16. Asset-liability management

Question 1

What are the two key principles of investment?

Answer 1

• A provider must select investments that are appropriate to the nature, term, currency, and uncertainty of liabilities and the provider’s appetite for risk
• Subject to the above – Investments should maximize overall return (both income and capital gain)

Question 2

What features need to be covered when asked to describe a cashflow?

6

Answer 2

• Direction
• Size
• Nature
• Term and timing
• Currency
• Certainty – timing + amount

Question 3

What are the cashflows on a single life immediate annuity from the perspective of the provider?

Answer 3

1. Single premium → positive initial lump sum
2. Annuity payments → regular series of negative cashflows
   * Timing → known
   * Amount → monetary or real terms
   * Term → unknown – lifetime of insured
3. Investment → initial negative cashflows – investment of premium
   * Series of positive cashflows = interest + capital payments
4. Expenses:
   * Initial lump sum negative cashflow → commission + setup expenses
   * Regular negative payments → admin of benefit payments
5. Expected to increase over time in line with wages/price inflation

Question 4

What are the cashflows of a term assurance from the perspective of the provider?

Answer 4

1. Premiums → regular series of positive cashflows
   * Timing is usually known in advance
   * Amount is usually fixed
   * Total term is unknown
   * A variation is a single premium contract
2. Benefit → a lump sum negative cashflow
   * Paid on death of the policyholder
   * Timing is unknown
   * Amount of sum assured is known
   * If survives term → no benefit cashflow
3. Investment
   * A series of positive cashflows of interest and capital
   * Negative cashflow when investments are purchased
4. Expenses
   * Initial lump sum negative cashflow to cover commission and setup expense
   * Regular negative cashflows → admin expense
   * Termination lump sum → negative cashflow payable on death → claims handling

Question 5

How do the cashflows from the perspective of the provider on a without-profit endowment assurance differ from those on a TA?

Answer 5

• Additional negative lump sum cashflow on maturity
  1. If the policyholder survives until the end of the term
  2. Amount will be known
• May be a lump sum negative cashflow if the policyholder surrenders
  1. Amount may or may not be known – depends on contract
• For a given sum assured → the premiums will be greater
• Investment income and gains would also be greater

Question 6

What are the cashflows of a repayment loan from the perspective of the provider?

Answer 6

1. Loan amount → initial negative cashflow equal to the amount of the loan
2. Interest and capital repayments → regular series of positive cashflows
   * Each payment = interest + capital
   * Capital component increases over the term
   * Interest component decreases over the term of the loan
   * Total amount may be fixed or variable
   * Or specified to increase or decrease
   * Timing and total term is usually known in advance unless it is paid early or a party defaults
3. Expenses
   * Initial lump sum negative cashflow to cover commissions and setup expense
   * Regular stream of negative cashflows → admin + collecting payments expected to increase in line with price or wage inflation

Question 7

How are the cashflows on an interest-only loan different from those of a repayment loan?

Answer 7

1. Interest-only → regular repayments only comprise interest
2. Interest may be fixed or variable
3. Additional lump sum positive inflow → capital repayment
   * Amount is known and equal to the initial loan amount
   * Timing is known = end of term
   * Unless borrower dies, repays early, or defaults

Question 8

What are the cashflows on a motor insurance contract from the perspective of the provider?

Answer 8

1. Premiums
   * Lump sum positive cashflow paid at the start of the year
   * Or a positive series of monthly cashflows paid throughout the year
   * Amount and timing are known unless endorsements are made or the policyholder defaults
2. Claims
   * Negative cashflows to cover admin
   * More than one claim payment may be made for the period of cover
   * Reporting or settling delays possible
   * Timing and amount are unknown
3. Investment
   * Series of positive cashflows from income and gains from investments
   * Negative cashflow when investments are purchased
4. Expenses
   * Initial negative cashflow → setup expenses + admin
   * Negative cashflows between claim reporting and settlement to cover claim expenses

Question 9

What is net liability outgo for a provider?

Answer 9

• Benefits (claims) + expenses – premium income/contribution

Question 10

What are the four types that liabilities can be divided into according to their nature?

Answer 10

• Guaranteed in money terms
• Guaranteed in terms of an index
• Discretionary (e.g. bonuses on with-profit contracts)
• Investment-linked (e.g. unit-linked liabilities)

Question 11

Where might expenses and premiums be categorized?

Answer 11

1. Expenses → tend to increase over time at a rate between price and earnings inflation → Guaranteed in terms of an index
2. Premiums/contributions → negative liabilities
   * Fixed in monetary terms → negative benefit payments guaranteed in monetary terms
   * Expected to increase in line with inflation → negative benefits guaranteed in terms of an index

Question 12

What is a good asset match for liabilities guaranteed in money terms?

5

Answer 12

• Conventional bonds of appropriate terms
• Exact match is unlikely → exact timing of A proceeds unlikely to match exactly with L outgo
• Available bonds may not be long enough in duration
• Bonds should be of high quality since the benefit is guaranteed
• Derivatives could be used → expensive + exact matching not always possible

Question 13

What is a good asset match for liabilities guaranteed in terms of an index?

2

Answer 13

1. Index-linked bonds at an appropriate term
   * May not be available and index may not be the same as liabilities
2. Equities and properties may provide a broad match

Question 14

What is a good match for discretionary liabilities?

Answer 14

• Assets expected to produce a high real yield → equity or property
• Consider policyholders’ expectations + provider’s risk appetite

Question 15

What is a good match for investment-linked liabilities?

3

Answer 15

• Provider can avoid any investment matching problems by investing in the same assets used to determine benefits
• If this requires tracking a market index (holding large numbers of small holdings) → it can be costly
• Use collective investment schemes to track the investment or a derivative strategy

Question 16

How Does the Existence of Free Assets (Surplus) Affect the Investment Strategy of an Insurance Company?

7

Answer 16

• Free assets provide a cushion against adverse investment experience.
• With free assets, the insurer can depart from a matched position and potentially achieve a higher overall return.
• Alternatively, insurers must use free assets to reduce risk and move to a more matched position.
• Sufficient assets are needed → Investing in high-risk assets and moving away from a matched position increases the risk of not meeting future obligations and insolvency.
• Competing uses of free assets:
  1. Writing new business
  2. Providing discretionary benefits
• Opportunities to depart from a matched position for guaranteed liabilities are limited.
• In some territories, mismatching of investment-linked liabilities may be restricted by law or regulation.

Question 17

How Can a Mismatching or Resilience Reserve Be Determined?

Answer 17

1. Deterministic Approach
   * Select assets (A) to exactly match liabilities (L).
   * Recalculate A and L values under stressed economic factors (e.g., interest rate changes).
   * If the stressed value of A < stressed value of L, the difference is the mismatching reserve that should be held.
2. Stochastic Approach
   * Perform stochastic simulation of market conditions using an economic scenario generator.
   * Inspect the tails of the stochastic output.
   * Determine the mismatch reserve as the amount of free assets needed to prevent insolvency at the desired probability level.

Question 18

How Might the Regulatory Framework Limit a Provider’s Investment Options?

Answer 18

TECH SCAM

• Types of assets a provider can invest in
• Extent to which mismatching is allowed
• Currency matching requirement
• Hold certain assets
• Single counterparty risk management→ restriction on maximum exposure
• Custodianship of assets (custodian holds investments and accounts for financial transactions)
• Amount of any one asset held to demonstrate solvency may be restricted
• Mismatching reserve requirements

Question 19

What is Pure Matching?

Answer 19

• Structuring the flow of income and maturity proceeds from assets so they coincide precisely (nature, timing, and currency) with net liability outgo under all circumstances.

Question 20

Why is Pure Matching Not Always Possible?

4

Answer 20

• Timing or amounts of asset proceeds or liability outgo may be uncertain.
• Pure matching may require excessive investment in certain securities → prohibitive.
• Pure matching may require zero-coupon bonds (ZCBs) with exact liability terms, which may not exist or be too expensive.
• Some liabilities are very long-term, and suitable dated assets may not exist.

Question 21

What is Liability Hedging?

Answer 21

• Assets are chosen to perform in a similar way to liabilities.
• Aims to select assets that behave exactly like liabilities in all scenarios.
• Usually not fully possible → Instead, liabilities are hedged against specific factors (e.g., currency matching, hedging unit-linked liabilities).

Question 22

What is Unit-Linked Liabilities Hedging?

Answer 22

• Establish a portfolio of assets and calculate the price of each unit from the asset values.
• Use this price to value units of liabilities, ensuring assets and liabilities remain aligned.

Question 23

What is Immunisation, basic explanation and conditions (3)?

Answer 23

• Investing assets so that the present value (PV) of assets and liabilities remains immune to small interest rate changes.
• Basic Explanation of Immunisation
  1. Used when pure matching is not possible → reduces risk of liabilities exceeding assets due to changing investment conditions.
  2. Assumes that securities exist with a uniform yield across all terms.
• Conditions for immunisation
  1. V(A) = V(L); PV(A) = PV(L)
  2. Discounted mean term (DMT) of asset proceeds = DMT of liability outgo: tV^tA_t/V^tA_t
  3. Spread/convexity of assets > Spread of liabilities
  t^2V^tA_t/V^tA_t

Question 24

What are the Limitations of Classical Immunisation Theory?

Answer 24

TAMARAI

• Timing of asset proceeds and liability outgoes may be uncertain.
• Aimed at meeting monetary liabilities, but investors may need to match real liabilities.
• Mismatch profits and losses are removed except for small second-order effects → limits investment in equities and property.
• Assumes a flat yield curve and the same interest rate change across all terms.
• Relies on small interest rate changes → may not protect against large changes.
• Assets with suitable long DMT may not exist.
  *

Question 25

What is an Asset-Liability Model (A-L Model)?

Answer 25

• Deterministic or stochastic model that helps institutional investors set an investment strategy.
• Defined by:
  1. Specified objective
  2. Measurable target
  3. Time horizon
  4. Confidence level
• A-L model projects future cashflows of both assets and liabilities and values them.
• The model is run iteratively to determine an optimal investment strategy.
• Should be dynamic → allows for correlation between A and L cashflows.

Question 26

How Can the Success of an Investment Strategy Be Monitored Using an A-L Model?

Answer 26

• Regular valuations.
• Compare valuation results with projections from the modelling process.
• Adjustments made to control the level of risk accepted by the strategy.
• Essentially, compare experience with expectations