Market, Foreign-Exchange and Credit-Spread Risk

Introduction and context

Treasury risk management concerns the possibility that changes in financial-market prices or rates will reduce a bank’s earnings, capital, liquidity, or solvency. The most important market-risk categories for a banking treasury are interest-rate risk, foreign-exchange (FX) risk, and credit-spread risk. They are distinct but interconnected: an exchange-rate movement may change the value of a foreign-currency bond; a spread widening may occur alongside a rise in risk-free rates; and hedging one risk can unintentionally create another.

A modern treasury therefore moves through four linked stages: identify positions, measure sensitivities and tail losses, establish limits, and manage or hedge exposures. No single metric is sufficient. Notional position measures scale, sensitivity measures first-order exposure, value at risk (VaR) describes a selected loss percentile, expected shortfall (ES) measures the average loss beyond that percentile, and stress testing examines severe but plausible scenarios that statistical models may not capture.

Learning objectives

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

1. Distinguish market, FX, interest-rate and credit-spread risk.
2. Calculate position-based sensitivities, duration-based exposures, FX exposures, VaR and ES.
3. Explain historical, parametric and Monte Carlo measurement approaches.
4. Design risk limits and interpret limit utilisation.
5. Evaluate hedge effectiveness and residual basis, model and liquidity risks.
6. Use stress testing and scenario analysis in treasury decisions.

1. Risk taxonomy and the treasury balance sheet

Market risk is the risk of loss from adverse movements in market variables. Interest-rate risk arises from changes in benchmark yields, swap rates or policy rates. FX risk arises when assets, liabilities, commitments or trading positions are denominated in different currencies. Credit-spread risk arises when the additional yield demanded for bearing credit or liquidity risk changes, even if the risk-free yield curve is unchanged.

Treasury exposures should be classified by instrument, currency, maturity, repricing date, cash-flow type, accounting treatment, legal entity and portfolio purpose. A bank may hold a corporate bond both as an investment and as a hedge for deposit duration; risk measurement must reflect the economic exposure rather than merely the accounting label.

A useful decomposition for a bond yield is:

where y is the observed yield, r is the relevant risk-free or benchmark yield, and s is the credit or liquidity spread. For small changes, the price change can be decomposed into rate and spread effects:

Here P is price, D_r is rate duration, D_s is spread duration, and ∆r and ∆s are changes expressed as decimals. The approximation is first-order and is most reliable for small movements and instruments with reasonably stable cash flows.

2. Position and sensitivity measures

2.1 Interest-rate position

A simple position report lists the present value of assets and liabilities by repricing bucket. The difference between rate-sensitive assets and liabilities indicates a repricing gap, but gap analysis alone ignores market value, timing within buckets and embedded options.

For a fixed-rate bond, modified duration is the percentage price sensitivity to a small change in yield:

where D_mod is modified duration in years, D_Macaulay is Macaulay duration in years, y is annual yield as a decimal, and m is the number of coupon-compounding periods per year. Under a parallel yield change:

For a portfolio, dollar duration or DV01 is often more operationally useful:

DV01 is the approximate currency loss from a one-basis-point increase in yield, assuming a linear response. A basis point is 0.0001, or 0.01 percent. For multiple curve tenors, key-rate duration measures sensitivity to a movement at one maturity while other key rates are held constant. This is superior to a single duration when the yield curve can twist, steepen or flatten.

Convexity improves the approximation for larger rate movements:

where C is convexity, measured in years squared. The formula assumes a sufficiently smooth price-yield relationship and does not fully capture callable or otherwise path-dependent instruments.

Worked example: rate sensitivity

A bond portfolio is worth CU 50 million and has modified duration of 4.2 years. If the relevant yield rises by 25 basis points, the estimated price change is:

The estimated loss is CU 525,000. If the portfolio’s convexity is 28, the convexity adjustment is:

Thus the second-order estimate is a loss of approximately CU 520,625. The positive adjustment reflects the normal positive convexity of a plain bond.

2.2 Foreign-exchange position

FX exposure exists when the value of assets, liabilities, revenues, expenses or capital changes with an exchange rate. Treasury distinguishes transaction exposure, translation exposure and economic exposure. Regulatory and internal limits usually focus on open positions, while strategic planning also considers longer-term economic effects.

If a bank is long foreign currency—holding more foreign-currency assets than liabilities—a depreciation of that currency generally causes a loss measured in the domestic currency. For a domestic-currency value V of a foreign-currency position and a domestic-currency price of foreign currency S, a small percentage exchange-rate movement gives:

The sign is determined by whether the position is long or short. Net open position reports must include spot, forward, swap, option delta and relevant off-balance-sheet commitments, subject to the bank’s policy and applicable regulation.

For an FX option, delta is not enough when the exposure is material. Gamma, vega and volatility-surface risk may become significant, particularly during market stress. Cross-currency swaps also create basis risk because the cross-currency basis may move independently of the underlying interest-rate curves.

2.3 Credit-spread position

Credit-spread exposure is commonly measured using spread duration, spread DV01 and scenario repricing. Spread duration estimates the percentage price response to a change in credit spread, holding the risk-free curve constant. A credit bond can therefore lose value even when government yields fall, if its spread widens sufficiently.

Spread risk includes issuer, sector, rating-transition, recovery, liquidity and basis components. A portfolio with low aggregate spread duration may still have substantial concentration in one issuer or industry. Limits should therefore combine sensitivity measures with name, sector, rating, maturity and liquidity constraints.

3. Value at Risk and expected shortfall

3.1 Value at Risk

VaR is a statistical estimate of the loss threshold that will not be exceeded over a specified holding period at a specified confidence level. For example, one-day 99% VaR of CU 10 million means that, under the model and assumptions, the loss should exceed CU 10 million on approximately 1% of comparable days. It does not mean that the maximum possible loss is CU 10 million.

VaR depends on four choices: portfolio definition, risk-factor mapping, holding period and confidence level. It may be reported as absolute loss or loss relative to expected profit. The latter requires careful treatment of expected carry and valuation conventions.

3.2 Parametric VaR

For a portfolio with linear exposures and normally distributed risk-factor changes, parametric VaR is:

where VaR_α is the loss quantile at confidence level α, z_α is the corresponding standard-normal quantile, σ_P is one-period portfolio standard deviation in currency units, and h is the number of periods in the horizon. The square-root-of-time rule assumes independent, identically distributed changes and is not reliable for autocorrelated, nonlinear or stressed markets.

For exposures represented by a vector w and risk-factor covariance matrix Σ,

The matrix must use consistent units—for example, all rate changes in decimals or all in basis points. Correlations are especially important: diversification reduces VaR when exposures do not move perfectly together, but correlations may rise sharply during crises.

3.3 Historical and Monte Carlo VaR

Historical simulation revalues the current portfolio using previously observed risk-factor changes. It preserves empirical non-normality but assumes the historical sample is relevant and sufficiently long. Monte Carlo simulation generates risk-factor scenarios from specified distributions and correlation structures, then revalues the portfolio. It is flexible but model-intensive.

A major distinction is between full revaluation and risk approximation. Delta-normal methods use linear sensitivities; delta-gamma methods add curvature; full revaluation reprices instruments under each scenario. Options, callable bonds and structured products generally require full or carefully validated nonlinear revaluation.

3.4 Expected shortfall

At confidence level α, expected shortfall is the expected loss conditional on loss being at or beyond the VaR threshold:

where L is the loss random variable. For a continuous loss distribution, ES is also the average of VaR over all confidence levels from α to 1:

ES provides information about tail severity that VaR omits. It is generally more sensitive to extreme observations, estimation error and model assumptions. In empirical samples, the calculation must specify how observations at the quantile boundary are weighted.

Worked example: historical VaR and ES

Suppose ten equally likely one-day portfolio losses, in CU million, are: 0.2, 0.4, 0.5, 0.7, 0.8, 1.0, 1.2, 1.5, 2.0 and 3.0. At a simplified 80% confidence level, the worst 20% consists of the two largest losses. VaR is therefore CU 2.0 million under this empirical convention, while:

The example is intentionally small and should not be treated as a production estimate. In practice, interpolation, a much larger sample and treatment of volatility clustering are required.

4. Stress testing and scenario analysis

VaR and ES are generally calibrated to ordinary historical or modelled variation. Stress testing asks what happens under severe but plausible conditions, including events absent from the sample. Scenarios may be historical, hypothetical, reverse stress tests, or sensitivity shocks.

A coherent stress test specifies the shock, valuation date, risk-factor relationships, management actions and interpretation. Examples include a parallel 300-basis-point rate rise, a sharp yield-curve steepening, a 15% currency depreciation, a 200-basis-point corporate spread widening, simultaneous market illiquidity and collateral calls, or a sovereign downgrade.

Stress results should be expressed in earnings, economic value, capital, liquidity and collateral terms. A scenario that produces a manageable market-value loss may nevertheless create a liquidity crisis if it triggers margin calls or reduces the value of collateral. Reverse stress testing begins with a failure outcome—such as a capital or liquidity breach—and identifies combinations of shocks capable of producing it.

5. Limits and governance

A risk appetite statement translates board-approved tolerance into measurable constraints. Common limits include:

Limit design must address gross and net positions, intraday versus overnight exposure, legal-entity aggregation, data cut-off, breaches, exceptions and escalation. A limit is not a target. Utilisation should be calculated consistently, for example:

A breach should trigger documented notification, independent review and a decision to reduce, hedge, obtain temporary approval or revise the limit through the proper governance process. Repeated temporary exceptions indicate weak risk appetite design rather than successful management.

The first line—treasury and trading—owns exposures. The second line—independent risk management—sets methodology, challenges assumptions and monitors limits. Internal audit provides third-line assurance. The asset-liability committee (ALCO) reviews structural exposures, hedge strategy, stress results and capital or liquidity implications. Model validation, valuation control and data governance are essential supporting functions.

6. Hedging and effectiveness

Hedges may use government securities, interest-rate swaps, futures, forward-rate agreements, FX forwards, currency swaps, options, credit default swaps or credit-index products. The choice depends on exposure, liquidity, basis risk, accounting treatment, collateral terms and counterparty risk.

A hedge is effective when it materially offsets the targeted risk under defined conditions. Effectiveness should be judged economically, not solely by whether accounting volatility is reduced. Important sources of residual risk include:

• Basis risk: the hedge and exposure respond differently to benchmark, tenor, currency or issuer movements.
• Curve risk: a hedge at one maturity does not offset a nonparallel curve movement.
• Gap risk: cash-flow timing differs between the hedge and the underlying item.
• Option risk: delta changes as the market moves; gamma and vega remain.
• Liquidity and funding risk: collateral or margin requirements create cash outflows.
• Counterparty and settlement risk: the hedge provider may default or settlement may fail.
• Model risk: valuation, volatility, correlation or recovery assumptions may be wrong.

A simple ex post hedge-effectiveness ratio can compare the change in hedging-instrument value with the opposite change in the hedged exposure:

where ∆V_H is the change in hedge value and ∆V_E is the change in exposure value. A ratio near 1 may indicate good offset for the observed period, but it is not proof of future effectiveness. Regression-based analysis can estimate the relationship:

The slope, residual variance, stability through time and performance under stress should all be examined. Accounting hedge documentation may impose additional formal requirements; economic and accounting effectiveness should not be conflated.

7. Integrated case: Meridian Bank treasury

This is an illustrative case. Meridian Bank reports in domestic currency and has the following exposures in its banking book: a CU 50 million fixed-rate bond portfolio with duration 4.2; a USD 20 million net long position at an exchange rate of CU 83 per USD; and a corporate-bond portfolio worth CU 30 million with spread duration 3.5.

Problem

Management wants to estimate first-order losses under three separate shocks: a 25-basis-point rate increase, a 10% depreciation of the domestic currency against USD, and a 100-basis-point spread widening. It also wants a control response.

Analysis

The rate shock produces approximately:

The domestic value of the USD position is:

Because the bank is long USD, a 10% USD depreciation produces an approximate loss of:

The spread shock produces:

These are separate first-order shocks, not a joint forecast. The very large FX loss demonstrates why currency units and position signs must be checked carefully. If the USD position was intended to be USD 20 million but the bank’s reporting system stored CU 20 million, the risk report would be materially wrong.

Approach and solution

ALCO could approve a USD forward to reduce the net long position, subject to counterparty, collateral and roll-over risk. It could use an interest-rate swap or futures position to reduce DV01, while recognising basis and curve risk. Spread duration could be reduced through bond sales, credit-index hedges or issuer diversification. The risk function should then run joint stress scenarios, including rate rise plus spread widening plus currency depreciation, rather than simply adding or netting unrelated standalone results.

Outcome and learning points

The case shows that exposure size alone is not enough: duration and spread duration convert market shocks into value changes, while FX exposure requires explicit currency conversion. It also shows why a hedge can reduce one metric but increase another. For example, a currency forward may create collateral liquidity needs and counterparty exposure. The bank should therefore monitor market value, VaR/ES, stress loss, liquidity, capital and hedge effectiveness together.

8. Limitations, technology and contemporary practice

Risk models are vulnerable to nonstationarity, regime changes, missing data, stale prices, poor correlations, liquidity discounts and procyclical behaviour. VaR may understate tail losses when distributions are fat-tailed; ES may be statistically unstable because it relies on fewer extreme observations. Duration may fail for callable instruments, mortgage portfolios and products with behavioural optionality. Stress tests are only as credible as their scenarios and governance.

Technology improves risk aggregation through real-time positions, automated data lineage, scenario engines and full-revaluation platforms. Machine-learning methods may assist anomaly detection, volatility forecasting or data-quality controls, but they do not eliminate the need for economic interpretation, explainability, validation and conservative overlays. AI-generated risk signals should be independently tested for drift, bias, leakage and unstable relationships. Human accountability remains essential for limit exceptions and hedge decisions.

Contemporary practice increasingly combines regulatory capital measures with internal economic-risk measures, climate and transition scenarios, intraday monitoring, central clearing and collateral analytics. Model inventories, challenger models, back-testing, P&L attribution and independent price verification are central to sound governance. A mature treasury treats measurement as a decision system—not as a single number produced by a model.

Chapter Summary

Market, FX and credit-spread risk arise from changes in rates, exchange rates and risk premia. Position reports establish scale; duration, DV01, key-rate duration and spread duration translate shocks into approximate value changes. FX risk requires careful treatment of currency direction and domestic-currency conversion. VaR estimates a loss quantile, whereas expected shortfall measures the average loss in the tail; both depend on data, horizon, confidence level and modelling assumptions. Stress testing complements statistical measures by examining severe and plausible scenarios, including joint shocks and liquidity effects. Effective governance combines limits, independent oversight, model validation, escalation and ALCO review. Hedging reduces targeted exposure but introduces basis, liquidity, counterparty, model and residual risks. Sound treasury management therefore integrates sensitivities, VaR, ES, stress testing and qualitative judgement.

Key Terms

Market risk: Risk of loss from adverse movements in market variables.

Interest-rate risk: Risk arising from changes in interest rates or yield curves.

Foreign-exchange risk: Risk from changes in currency exchange rates.

Credit-spread risk: Risk from changes in the spread over a benchmark risk-free rate.

Repricing gap: Difference between rate-sensitive assets and liabilities over a period.

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

DV01: Approximate currency value change for a one-basis-point yield movement.

Key-rate duration: Sensitivity to a movement at a particular curve tenor.

Convexity: Second-order measure of the curvature of the price-yield relationship.

Net open position: Net exposure to a currency after permitted offsets.

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

Value at Risk: Loss threshold associated with a selected confidence level and horizon.

Expected shortfall: Average loss conditional on losses exceeding VaR.

Historical simulation: Risk measurement using observed historical risk-factor changes.

Monte Carlo simulation: Risk measurement using generated scenarios from specified models.

Stress testing: Analysis of losses under severe but plausible scenarios.

Limit utilisation: Exposure expressed as a percentage of an approved limit.

Hedge effectiveness: Degree to which a hedge offsets the targeted exposure.

ALCO: Management committee responsible for balance-sheet and asset-liability risk oversight.

Model risk: Risk of loss from incorrect models, assumptions, implementation or use.

Review Questions

Short Answer Questions

1. What is the difference between market risk and credit-spread risk?
2. Define DV01 and state its unit of measurement.
3. Why does a bank distinguish between VaR and expected shortfall?
4. What is basis risk in a hedging relationship?
5. State two limitations of the square-root-of-time rule.

Long Answer Questions

1. Explain how a treasury should measure and control interest-rate risk using repricing gaps, duration, DV01 and key-rate duration.
2. Compare parametric, historical and Monte Carlo VaR, including their assumptions and limitations.
3. Explain the role of stress testing alongside VaR and expected shortfall.
4. Discuss the governance framework for market-risk limits, breaches and model validation.
5. Analyse the principal risks that remain after a bank enters an interest-rate or FX hedge.

Analytical / Application Questions

1. A CU 80 million bond portfolio has modified duration 5.1. Estimate the first-order loss from a 40-basis-point yield increase and explain why the estimate may differ from the actual loss.
2. A bank is long USD 12 million at CU 82 per USD. Calculate the approximate domestic-currency loss from a 7% USD depreciation and explain the sign of the exposure.
3. A portfolio has CU 15 million of spread-sensitive bonds and spread duration 4.0. Compare the estimated loss under a 75-basis-point spread widening with the loss under a 150-basis-point widening, and identify assumptions behind the comparison.

Multiple Choice Questions with Answers

Question 1

A bond portfolio worth CU 40 million has modified duration 3. What is its approximate loss when yield rises by 20 basis points?

A. CU 24,000

B. CU 240,000

C. CU 2,400,000

D. CU 4,000,000

Correct Answer: B. CU 240,000

Question 2

Which measure represents the average loss conditional on losses exceeding a selected VaR threshold?

A. DV01

B. Duration

C. Expected shortfall

D. Convexity

Correct Answer: C. Expected shortfall

Question 3

A bank that holds more USD assets than USD liabilities is generally exposed to which outcome if USD depreciates?

A. A gain in domestic currency

B. No exposure under any circumstances

C. A loss in domestic currency

D. A guaranteed gain from basis risk

Correct Answer: C. A loss in domestic currency

Question 4

Which risk is most directly measured by spread duration?

A. Sensitivity to credit-spread changes

B. Sensitivity to exchange-rate changes

C. Settlement finality risk

D. Operational fraud risk

Correct Answer: A. Sensitivity to credit-spread changes

Question 5

For a linear portfolio with normally distributed risk-factor changes, parametric VaR commonly uses which key input?

A. The covariance matrix

B. Only the largest historical loss

C. The accounting depreciation schedule

D. The recovery rate alone

Correct Answer: A. The covariance matrix

Question 6

What is the principal purpose of reverse stress testing?

A. To calculate coupon income

B. To identify scenarios capable of producing a specified failure outcome

C. To eliminate all model risk

D. To replace limit governance

Correct Answer: B. To identify scenarios capable of producing a specified failure outcome

Question 7

A positive hedge-effectiveness ratio close to one, using the convention −∆V_H/∆V_E, generally suggests that:

A. The hedge approximately offsets the exposure for the observed change

B. The hedge has no market value

C. The exposure is necessarily risk-free

D. The counterparty cannot default

Correct Answer: A. The hedge approximately offsets the exposure for the observed change

Question 8

Which measure is particularly useful for identifying exposure to a nonparallel yield-curve movement?

A. Notional value alone

B. Key-rate duration

C. Gross revenue

D. Settlement date

Correct Answer: B. Key-rate duration

Question 9

A portfolio has CU 30 million value and spread duration 2. If spreads widen by 100 basis points, the first-order estimated loss is:

A. CU 6,000

B. CU 60,000

C. CU 600,000

D. CU 6,000,000

Correct Answer: C. CU 600,000

Question 10

Which statement about VaR is correct?

A. It is the maximum possible loss

B. It is independent of confidence level

C. It is a model-based loss threshold for a specified horizon and confidence level

D. It always exceeds expected shortfall

Correct Answer: C. It is a model-based loss threshold for a specified horizon and confidence level