FX and Interest-Rate Risk Analytics

Introduction and Context

Foreign-exchange and interest-rate exposures are central to investment banking. A bank may lend in one currency while funding in another, arrange a cross-border acquisition, warehouse bonds before distribution, provide market-making liquidity, or hold subsidiaries whose functional currencies differ from the reporting currency. These activities create risks that cannot be managed reliably by observing accounting profit alone.

Risk analytics converts exposures into measurable quantities. The objective is not to predict every market movement, but to answer disciplined questions: How much value changes when an exchange rate moves? How sensitive is a portfolio to a one-basis-point change in yields? What happens under a severe but plausible shock? How much loss might occur over a specified horizon, and how much additional loss could arise beyond a high percentile? Can the institution meet collateral and settlement obligations if markets become illiquid?

This chapter develops an integrated framework for transaction, translation, economic, liquidity, basis and counterparty risk. It combines sensitivities, duration, stress testing, scenario analysis, value at risk (VaR), expected shortfall (ES), and governance controls. The methods are useful for treasury, markets, investment banking, risk management, valuation control and regulatory reporting.

Learning Objectives

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

1. Distinguish transaction, translation and economic FX risk.
2. Measure FX and interest-rate exposure using linear and nonlinear sensitivities.
3. Apply modified duration, DV01, convexity and key-rate measures.
4. Explain liquidity, basis and counterparty risks and their interactions.
5. Construct historical, parametric and Monte Carlo VaR and ES measures.
6. Design stress tests and scenarios relevant to FX and money-market portfolios.
7. Interpret model limitations and establish effective governance and escalation.

1. The Architecture of Market Risk

Market risk is the possibility that changes in observable market variables reduce the economic value, income or liquidity of a position. For an FX and interest-rate portfolio, the principal risk factors include:

• spot exchange rates and forward points;
• domestic and foreign yield curves;
• cross-currency basis spreads;
• credit and funding spreads;
• volatility surfaces;
• market liquidity, bid–offer spreads and market depth; and
• correlations among these variables.

A useful first distinction is between exposure and risk. Exposure is the amount or sensitivity linked to a risk factor. Risk is the uncertain adverse outcome after considering movements, time horizon, nonlinearity, liquidity and dependence among factors. A USD 100 million receivable is an exposure; its potential loss in the reporting currency over ten days is a risk measure.

Risk-factor mapping

Every position should be mapped to economically meaningful risk factors. A foreign-currency loan may have an FX delta, domestic-rate duration, foreign-rate duration, basis sensitivity and counterparty exposure. A currency swap has at least two interest-rate curves, an FX spot component, collateral and funding effects. Mapping prevents material risks from being hidden in broad accounting categories.

A first-order portfolio change can be written as:

Here, ∆V is the change in portfolio value, ∆xᵢ is the change in risk factor i, Δᵢ = ∂V/∂xᵢ is delta, and Γᵢⱼ = ∂²V/(∂xᵢ∂xⱼ) is the second-order sensitivity. The first-order approximation is appropriate for small changes and approximately linear instruments. The gamma term becomes important for options, callable securities and large shocks.

2. Foreign-Exchange Risk

2.1 Transaction risk

Transaction risk is the uncertainty in the domestic-currency value of a contracted foreign-currency cash flow. Examples include a EUR receivable of a UK company, a USD bond held by a euro-based bank, or a committed purchase price payable in JPY.

Suppose a firm will receive foreign currency amount F at time T. If the quotation is domestic currency per unit of foreign currency, the domestic value is:

where S is the spot exchange rate in domestic currency per foreign currency. A change in value is:

This formula assumes the foreign amount is fixed, the quotation is correctly specified, and interest, credit and timing effects are ignored. For a payable, the sign is reversed. If the position is option-like or its amount changes with the exchange rate, delta and gamma are required rather than a fixed-notional calculation.

Worked example. A euro-based company expects to receive USD 10 million. The quotation is EUR per USD, and the spot rate rises from 0.9200 to 0.9350. The euro value rises by:

10,000,000 × (0.9350 − 0.9200) = EUR 150,000.

The company has a positive USD exposure. A USD payable of the same size would lose EUR 150,000 under the same movement.

Forward contracts can hedge the amount and timing, but they introduce forward-point, rollover, credit-support and liquidity considerations. A hedge that removes spot risk may still leave basis or funding risk.

2.2 Translation risk

Translation risk arises when the financial statements of a foreign operation are converted into the parent’s reporting currency. It is primarily an accounting and reporting exposure, although it can affect covenants, capital ratios, investor perceptions and taxable income.

The translated value of a foreign net asset position approximately changes according to:

where N_foreign is the net foreign-currency asset and S is the reporting-currency value per unit of foreign currency. Translation adjustments may be recorded in other comprehensive income rather than current-period profit, depending on the applicable accounting framework. Accounting treatment does not eliminate economic exposure: the foreign subsidiary’s local-currency assets, liabilities, revenues and costs may still be affected by exchange rates.

2.3 Economic or operating risk

Economic risk is the longer-term effect of exchange-rate changes on competitiveness, prices, volumes, margins and future cash flows. It is less mechanical than transaction risk. An exporter may benefit from a weaker domestic currency, but imported inputs may become more expensive. A bank’s foreign branch may experience changes in loan demand, credit quality and funding costs.

Economic exposure is usually assessed through scenarios and forecasts rather than a single contractual amount. Useful variables include revenues by currency, costs by currency, price elasticity, competitor currency, supply-chain dependencies and expected hedging ratios. A static hedge may protect a forecast cash flow but fail to protect market share or future margins.

2.4 FX sensitivities

For a linear foreign-currency position, FX delta is the change in domestic value for a one-unit change in the exchange rate:

For a foreign asset of amount F, Δ_FX = F. For an option, delta depends on spot, strike, volatility, maturity and interest rates. FX gamma measures the change in delta:

FX options also possess vega, measuring sensitivity to implied volatility, and rho, measuring sensitivity to interest rates. A portfolio that is delta-neutral can still lose materially because of gamma or volatility movements.

3. Interest-Rate Risk Analytics

3.1 Present value and discounting

The present value of deterministic cash flows is:

where CFₜ is the cash flow at time t and DFₜ is the discount factor for that date. Under annual effective compounding with a constant yield y, DFₜ = 1/(1+y)ᵗ. In professional valuation, discount factors are normally derived from a curve, and the compounding convention, day-count basis and payment calendar must be consistent.

A zero-coupon bond paying face value F at maturity T has:

The valuation of swaps and floating-rate instruments requires projection curves as well as discount curves. Using an inappropriate single curve can misstate both value and sensitivities, especially when collateral, funding and basis spreads are material.

3.2 Duration and modified duration

Macaulay duration is the cash-flow-weighted average time to receipt:

It is measured in years when t is measured in years and the yield convention matches the discounting formula. Modified duration converts a small yield change into an approximate percentage price change:

for a nominal annual yield compounded m times per year. Under this convention:

The approximation assumes a parallel, small yield movement and a fixed cash-flow structure. It is less reliable for large shocks, callable instruments, mortgage products and instruments whose cash flows change with rates.

Worked example. A bond has market value USD 50 million and modified duration 4.8. If its yield rises by 25 basis points, ∆y = 0.0025. The approximate value change is:

∆P ≈ −50,000,000 × 4.8 × 0.0025 = −USD 600,000.

The result is a first-order estimate. Actual repricing differs because of convexity, curve shape and spread movements.

3.3 DV01 and key-rate duration

DV01, also called PV01 in some settings, is the value change for a one-basis-point increase in yield:

The sign convention varies. Some systems report positive risk as the loss from a yield increase; others report the signed value change. The convention must be stated explicitly.

For the bond above, the absolute DV01 is 50,000,000 × 4.8 × 0.0001 = USD 24,000 per basis point.

Parallel duration can conceal curve risk. Key-rate duration measures sensitivity to a localized movement at a specified maturity, such as two, five or ten years, while other curve points are held according to the chosen interpolation rule. It is especially important for portfolios containing cash flows concentrated at different maturities and for hedges that match total duration but not curve shape.

3.4 Convexity

Convexity improves the duration approximation for larger rate movements:

where C is convexity, measured in years squared under the corresponding convention. For a standard option-free bond, positive convexity means the price rises more when yields fall than it falls when yields rise by the same amount. Callable bonds may exhibit negative convexity over relevant ranges because expected cash flows shorten when rates decline.

3.5 Money-market instruments

Treasury bills, certificates of deposit, commercial paper and repurchase agreements require careful treatment of day-count, settlement and discount conventions. A simple-money-market price may be represented as:

where F is maturity value, r is the annualized simple rate and τ is the year fraction. The formula assumes simple interest and must not be mixed with a continuously compounded or bond-equivalent quote without conversion. Short maturity does not imply negligible risk: a large notional, a widening funding spread or a failed rollover can generate significant losses.

4. Basis Risk and Cross-Currency Exposures

Basis risk is the possibility that two rates or prices expected to move together do not do so. Examples include:

• three-month benchmark funding hedged with a one-month instrument;
• a loan priced on one reference rate hedged with a swap referencing another;
• a local-currency asset hedged with an imperfect offshore instrument;
• a cross-currency swap whose basis spread changes independently of spot FX; and
• a bond spread hedged with a government curve while credit or liquidity spreads move.

For a two-rate position, a simplified value change is:

where S₁ and S₂ are sensitivities to the two rates, S_b is basis sensitivity, and ∆b is the basis-spread movement. A hedge may set net sensitivity to r₁ near zero while leaving material r₂ or basis exposure.

Cross-currency swaps also create settlement and collateral risks. The exchange of principal at maturity can make the exposure large even when the mark-to-market value is near zero. Netting agreements, collateral terms and close-out provisions therefore matter as much as market sensitivities.

5. Liquidity Risk

Liquidity risk has two dimensions. Market liquidity risk is the cost or inability to transact without materially moving the price. Funding liquidity risk is the inability to meet payment, margin or collateral obligations when due.

Common measures include bid–offer cost, market depth, liquidation horizon, concentration, stressed haircuts, cash-flow gaps and collateral availability. A position’s risk over a one-day horizon may be very different from its risk over ten days if the position cannot be liquidated quickly.

A simple liquidity-adjusted loss estimate can add a transaction-cost allowance:

where L_market is estimated market loss, Q is the quantity liquidated and Spread is the full bid–offer spread per unit. This is an approximation: price impact is often nonlinear, and spread estimates become unreliable in stressed markets.

Liquidity analysis should connect market risk to cash management. A stressed FX move can trigger variation margin; a rate shock can reduce collateral value; a downgrade can increase initial margin or terminate funding. The relevant question is therefore not only “What is the mark-to-market loss?” but also “What cash must be delivered, when, and from which sources?”

6. Counterparty and Settlement Risk

Counterparty risk is the possibility that the other party fails to perform. For derivatives, exposure is often separated into current replacement cost and potential future exposure. A simplified positive exposure is:

where MtM is current mark-to-market from the institution’s perspective and PFE is potential future exposure over a defined horizon and confidence level. This is not a universal regulatory formula; legal netting, collateral, margin period of risk, wrong-way risk and applicable capital rules must be incorporated.

Wrong-way risk occurs when exposure to a counterparty increases as that counterparty’s credit quality deteriorates. For example, a bank may be most exposed to an energy producer through an oil-linked derivative when falling oil prices simultaneously weaken the producer’s ability to pay.

Settlement risk is distinct from replacement-cost exposure. In payment-versus-payment FX settlement, one party may deliver currency before receiving the other currency. Settlement systems, cut-off times, payment netting and operational controls are therefore part of risk analytics.

7. VaR and Expected Shortfall

7.1 Value at Risk

For loss random variable L, VaR at confidence level α is the loss threshold not exceeded with probability α:

If returns rather than losses are modelled, sign conventions must be converted carefully. VaR requires a holding period, confidence level, portfolio definition, valuation methodology and data window. “One-day 99% VaR” is incomplete unless these choices are specified.

Three main approaches are used:

1. Historical simulation. Historical changes in risk factors are applied to today’s portfolio. It captures empirical dependence and nonlinear revaluation if full repricing is used, but assumes the historical sample is relevant.
2. Parametric VaR. Risk factors are summarized by means, volatilities and a covariance matrix. For a linear portfolio with normally distributed risk factors, portfolio standard deviation is:

where w is the vector of exposures and Σ is the covariance matrix. Under zero mean and normality, VaR_α = z_ασ_P for a one-period loss convention, where z_α is the standard-normal quantile. The normality assumption can materially understate fat tails.

1. Monte Carlo simulation. Risk-factor paths are generated from specified stochastic models and the portfolio is revalued. It is flexible but computationally intensive and model-dependent.

7.2 Expected shortfall

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

For continuous distributions this definition is direct. For discrete samples, a consistent tail-average convention is required. ES is more informative than VaR about the severity of extreme losses and is a coherent risk measure under standard conditions, but it is more statistically noisy because it uses fewer observations in the tail.

Illustrative historical calculation. Suppose ten equally weighted one-day losses, in USD millions, are: 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.5, 2.0, 3.0 and 5.0. At a 90% empirical confidence level, the largest observation gives a simple historical VaR of USD 5.0 million. With a one-observation tail convention, ES is also USD 5.0 million. This example demonstrates sample discreteness, not a claim that ten observations are adequate for production risk management.

7.3 Backtesting and validation

VaR must be backtested by comparing forecasts with actual and hypothetical profit and loss. Exceptions should be investigated, not merely counted. Causes include bad data, booking errors, omitted risk factors, volatility changes, model misspecification and extraordinary events. ES backtesting is more difficult and often uses joint VaR–ES methods, tail-loss diagnostics and stress comparisons.

8. Stress Testing and Scenario Analysis

VaR describes a distribution under model assumptions; stress testing asks what happens under a specified adverse event. A scenario may be historical, hypothetical or reverse-engineered.

Examples include:

• a 15% depreciation of an emerging-market currency;
• a parallel 250-basis-point yield increase;
• a steepening in which long rates rise while short rates remain stable;
• a sudden widening of cross-currency basis;
• a reduction in market depth combined with doubled bid–offer spreads;
• counterparty downgrade, collateral call and partial default; and
• simultaneous FX depreciation, funding-spread widening and deposit outflows.

A robust scenario has a narrative, factor shocks, valuation rules, liquidity assumptions, management actions and reporting outputs. Stress testing should include nonlinear revaluation, collateral flows, hedge ineffectiveness and second-round effects. It should also distinguish instantaneous value loss from cumulative cash-flow stress.

Reverse stress testing begins with an unacceptable outcome, such as a capital breach or inability to meet margin, and identifies the combination of shocks capable of producing it. This helps reveal concentrations that ordinary sensitivity reports may miss.

9. Integrated Illustrative Case

Background

The following is a fictional illustrative case. Meridian Bank’s treasury holds a USD 100 million, five-year fixed-rate bond funded partly through three-month euro liabilities. The bank reports in EUR. It also has a USD receivable from an investment-banking client and hedges part of the position with a EUR/USD forward and a pay-fixed, receive-floating interest-rate swap.

Problem

The treasury reports that total parallel DV01 is close to zero. However, risk management observes losses during a period in which EUR/USD depreciates, long-term USD yields rise, three-month EUR funding spreads widen and the cross-currency basis moves adversely.

Analysis

The bond’s modified duration is 4.8 and market value is USD 100 million. Its approximate DV01 is:

100,000,000 × 4.8 × 0.0001 = USD 48,000 per basis point.

The hedge offsets much of the five-year USD-rate exposure but is concentrated at a different maturity and references a different curve. Key-rate analysis shows residual five-year and ten-year exposure. The EUR funding creates sensitivity to short-term EUR rates and funding spreads, which the USD swap does not eliminate.

The USD receivable creates positive FX exposure. If EUR/USD is quoted as EUR per USD, a fall in the quote reduces the EUR value of USD assets. The forward offsets only the contracted amount and maturity; it does not hedge the bond’s changing EUR value or the client receivable’s timing uncertainty.

A stress scenario applies: EUR/USD −12%, USD five-year yield +150 basis points, EUR three-month funding spread +80 basis points, cross-currency basis −50 basis points, and a doubling of bid–offer spreads. Full revaluation shows a larger loss than the linear dashboard because the forward hedge is imperfect, basis sensitivity is omitted from the simple DV01 report, and liquidation costs increase.

Approach and solution

Meridian should:

1. report FX delta and gamma by currency and legal entity;
2. replace total DV01 with key-rate DV01 for each relevant curve;
3. add explicit basis, funding-spread and liquidity sensitivities;
4. model collateral and margin cash flows under the stress;
5. assess counterparty exposure after netting and collateral;
6. establish limits for stress loss, liquidity usage and basis exposure; and
7. perform historical and hypothetical scenario analysis at least as frequently as the portfolio’s liquidity and market conditions require.

Outcome

After redesign, the bank recognizes that the apparent duration hedge was only a parallel-risk hedge. The revised framework identifies residual curve, basis, FX, funding and liquidity risks and assigns escalation thresholds. The bank increases hedge-maturity alignment, diversifies funding, pre-positions collateral and documents model limitations.

Learning points

A net aggregate sensitivity can conceal offsetting exposures. Market, liquidity and counterparty risks interact. A hedge should be evaluated against the actual risk factors, cash-flow dates, collateral terms and stress behaviour—not merely against a single headline number.

10. Governance, Technology and Professional Practice

Effective analytics requires disciplined data and governance. Market data should be sourced from controlled providers, timestamped, validated and checked for stale or crossed prices. Curves require documented instruments, interpolation, bootstrapping, compounding and fallback conventions. Position data must reconcile with the general ledger and trading systems.

Model risk controls include independent validation, conceptual review, benchmark comparisons, sensitivity testing, challenger models and documented limitations. Changes to pricing libraries, curves or risk-factor mappings should follow change control. Explainability is particularly important when machine-learning tools are used for anomaly detection, liquidity forecasting or scenario generation. AI may support analysis, but it should not override approved valuation, limit or model-governance processes without human accountability.

Regulatory and accounting requirements vary by jurisdiction, but common principles include prudent valuation, independent risk control, capital adequacy, legal enforceability of netting, collateral recognition, data retention and clear senior-management reporting. Ethical practice requires avoiding misleading precision. A VaR number with weak data, an unstable covariance matrix or an unreported liquidity assumption should not be presented as objective certainty.

Best practice is to use a hierarchy of measures:

No single metric is sufficient. Sensitivities are transparent but local; VaR is compact but model-dependent; ES describes tails but is statistically difficult; stress tests are intuitive but scenario-dependent; liquidity and counterparty measures require legal and operational information beyond market prices.

Chapter Summary

FX and interest-rate risk analytics begins with accurate mapping of positions to risk factors. Transaction risk concerns contracted foreign-currency cash flows, translation risk concerns reporting-currency conversion, and economic risk concerns longer-term operating cash flows and competitiveness. FX delta and gamma quantify local exposure, while duration, modified duration, DV01, key-rate duration and convexity measure interest-rate sensitivity.

Basis risk arises when related rates do not move together. Liquidity risk concerns both trading conditions and the ability to meet funding or collateral obligations. Counterparty analysis combines current exposure, potential future exposure, collateral, netting, wrong-way risk and settlement controls. VaR summarizes a loss percentile, whereas ES estimates the average loss in the tail. Both require explicit horizons, confidence levels, data and model assumptions.

Stress testing complements statistical measures by examining severe, coherent narratives, including interaction among FX, rates, basis, liquidity and credit. Professional practice requires independent validation, reliable data, transparent assumptions, backtesting, escalation and recognition that a near-zero aggregate sensitivity does not imply low risk.

Key Terms

Transaction risk: Risk that a contracted foreign-currency cash flow changes in reporting-currency value.

Translation risk: Reporting-currency risk arising from converting foreign operations or balances.

Economic risk: Long-term effect of exchange rates on revenues, costs, competitiveness and future cash flows.

FX delta: Change in portfolio value for a unit change in an exchange rate.

FX gamma: Change in FX delta for a unit change in the exchange rate.

Duration: Measure of the timing and interest-rate sensitivity of fixed-income cash flows.

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

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

Key-rate duration: Sensitivity to a localized movement at a particular maturity point.

Convexity: Second-order sensitivity of bond price to yield changes.

Basis risk: Risk that related prices, rates or spreads diverge.

Market liquidity risk: Risk of loss or inability to transact because market depth is inadequate.

Funding liquidity risk: Risk of inability to meet cash, margin or collateral obligations.

Counterparty risk: Risk that the other party fails to perform.

Potential future exposure: Estimate of possible future counterparty exposure over a specified horizon.

Wrong-way risk: Exposure that increases as counterparty credit quality deteriorates.

Value at Risk: Loss threshold associated with a specified probability and horizon.

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

Stress testing: Evaluation of portfolio outcomes under severe specified shocks.

Backtesting: Comparison of model forecasts with realized or hypothetical outcomes.

Review Questions

Short Answer Questions

1. Distinguish transaction risk from translation risk.
2. What does DV01 measure, and why must its sign convention be stated?
3. Why can a duration-neutral portfolio still have material interest-rate risk?
4. Differentiate market liquidity risk from funding liquidity risk.
5. What information does expected shortfall provide that VaR does not?

Long Answer Questions

1. Explain how FX delta, gamma and scenario analysis can be combined to assess an option-containing FX portfolio.
2. Derive the modified-duration approximation and discuss its assumptions and limitations.
3. Compare historical simulation, parametric VaR and Monte Carlo VaR for an investment-bank portfolio.
4. Explain how basis risk can remain after a cross-currency or interest-rate hedge is entered.
5. Discuss the governance requirements for reliable FX and interest-rate risk analytics.

Analytical / Application Questions

1. A EUR-based bank holds a USD 40 million receivable. EUR/USD rises from 0.9100 to 0.9250. Calculate the approximate change in euro value and state whether it is a gain or loss.
2. A bond portfolio worth USD 80 million has modified duration 3.75. Estimate the value change if yields rise by 40 basis points. Explain why the actual result may differ.
3. Design a stress scenario combining an FX shock, a yield-curve shock, a basis movement and a liquidity event. Identify the market, cash-flow, counterparty and governance outputs that should be reported.

Multiple Choice Questions with Answers

Question 1

A euro-based firm has a fixed USD receivable. If the EUR-per-USD exchange rate rises, what is the immediate effect, ignoring other factors?

A. The euro value of the receivable rises

B. The euro value of the receivable falls

C. The USD amount automatically falls

D. There is no valuation effect

Correct Answer: A. The euro value of the receivable rises

Question 2

A bond portfolio is worth USD 50 million and has modified duration 4.8. What is the approximate loss from a 25-basis-point yield increase?

A. USD 60,000

B. USD 120,000

C. USD 600,000

D. USD 6,000,000

Correct Answer: C. USD 600,000

Question 3

Which measure captures sensitivity to a localized movement at a particular point on the yield curve?

A. Parallel duration

B. Key-rate duration

C. FX gamma

D. Expected shortfall

Correct Answer: B. Key-rate duration

Question 4

Which statement best describes basis risk?

A. Risk that a counterparty defaults immediately

B. Risk that related rates or prices do not move together as expected

C. Risk caused only by option volatility

D. Risk that accounting standards change

Correct Answer: B. Risk that related rates or prices do not move together as expected

Question 5

For a continuous loss distribution, expected shortfall at confidence level α is best described as:

A. The smallest daily loss

B. The median portfolio return

C. The expected loss conditional on exceeding VaR at α

D. The average of all gains

Correct Answer: C. The expected loss conditional on exceeding VaR at α

Question 6

Which VaR method directly applies observed historical risk-factor changes to the current portfolio?

A. Historical simulation

B. Macaulay duration

C. Bootstrapped discounting only

D. Settlement netting

Correct Answer: A. Historical simulation

Question 7

A portfolio has a positive USD asset exposure in a EUR reporting entity. Which event generally causes an immediate EUR valuation loss, all else equal?

A. EUR per USD increases

B. EUR per USD decreases

C. USD interest rates remain unchanged

D. The reporting date is unchanged

Correct Answer: B. EUR per USD decreases

Question 8

Which situation is an example of wrong-way risk?

A. Exposure falls when the counterparty weakens

B. Exposure is unrelated to counterparty credit quality

C. Exposure increases as the counterparty’s credit quality deteriorates

D. A trade is fully settled on time

Correct Answer: C. Exposure increases as the counterparty’s credit quality deteriorates

Question 9

If a bond has market value USD 100 million and modified duration 4.8, its approximate absolute DV01 is:

A. USD 4,800

B. USD 48,000

C. USD 480,000

D. USD 4.8 million

Correct Answer: B. USD 48,000

Question 10

What is a principal limitation of a first-order duration estimate?

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

B. It ignores all cash flows

C. It becomes less accurate for large yield changes and nonlinear instruments

D. It measures only counterparty default

Correct Answer: C. It becomes less accurate for large yield changes and nonlinear instruments