary benefits

 Main aim of provider will be to maximise these and hence the investment strategy should thus also aim to do that

 This means investing in assets that will produce highest expected return

 In theory, this suggest a great deal of investment risk is acceptable

 This is subject to provider’s appetite for risk and risk expectations of the client

Question 15

How are assets selected by nature of liabilities, when we have investment-linked liabilities?

Answer 15

Investment-linked

 Benefits guaranteed to extent that their value can be determined at any time in accordance with definite formula based on value of specified fund of assets or index

 Investment matching problems can be avoided by investing in same assets as used to determine benefits

 Replicating a market index may involve holding large number of small holdings and thus be too costly

 Companies might use CISs or derivative strategy to achieve this

Currency

 Liabilities denominated in particular currency should be matched by assets in that currency – reduce currency risk

Question 16

When is matching used and what are the key influences on the provider’s degree of mismatch?

Answer 16

Mismatching

 Look at maximising returns (involve degree of mismatching)

 Consider two key influences on provider’s decision on balance between risk and return:

1. the level of free assets
2. any (regulatory) constraints

Question 17

How do free assets allow for improved overall returns?

How does the level of free assets affect a provider’s decision to mismatch?

Answer 17

1. Free assets/surplus

 Existence of free assets or surplus means that provider can depart from matching strategies outlined above to improve overall return on its assets and thereby benefit its:

• clients – higher benefits or lower premium/contribution rates
• shareholders (if any) – higher dividends

 Almost always the case that assets with highest expected return also have highest variance of that return

Question 18

How do free assets affect the matching of guaranteed benefits?

Answer 18

Guaranteed benefits

 If assets supporting guaranteed benefits are invested to produce highest expected return without though to nature of liabilities – probability that asset proceeds will be inadequate to meet liabilities will be high

 If there are free assets – they can be used to make up shortfall in these circumstances

 If no free assets or not enough this approach can lead to insolvency

 So, where liabilities are fixed in money terms (guaranteed benefits) – variability in asset return can only be tolerated if there are free assets to act as cushion for variability

 But then what size of free assets is appropriate given specified variance of return

 Deterministic approach can be used to assess appropriate provision to cover mismatching of assets and liabilities:

• Assets are selected to match value of liabilities exactly
• Specified ‘time zero’ changes in value of these assets and economic factors – e.g. interest rates assumed, and value of assets and liabilities recalculated
• Difference (if value of assets is less than value of liabilities) is the provision required or amount of free reserves needed to set aside

Example

 Main technique used to determine how much free assets/surplus is needed to reduce probability of insolvency to acceptable level is same as that used to assess risk-based capital requirement against market risk

 Involves running stochastic simulation of markets in which funds are invested using economic scenario generator

 Each run will choose particular combo of funds for consideration

 Capital required to just prevent insolvency at any desired probability can be determined by inspecting the tails of the output from stochastic simulations

 Using free assets to maintain deliberately mismatched policy has to compete with other uses of free assets – financing new business growth or other new ventures

 Often means that opportunities to depart from matched policy for guaranteed liabilities are limited

 When allocating free assets to support mismatched investment policy – NB to take into account that investment in which the free assets are invested will also be affected by market value changes

Question 19

How do free assets affect the matching of discretionary benefits?

Answer 19

Discretionary benefits

 Could be argued that matching is irrelevant where there are discretionary benefits

 Since provider will want to invest in securities with highest expected return

 But although benefits are fully discretionary, beneficiaries will expect to receive something and moreover will have expectation as to a min level

 Provider will want to make use of some of surplus or limited matching strategy – to ensure that probability of discretionary benefits falling below particular level stay within acceptable limits

Question 20

How do free assets affect the matching of investment-linked benefits?

Answer 20

Investment-linked

 Could be argued that it is a reasonable use of free assets/surplus to mismatch investment-linked benefits if company can expect to achieve higher return

 If done any return achieved above that on matched assets will not accrue to beneficiaries of investment-linked contracts but to provider

 For many institutions matching considerations may outweigh return considerations

 In particular, for risk-averse providers who have chosen to offer benefits that are investment linked rather than guaranteed

 Uncommon for providers to mismatch investment-linked liabilities

 High-risk strategy and in many countries mismatching investment-linked benefits is disallowed by law or regulation

Question 21

How does the regulatory constraint affect a provider’s decision to mismatch?

Answer 21

2. Regulatory framework
   - May limit what provider may be able to do in terms of investment
   - The following controls may be implemented:

 restrictions on types of assets that provider can invest in

 restrictions on amount of any type of asset than can be taken into account for purpose of demonstrating solvency

 requirement to match assets and liabilities by currency

 restriction on max exposure to single counterparty

 custodianship of assets

 requirement to hold certain proportion of total assets in particular class e.g. government stock

 requirement to hold mismatching reserve

 limit on extent to which mismatching is allowed at all

Question 22

What are the forms of investment matching?

Answer 22

1. Pure matching
2. Liability hedging
3. Immunisation

Question 23

Discuss the pure matching approach to investment matching.

Answer 23

Pure matching

 Matching in purest form involves structuring the flow of income and maturity proceeds from assets so that they coincide precisely with net outgo from liabilities under all circumstances

 Requires sensitivity of timing and amount of asset proceeds and net liability outgo to be known with certainty and to be identical with respect to all facts

 Some liability cashflows may be difficult to match – complete or pure matching rarely possible

 Unless risk-free zero-coupon used rarely possible to achieve pure matching

 Close approximation to perfect match may be possible for certain life insurance products e.g. guaranteed income bonds

 Relative price of bonds chosen for matching may deter all but most dogmatic institutions

 Problem: for some funds term and size of liability may be such that complete matching is unattainable because suitable assets aren’t available

 Thus, in practice, matching usually means approximate matching

 Useful to view complete matching as benchmark position against which to judge investor’s asset allocation

Question 24

Discuss the liability hedging approach to investment matching.

Answer 24

Liability hedging

 Where assets are chosen in such a way as to perform in a similar way to the liabilities

 I.e. hedging against or matching all of unpredictable changes in liabilities that arise from unpredictable changes in factors that influence liability values

Approximate liability hedging

 In most situations hedging liabilities with respect to all factors that affect liabilities will not be possible

 Investor might try to hedge liabilities with respect to specific factors that affect liability values

 Familiar forms of hedging – matching by currency and consideration of real or nominal nature of liabilities when determining choice of assets

 These examples relate only to specific characteristics of liabilities – liability hedging aims to select assets that perform exactly like liabilities in all events

Full liability hedging

 Possible when considering unit-linked liabilities

 When choosing assets to hedge unit-linked liabilities – normal approach is to establish portfolio of assets + determine unit price by reference to value of asset portfolio + then use price to value units and hence liabilities

 Value of the liabilities is then implied by values of the assets

Question 25

Discuss the immunisation approach to investment matching.

Answer 25

Immunisation

 Investment of assets in such a way that the PV of assets less PV of liabilities is immune to general small change in rate of interest

Basic explanation of immunisation

 Purpose is same as that of matching

 I.e. to reduce the risk of failing to meet liabilities as they fall due, arising from change in investment conditions

 Might be used when pure matching is not possible

 For example, when investment income is initially greater than net liability outgo, then liabilities cannot be matched

 But they may be immunised

 Note that immunisation relates to ensuring that PV of assets is no less than that of liabilities

 Rather than matching dates and mounts of individual cashflows

 The conditions for immunisation are:

1. The PV of the liability-outgo and asset-proceeds are equal
2. The discounted mean term of the value of asset-proceeds must equal the discounted mean term of the value of the liability-outgo
   - The spread (or convexity) about the discounted mean term of the value of the asset-proceeds should be greater than the spread of the value of liability-outgo

Algebraic explanation of the conditions for immunisation

 We are concerned about the impact of changes in interest rate on V(A)-V(L)

 From the 1st condition for immunisation we know that 1st expression is zero (V(A)=V(L))

 From 2nd condition for immunisation we know that 2nd expression is zero

 From 3rd condition for immunisation we know that 3rd expression is positive – because assets have greater spread/convexity by term than liabilities

 So, if epsalon is small then all further terms become insignificant

 Thus, under the terms for immunisation, the value of assets exceeds the value of liabilities after change in interest rates

Question 26

What are the limitations of the immunisation theory?

Answer 26

The limitations of classical immunisation theory

 Immunisation is aimed at meeting fixed monetary liabilities – many investors need to match real liabilities, but the theory can be applied to index-linked liabilities by using index-linked bonds

• May be problems in practice due to time lag associated with indexation

 The possibility of mismatching profits as well as losses is removed apart from small second-order effect

• Rules out investment in assets with high expected but uncertain returns

 Theory relies upon small changes in interest rates – fund may not be protected against large changes

 Theory assumes flat yield curve and requires the same change in interest rates at all terms – in practice yield curve does changes shape from time to time

 In practice portfolio must be rearranged constantly to maintain the correct balance of equal discounted mean term & greater spread of asset proceeds

• This is because formulae for duration and convexity depend upon times to each payment – which are continuously changing
• Note this is not the case with pure matching where asset proceeds emerge as and when required to meet liability outgo

 Theory ignores dealing costs of a daily or even monthly rearrangement of assets

 Assets of suitably long discounted mean term may not exist

• Problem reduced by existence of zero-coupon bonds

 Timing of asset proceeds and liability outgo may not be known

• Formulae implicitly assume that date of all cashflows are known with certainty

Question 27

How is an asset-liability model used to determine the investment strategy?

Answer 27

Using a model to determine investment strategy

 Asset-liability model is tool to help determine what assets to invest in given particular objective

 For example, used to address the questions of:

• how fare from perfectly matched investment position an investor is able to move because of its free assets
• how well cashflows from a chosen set of assets match liability cashflows in range of future economic scenarios

 Investor’s objectives normally stated with reference to both assets and liabilities

 In setting investment strategy to control the risk of failing to meet objectives – method that considers the variation in assets simultaneously with variation in liabilities is required

 Done by constructing model to project the asset proceeds and liability outgo into the future

 Advantage – encourages investors to formulate explicit objectives

 Objectives should include quantifiable and measurable performance target, defined performance horizons and quantified confidence levels for achieving target

 Outcome of particular investment strategy is examined with model and compared with investment objectives

 Strategy adjusted in light of results obtained and process repeated until optimum strategy reached

Question 28

Modelling can either be deterministic or stochastic. What do the two methods entail and what are the pros and cons?

Answer 28

Modelling can either be deterministic or stochastic

 Deterministic model – parameter values are fixed and result of running model is a single outcome

 Need to carry out a number of re-runs of model based on different sets of assumptions to understand how robust the strategy is

 Stochastic model – at least on of parameters is assigned a probability distribution

 Model is run many times to generate distribution of outcomes

 Arguably most appropriate way of allowing for volatility and uncertainty underlying assets and liabilities

 Advantage – it encourages investors to formulate explicit objectives

 Objectives should include quantifiable and measurable performance target, defined performance horizons and quantified confidence levels for achieving target

 For financial institution – objectives might be specified in terms of results of valuation carried out at specified time in future

 In practice, likely to be feedback between the model output and setting of objectives

 Success of strategy monitored by means of regular valuations

 Valuation results compared with projections from modelling process and adjustments made to strategy to control level of risk accepted by strategy (if necessary)