Asset–Liability Management and Enterprise Risk

Introduction and Context

Asset–liability management (ALM) is the coordinated management of an institution’s assets, liabilities, capital, liquidity, and risk exposures. It is especially important for banks, insurance companies, pension funds, mortgage lenders, finance companies, and other institutions whose financial performance depends on transforming maturities, yields, currencies, or credit risk.

Fixed-income securities are central to ALM because both sides of an institution’s balance sheet are strongly influenced by interest rates, credit spreads, inflation, liquidity conditions, and refinancing costs. A bank may hold government bonds, mortgages, loans, and derivatives as assets while funding them with deposits, wholesale borrowings, bonds, and equity. An insurer may invest premiums in bonds while owing long-duration claims. A pension fund may hold fixed-income securities to meet contractual benefit payments over several decades.

The central ALM problem is not simply to maximize the yield on assets. It is to earn an acceptable risk-adjusted return while ensuring that contractual and expected obligations can be met under normal and adverse conditions. This requires integration of portfolio construction, funding strategy, capital planning, liquidity management, risk measurement, stress testing, governance, and managerial limits.

Learning Objectives

By the end of this chapter, readers should be able to:

1. Explain the purpose and scope of asset–liability management.
2. Measure duration, convexity, repricing gaps, and economic-value sensitivity.
3. Distinguish funding, liquidity, solvency, interest-rate, spread, and basis risk.
4. Apply ALM principles to banks, pension funds, and insurance companies.
5. Interpret value at risk (VaR), expected shortfall (ES), and stress-test results.
6. Design managerial risk limits and escalation procedures.
7. Evaluate the strengths and limitations of ALM models and governance systems.
8. Integrate fixed-income investment decisions with capital and liquidity strategy.

1. The ALM Framework

1.1 Balance-sheet perspective

An institution’s balance sheet can be represented as:

Assets generate cash inflows and include securities, loans, cash, receivables, and derivatives with positive value. Liabilities generate cash outflows and include deposits, insurance reserves, pension obligations, debt, and derivatives with negative value. Equity absorbs unexpected losses and provides the institution’s risk-bearing capacity.

ALM examines the timing, amount, currency, interest-rate characteristics, credit quality, and liquidity of these cash flows. A position is exposed when asset cash flows do not sufficiently match liability cash flows or when their values respond differently to market changes.

The fundamental economic objective is to preserve the institution’s ability to meet obligations while maintaining profitability and capital adequacy. This objective involves trade-offs. Longer-duration assets may offer higher expected yields but can lose substantial value when rates rise. Short-term funding may be inexpensive in stable markets but difficult or expensive to roll over during stress.

1.2 Main risk categories

These risks interact. For example, rising interest rates may reduce the market value of bond assets, increase deposit withdrawals, raise refinancing costs, and weaken borrowers’ credit quality simultaneously.

2. Interest-Rate Exposure and Duration Gaps

2.1 Present value and interest-rate sensitivity

For a fixed-income instrument with cash flow CF_t at time t, yield per period y, and n periods, its price is:

Here, P and CF_t are measured in currency units, y is the effective yield per period, and t is measured in periods. The formula assumes known cash flows and a constant yield applied to each period. It is less directly applicable to instruments with uncertain or path-dependent cash flows unless expected cash flows or a valuation model is used.

Macaulay duration is the present-value-weighted average time to receive the cash flows:

Macaulay duration is expressed in periods. Modified duration measures approximate percentage price sensitivity to a yield change:

For a small change in yield, the price change is approximately:

The negative sign reflects the inverse relationship between price and yield. ∆y must be expressed as a decimal, not in percentage points. For example, a 100-basis-point increase is ∆y = 0.01. The approximation is most reliable for small yield changes and instruments without significant embedded options.

2.2 Convexity

Duration is a first-order approximation. Convexity improves the estimate for larger yield changes because the price–yield relationship is curved:

where C is convexity, measured in squared periods. For a bond with known cash flows, convexity can be estimated as:

This expression assumes discrete compounding and fixed cash flows. Callable bonds, mortgage-backed securities, and other instruments with embedded options may exhibit negative or changing convexity, so option-adjusted models are usually required.

2.3 Portfolio duration and the duration gap

For a portfolio, dollar duration is more useful than duration alone:

where MV is market value and D_mod is modified duration. If the yield change is expressed as a decimal, the approximate value change is:

For an institution with interest-sensitive assets and liabilities, a simple economic-value duration gap is:

where D_A and D_L are the modified durations of assets and liabilities, and A and L are their market values. Equity-value sensitivity is approximately:

This simplified formula assumes a parallel yield-curve shift, identical rate units, no convexity effect, and stable cash flows. In practice, liabilities may not have observable market values, and their duration must be estimated from projected cash flows.

A positive duration gap means asset value is more sensitive than liability value. A rate increase then tends to reduce economic equity, whereas a rate decline tends to increase it. A negative gap produces the opposite directional effect. A zero gap does not eliminate risk because yield curves can twist, spreads can change, cash flows can be uncertain, and basis relationships can fail.

Worked Example: Economic-Value Sensitivity

Suppose a financial institution has assets valued at CU 500 million with modified duration 4.8 years. Its liabilities are valued at CU 460 million with modified duration 2.1 years.

If all relevant yields rise by 1 percentage point:

Thus, before considering convexity, credit spreads, taxes, or behavioral changes, economic equity falls by approximately CU 14.34 million. If opening equity is CU 80 million, the estimated percentage decline is 17.9%:

The result signals a material interest-rate exposure even though the institution may remain accounting-solvent under the scenario.

3. Repricing, Cash-Flow, and Key-Rate Analysis

3.1 Repricing gap

A repricing gap compares rate-sensitive assets and liabilities that reprice or mature within a specified time bucket:

where RSA_k is rate-sensitive assets and RSL_k is rate-sensitive liabilities in bucket k. A positive one-year gap means more assets than liabilities reprice within one year. If rates rise, asset income may increase more rapidly than liability expense, improving short-term net interest income. However, the result depends on repricing timing, spreads, floors, caps, and customer behavior.

Repricing analysis focuses on income over a horizon, whereas duration-gap analysis focuses on the market value of equity. They can produce different conclusions. An institution may benefit from rising short-term rates through higher net interest income while suffering a decline in the market value of long-term assets.

3.2 Key-rate duration

A parallel shift assumption can hide important exposures. Key-rate duration measures sensitivity to a change at a particular maturity point, such as two, five, ten, or thirty years. If KRD_j is key-rate duration for maturity node j, then a multi-node approximation is:

where ∆y_j is the change in the yield at node j. Key-rate analysis is useful for identifying steepening, flattening, and localized curve movements. It is particularly relevant to pension and insurance portfolios with long-dated liabilities.

3.3 Cash-flow matching and immunization

Cash-flow matching selects assets whose contractual cash flows cover liability payments in each relevant period. It reduces dependence on reinvestment assumptions but may be expensive and can create concentration risk.

Classical immunization seeks to protect the value of a liability-funded portfolio against small parallel rate changes by matching present value and duration. For a single liability date, the basic conditions are:

and

where subscripts A and L refer to assets and liabilities. Immunization is only approximate. It assumes parallel shifts, stable cash flows, adequate convexity, and periodic rebalancing. In practice, key-rate matching, scenario analysis, and liability-driven investment are more robust.

4. Funding and Liquidity Management

4.1 Funding structure

Funding decisions determine the stability, maturity, currency, and cost of liabilities. Common sources include retail deposits, institutional deposits, commercial paper, repurchase agreements, covered bonds, senior debt, subordinated debt, and equity.

A sound funding strategy considers:

• maturity concentration and refinancing calendars;
• secured versus unsecured funding;
• investor and depositor concentration;
• collateral availability and encumbrance;
• currency and interest-rate mismatches;
• contingent funding capacity;
• market access under stress; and
• reputational and regulatory constraints.

Funding cost is not merely the current interest rate. It includes credit spreads, liquidity premiums, issuance fees, collateral costs, hedging costs, and the option value of unused liquidity facilities.

4.2 Liquidity horizons and survival analysis

Liquidity risk is assessed through projected cash inflows, outflows, collateral calls, margin requirements, and available liquid assets. A liquidity gap for time bucket k can be written as:

A negative value indicates a shortfall in that bucket. Institutions often construct a survival horizon: the period for which they can meet obligations under a specified stress scenario without extraordinary external support.

Liquid assets should be assessed after haircuts, not at unadjusted market value. If a security has market value V and haircut h, its stress-usable value is:

The haircut should reflect price volatility, bid–ask spreads, market depth, collateral eligibility, and the possibility that many institutions sell simultaneously.

4.3 Liquidity and duration trade-offs

Long-duration bonds may provide useful liability matching but may be less liquid during market stress. Short-term government securities are often highly liquid but expose the institution to reinvestment and refinancing risk. A barbell or layered maturity strategy can combine liquidity reserves with longer-term return and matching objectives.

Liquidity buffers should not be treated as idle assets. Their size and composition should be determined by stress outflows, collateral needs, regulatory requirements, and management’s risk appetite. However, using the buffer for yield enhancement can undermine its purpose.

5. Pension and Insurance ALM

5.1 Pension liabilities

Defined-benefit pension plans promise benefits whose timing depends on employee demographics, salary growth, retirement behavior, longevity, and inflation. The present value of projected benefits is sensitive to discount rates and actuarial assumptions.

A pension fund can pursue liability-driven investment (LDI), in which assets are selected to hedge the economic drivers of liabilities. Long-duration government bonds, inflation-linked bonds, interest-rate swaps, and longevity hedges may be used. The objective is generally to control the funding ratio rather than simply maximize portfolio return.

The funding ratio is:

A funding ratio below 100% indicates that assets are less than measured liabilities under the selected assumptions. The ratio can fall because of falling discount rates, increased longevity, poor asset performance, or inflation changes.

5.2 Insurance liabilities

Insurers receive premiums and make uncertain future payments. Life-insurance liabilities may be long-duration and sensitive to mortality, lapse behavior, guarantees, and interest rates. Property and casualty liabilities may be shorter but exposed to catastrophe frequency, inflation, and claims development.

Insurance ALM must therefore combine deterministic cash-flow matching with stochastic modeling. Reinvestment risk, surrender options, policyholder behavior, and regulatory capital requirements can materially alter the optimal asset portfolio.

5.3 Surplus management

The relevant risk for a pension fund or insurer is often surplus risk:

A portfolio can lose value and still improve surplus if liabilities decline more. Conversely, an asset portfolio with positive absolute returns may underperform liabilities and reduce financial security.

6. Value at Risk, Expected Shortfall, and Stress Testing

6.1 Value at risk

Value at risk estimates a loss threshold over a specified horizon and confidence level. A one-day 99% VaR of CU 10 million means that, under the model and assumptions, the loss is expected to exceed CU 10 million on approximately 1% of comparable days.

VaR does not describe the average loss beyond the threshold. It is also sensitive to horizon scaling, distributions, correlations, liquidity assumptions, and historical sample selection.

For a linear portfolio with normally distributed returns, portfolio VaR can be approximated by:

where z_α is the standard-normal quantile for confidence level α, σ_P is portfolio return volatility over the horizon, and V is portfolio value. This formula assumes linear exposures, normal returns, stable volatility, and consistent units. It is often inadequate for bonds with options or portfolios exposed to jumps and illiquidity.

6.2 Expected shortfall

Expected shortfall at level α is the average loss conditional on losses exceeding VaR:

where L is the loss random variable. ES is generally more informative about tail severity and is coherent under broad conditions, although its estimation can be statistically noisy, especially with limited observations.

6.3 Historical, variance–covariance, and Monte Carlo methods

Historical simulation revalues the current portfolio using observed historical changes. It is transparent but dependent on the chosen period and may omit unprecedented events.

The variance–covariance approach estimates volatility and correlations, often assuming elliptical or normal returns. It is computationally efficient but weak for nonlinear instruments and fat-tailed risks.

Monte Carlo simulation generates scenarios from specified stochastic models and revalues the portfolio. It can capture nonlinearity and complex dependencies but introduces model, calibration, and computational risk.

6.4 Stress testing

Stress testing asks what could happen under severe but plausible conditions. Examples include:

• a rapid parallel increase in rates;
• a sharp fall in long-term rates;
• yield-curve steepening or inversion;
• widening corporate and sovereign spreads;
• a downgrade of major holdings;
• deposit outflows and wholesale-market closure;
• collateral haircuts and margin calls;
• inflation and currency shocks; and
• simultaneous market and operational disruption.

Reverse stress testing begins with an unacceptable outcome—such as a breach of minimum capital or a liquidity failure—and identifies the combination of events that could produce it. This is useful for discovering hidden concentrations and weak contingency plans.

Stress tests should combine market-value effects, income effects, behavioral responses, liquidity effects, capital impacts, and management actions. A static shock to bond prices is not a complete enterprise stress test.

7. Capital, Risk Appetite, and Managerial Limits

7.1 Capital as risk capacity

Capital is the primary buffer against unexpected losses. ALM decisions must therefore be evaluated against regulatory capital, internal economic capital, earnings capacity, and access to external funding.

A simplified capital ratio is:

The exact regulatory definition depends on jurisdiction and institution type. Market-value losses may affect capital immediately, gradually through accounting rules, or not at all under some classifications. Management must understand the difference between accounting presentation and economic exposure.

7.2 Risk appetite and limits

A risk appetite statement translates strategy into measurable boundaries. Limits may include:

• maximum duration gap;
• key-rate duration limits;
• net interest income sensitivity;
• economic-value-of-equity sensitivity;
• VaR and expected-shortfall limits;
• spread-duration and credit-concentration limits;
• minimum liquidity coverage and survival horizon;
• maximum maturity mismatch;
• foreign-currency open positions;
• collateral and encumbrance limits; and
• stress-loss and capital-consumption limits.

Effective limits have an owner, measurement frequency, escalation threshold, breach protocol, and documented remediation process. A limit is not effective if data arrive too late or if exceptions are routinely approved without independent challenge.

7.3 Governance and the three lines of defense

A practical governance model includes:

1. First line: business and treasury managers who own positions and risks.
2. Second line: independent risk management that sets methodology, monitors limits, and challenges decisions.
3. Third line: internal audit that evaluates controls, data, models, and governance.

An asset–liability committee (ALCO) typically reviews funding, liquidity, interest-rate risk, capital, hedging, balance-sheet strategy, and stress tests. ALCO minutes should record decisions, assumptions, dissenting views, and follow-up actions.

8. Worked Integrated Application: Illustrative Bank Case

Background

The following is a fictional illustrative case. Meridian Commercial Bank has assets of CU 1.2 billion and liabilities of CU 1.1 billion. Its assets include mortgages, government bonds, and corporate loans. Funding consists of retail deposits, term deposits, and wholesale borrowings. Equity is CU 100 million.

Problem

The bank’s assets have an average modified duration of 4.6 years, while liabilities have an estimated duration of 1.9 years. Management is considering purchasing CU 100 million of ten-year corporate bonds with modified duration 7.2 years to improve portfolio yield. The investment would be funded by three-year wholesale debt with duration 2.6 years.

Analysis

Before the proposed transaction, the approximate duration gap is:

After the transaction, asset value becomes CU 1.3 billion and liabilities become CU 1.2 billion. Approximate asset dollar duration is:

The additional liability dollar duration is:

Therefore:

A 1% parallel increase in rates would reduce economic equity by approximately CU 38.9 million after the transaction, compared with CU 34.3 million before it. The incremental exposure is approximately CU 4.6 million for the same shock.

The yield pickup must be compared with expected spread losses, capital charges, liquidity costs, and the bank’s risk limit. If corporate spreads widen by 150 basis points and the bond’s spread duration is 6.5 years, the approximate price effect from spread widening alone is:

On CU 100 million, this is approximately CU 9.75 million before convexity and default losses. The combined rate and spread scenario could therefore be materially larger than the rate-only estimate.

Approach and solution

ALCO should not approve the purchase solely because its coupon exceeds current funding cost. A complete decision would:

• compare the bond’s total expected return with its duration and spread risk;
• assess liquidity, concentration, rating migration, and capital treatment;
• evaluate whether the bond’s cash flows improve or worsen liability matching;
• consider an interest-rate hedge, such as a receive-fixed/pay-floating or pay-fixed/receive-floating swap, depending on the exposure;
• test parallel, steepening, spread-widening, and funding-stress scenarios;
• determine whether the transaction breaches economic-value or stress-loss limits; and
• identify the exit strategy if liquidity deteriorates.

If the objective is yield enhancement rather than liability matching, management may reduce the position size, use shorter duration, diversify issuers, or hedge a portion of rate exposure. If the objective is strategic carry, the bank should recognize that carry trades can perform well in normal markets while producing large losses during funding or spread shocks.

Outcome

Assume ALCO approves only CU 60 million, requires a maximum issuer concentration, and hedges part of the duration exposure. It also raises the liquidity haircut applied to the bond and adds a spread-widening trigger to the monitoring dashboard. The result is a lower expected yield than the original proposal but a more acceptable impact on capital, liquidity, and stress losses.

Learning points

1. Asset yield is not equivalent to risk-adjusted return.
2. Funding duration matters as much as asset duration.
3. Rate risk, spread risk, and liquidity risk can reinforce one another.
4. A hedge may reduce one risk while introducing basis, collateral, or counterparty risk.
5. ALCO decisions require both quantitative analysis and managerial judgment.

9. Limitations, Technology, and Contemporary Practice

ALM models are only as reliable as their assumptions and data. Common weaknesses include incorrect behavioral assumptions for non-maturing deposits, unstable prepayment models, insufficient tail scenarios, stale prices for illiquid securities, and failure to model management actions realistically.

Deposit balances may be modeled as stable and long-duration even though customers can withdraw funds quickly. Mortgage cash flows may change when refinancing incentives change. Insurance policyholders may surrender contracts when market conditions shift. These behaviors create optionality that simple duration measures cannot capture.

Technology supports real-time balance-sheet dashboards, scenario engines, automated limit monitoring, and high-frequency liquidity projections. Machine-learning methods may improve forecasting of prepayments, withdrawals, or claims, but they do not eliminate model risk. AI systems require explainability, validation, protection against data drift, controls over training data, and human accountability. A model that predicts behavior accurately in ordinary conditions may fail precisely when the institution most needs it.

Contemporary ALM practice increasingly combines:

• market-value and earnings-based measures;
• deterministic and stochastic scenarios;
• climate and transition-risk analysis where material;
• intraday liquidity monitoring;
• integrated capital and liquidity stress testing;
• collateral optimization; and
• continuous model validation and independent challenge.

Ethically, management should avoid exploiting information asymmetries, concealing liquidity vulnerabilities, or designing compensation that rewards short-term yield while transferring tail risk to depositors, policyholders, pension beneficiaries, taxpayers, or future shareholders. Governance should ensure that risk disclosures are understandable and not technically accurate but economically misleading.

Best-Practice Checklist

A mature ALM framework should:

1. Define risk appetite in quantitative and qualitative terms.
2. Maintain reliable, timely, reconciled balance-sheet data.
3. Measure both earnings sensitivity and economic-value sensitivity.
4. Use key-rate, spread, basis, optionality, and liquidity analysis.
5. Revalue positions under severe but plausible scenarios.
6. Include behavioral assumptions and validate them regularly.
7. Link limits to capital, liquidity, and funding capacity.
8. Distinguish risk ownership from independent oversight.
9. Document model limitations and management actions.
10. Test contingency funding plans through realistic exercises.
11. Escalate limit breaches promptly and record remediation.
12. Review strategy when market structure, regulation, or liabilities change.

Chapter Summary

Asset–liability management integrates fixed-income investment decisions with funding, liquidity, capital, and enterprise risk. Its central purpose is to preserve the institution’s ability to meet obligations while achieving an acceptable risk-adjusted return.

Duration and dollar duration provide first-order measures of interest-rate sensitivity, while convexity improves estimates for larger yield movements. Duration gaps compare the sensitivity of assets and liabilities, but they do not capture yield-curve twists, credit spreads, basis risk, optionality, or liquidity effects. Repricing gaps focus on income sensitivity, whereas economic-value measures focus on market-value changes in equity.

Cash-flow matching and immunization are important tools for pension and insurance liabilities, but they require assumptions about discount rates, inflation, longevity, policyholder behavior, prepayments, and reinvestment. Funding strategy must consider maturity, concentration, collateral, market access, and stress refinancing costs.

VaR summarizes a modeled loss threshold, while expected shortfall measures the average loss in the tail beyond that threshold. Neither substitutes for stress testing. Effective stress tests integrate market values, earnings, liquidity, capital, behavioral responses, and management actions.

Finally, ALM is a governance discipline as much as a quantitative one. Clear risk appetite, independent oversight, reliable data, model validation, ALCO decision-making, and enforceable limits are essential. The most important managerial question is not whether a portfolio earns yield in normal conditions, but whether the institution remains solvent, liquid, and strategically capable when conditions deteriorate.

Key Terms

Asset–liability management: Coordinated management of assets, liabilities, capital, liquidity, and related risks.

Duration gap: Difference between the dollar duration of assets and liabilities.

Macaulay duration: Present-value-weighted average time to receive a security’s cash flows.

Modified duration: Approximate percentage price sensitivity to a change in yield.

Dollar duration: Market value multiplied by modified duration.

Convexity: Measure of the curvature of the price–yield relationship.

Repricing gap: Rate-sensitive assets minus rate-sensitive liabilities within a time bucket.

Key-rate duration: Sensitivity to a yield change at a particular maturity point.

Immunization: Strategy designed to protect a portfolio’s value against specified interest-rate changes.

Cash-flow matching: Structuring asset cash flows to cover liability payments.

Liability-driven investment: Investment approach centered on the behavior and risks of liabilities.

Funding risk: Risk that liabilities cannot be refinanced at an acceptable cost.

Liquidity risk: Risk of being unable to meet obligations without unacceptable loss.

Spread risk: Risk of loss from changes in credit or liquidity spreads.

Basis risk: Risk that a hedge and the exposure do not respond identically.

Value at risk: Modeled loss threshold at a specified confidence level and horizon.

Expected shortfall: Average loss conditional on exceeding a specified VaR threshold.

Stress testing: Analysis of portfolio and institutional outcomes under severe scenarios.

Risk appetite: The amount and type of risk an institution is willing to accept.

Asset–liability committee: Governance body responsible for balance-sheet and ALM decisions.

Review Questions

Short Answer Questions

1. What is the principal objective of asset–liability management?
2. How does modified duration differ from Macaulay duration?
3. What does a positive duration gap imply about the effect of rising interest rates on economic equity?
4. Why can a liquidity haircut be necessary when valuing liquid assets under stress?
5. What information does expected shortfall provide that VaR does not?

Long Answer Questions

1. Explain how duration, convexity, repricing gaps, and key-rate durations complement one another in measuring interest-rate risk.
2. Discuss the major funding and liquidity risks faced by a bank that relies heavily on short-term wholesale funding.
3. Explain how liability-driven investment can be applied to a defined-benefit pension plan.
4. Compare historical simulation, variance–covariance VaR, and Monte Carlo simulation.
5. Describe the governance responsibilities of an asset–liability committee and the three lines of defense.

Analytical / Application Questions

1. An institution has CU 800 million of assets with duration 5.0 years and CU 740 million of liabilities with duration 2.4 years. Estimate the change in economic equity from a 75-basis-point parallel rate increase. State your assumptions.
2. Design a stress-testing program for an insurer exposed to long-duration government bonds, corporate bonds, policyholder surrenders, and collateral calls. Identify at least five linked scenarios.
3. A bank’s portfolio has a positive duration gap but a negative one-year repricing gap. Explain how both conditions can exist and evaluate the implications for net interest income and economic value under rising rates.

Multiple Choice Questions with Answers

Question 1

Which statement best describes the primary objective of asset–liability management?

A. Maximize the coupon yield of the asset portfolio regardless of funding conditions

B. Coordinate assets, liabilities, capital, and liquidity to meet obligations at acceptable risk

C. Eliminate every possible change in market value

D. Replace all fixed-income assets with cash

Correct Answer: B. Coordinate assets, liabilities, capital, and liquidity to meet obligations at acceptable risk

Question 2

A bond has modified duration 6.0 years. Approximately what is its percentage price change for a 50-basis-point increase in yield, ignoring convexity?

A. −0.30%

B. −3.00%

C. +3.00%

D. +0.30%

Correct Answer: B. −3.00%

Question 3

If asset dollar duration is CU 2,400 million-years and liability dollar duration is CU 1,900 million-years, what is the approximate equity impact of a 1% parallel rate increase?

A. Gain of CU 5 million

B. Loss of CU 5 million

C. Gain of CU 50 million

D. Loss of CU 50 million

Correct Answer: D. Loss of CU 50 million

Question 4

Which measure focuses most directly on sensitivity to a yield change at a specific maturity point?

A. Key-rate duration

B. Funding ratio

C. Recovery rate

D. Liquidity haircut

Correct Answer: A. Key-rate duration

Question 5

A security with market value CU 20 million is subject to a 15% liquidity haircut. What is its stress-usable value?

A. CU 3 million

B. CU 17 million

C. CU 20 million

D. CU 23 million

Correct Answer: B. CU 17 million

Question 6

What is a principal limitation of a simple duration gap?

A. It cannot be used for any fixed-income instrument

B. It assumes that liabilities have no cash flows

C. It may fail to capture yield-curve twists, optionality, and spread changes

D. It measures only credit default probabilities

Correct Answer: C. It may fail to capture yield-curve twists, optionality, and spread changes

Question 7

Expected shortfall at a specified confidence level is best defined as:

A. The smallest daily loss in the sample

B. The average loss conditional on losses exceeding VaR

C. The average portfolio return

D. The maximum historical asset value

Correct Answer: B. The average loss conditional on losses exceeding VaR

Question 8

Which scenario is most clearly a liquidity stress scenario?

A. A stable yield curve with unchanged funding access

B. A decline in accounting depreciation expense

C. Wholesale funding markets close while deposit outflows accelerate

D. A bond’s coupon payment occurs as scheduled

Correct Answer: C. Wholesale funding markets close while deposit outflows accelerate

Question 9

In a defined-benefit pension plan, liability-driven investment primarily seeks to:

A. Maximize equity exposure without regard to liabilities

B. Match or hedge the economic drivers of promised benefits

C. Avoid holding any long-duration assets

D. Use only short-term deposits

Correct Answer: B. Match or hedge the economic drivers of promised benefits

Question 10

Which governance arrangement provides independent challenge to business risk-taking?

A. The first line alone

B. The second line of risk management

C. The trading desk’s sales function

D. External borrowers

Correct Answer: B. The second line of risk management