The big picture
A difference between two bond yields is not automatically free profit. Securities can differ in maturity, cash-flow timing, liquidity, tax treatment and financing. Many strategies called fixed-income arbitrage are leveraged relative-value trades that can lose money before or instead of convergence. This topic develops a research framework using Pakistan government securities as context. It does not assume that short selling, repo, swaps or institutional dealing facilities are available to a particular investor.
Core concepts
Learning objectives
- Build a consistent security and quotation sheet.
- Estimate first-order rate exposure and explain its limitations.
- Separate curve views from a parallel-rate view.
- Evaluate net carry and stress losses before considering execution.
Construct a valid comparison before naming a spread
1.1 Security terms and quotation conventions
Start with each instrument’s identifier, coupon type, cash-flow dates, maturity, day-count basis and settlement convention. Market Treasury Bills and different Pakistan Investment Bond types should not be treated as identical cash flows. A quoted yield is meaningful only with its convention and price basis. Dirty price includes accrued interest where applicable; confusing it with clean price distorts settlement cash. Use executable bid and offer indications, not only auction headlines or stale marks.
1.2 Curve shape is an observation, not a forecast
A yield curve compares yields across maturities on a sufficiently consistent basis. Steepening means the selected longer-minus-shorter yield spread widens; flattening means it narrows. Either can happen as rates rise or fall, and the cause can involve inflation, policy expectations, supply, liquidity or risk premiums. The curve alone does not prove growth or recession. A T-bill/PIB yield difference is not a pure basis opportunity until duration, cash flows and other differences are controlled.
Step-by-step method
- Record terms, accrued interest and settlement cash for every leg.
- Align quotation times, conventions and executable sides.
- State which spread is measured and which risks differ.
If a long PIB yield rises while a short bill yield rises even more, their spread narrows although both yields increase. Calling all flattening a bond rally would describe the same observation incorrectly.
Measure duration and convexity explicitly
2.1 First-order sensitivity and DV01
For a small yield move, the approximate percentage price change is minus modified duration times the yield change in decimal form. DV01 estimates currency value change for a one-basis-point yield move; one basis point is0.0001. For a position valueV and modified durationD, DV01 is approximatelyV×D×0.0001. Check the convention, instrument type and model rather than applying a fixed-rate formula mechanically to every floating or optional instrument.
2.2 Why matching is only approximate
Convexity captures curvature omitted by the first-order estimate. The familiar approximation adds one-half times convexity times the squared yield change, with conventions kept consistent. Duration matching can reduce parallel-shift exposure but leaves curve, convexity and cash-flow risks. Key-rate durations examine sensitivity at different maturity points. Model estimates should be checked against full repricing for larger shocks and changes in spreads or optionality.
Step-by-step method
- Calculate market value and the relevant duration measure.
- Convert a small rate shock into a signed currency estimate.
- Use full cash-flow repricing and key-rate shocks for stress tests.
Teaching assumptions: aPKR10 million fixed-rate position with modified duration6 has DV01 aboutPKR6,000. A100-basis-point yield rise implies an approximatePKR600,000 loss before convexity and other effects. This is a sensitivity illustration, not a quoted PIB duration.
Design the curve view without hiding the legs
3.1 Neutralising one exposure does not remove all risk
A curve strategy takes a view on relative movements at different maturities. A DV01-matched combination sizes legs so their first-order parallel-rate sensitivities offset approximately. Equal nominal amounts usually do not accomplish that. A long-duration exposure paired with an offsetting short exposure remains sensitive to non-parallel moves, convexity, financing and differences in executable prices. Record each leg’s sign to avoid reversing the intended trade.
3.2 Access and execution are gating conditions
Before analysing implementability, verify that each required transaction is permitted, suitable and available under the investor’s actual arrangements. Borrowing a security, entering a repo or executing a swap can involve documentation, collateral, counterparty limits and eligibility. A conceptual hedge is not an instruction to improvise unavailable access. If a short leg cannot legally be established or maintained, the proposed relative-value package does not exist for that investor.
Step-by-step method
- State the expected relative-yield change and why it may occur.
- Size legs using comparable sensitivities and explicit signs.
- Verify access, documentation, collateral and exit conditions.
Assume a long leg has DV01PKR6,000 and an eligible offsetting legPKR2,000 per chosen lot. Three opposite-signed lots approximately match first-order parallel exposure. That sizing says nothing about whether borrowing is available or whether a curve twist will be profitable.
Calculate carry, funding and convergence costs
4.1 Gross yield is not net carry
Carry is the income and financing effect of holding the package over a specified horizon. Include coupon or accrual, funding interest, borrowing fees, collateral opportunity cost, bid-offer spreads, transaction costs and applicable taxes. Roll-down is the potential price effect as an instrument ages along an assumed unchanged curve; it is conditional, not a coupon or a guaranteed gain. Reinvestment and reset assumptions must be visible.
4.2 A widening spread can force closure
A trade can have positive expected carry while losing far more through price changes. Financing may reprice, collateral haircuts may increase and an apparently attractive spread may widen. Convergence timing is uncertain, and margin pressure can force liquidation before any correction. Even government exposures retain interest-rate, liquidity, settlement, inflation and sovereign risks; a spread between different issuers adds credit risk. Swaps introduce contract-specific counterparty and collateral risks.
Step-by-step method
- Build a horizon cash-flow schedule for both legs and funding.
- Subtract all financing, access, tax and execution costs.
- Stress adverse prices and collateral demands before expected convergence.
Assumed annual income isPKR1.40 million, fundingPKR1.20 million and other costsPKR0.10 million: net carry isPKR0.10 million before price movements. An adverse mark-to-market loss ofPKR0.60 million overwhelms that income, even before any additional margin funding.
Produce a risk-reviewed relative-value note
5.1 Scenarios and limits
A complete note separates thesis, valuation, implementability and funding survival. Show parallel shifts, steepening, flattening, spread widening, funding-rate changes and a liquidity freeze. Include combined shocks rather than treating risks as independent. Specify maximum loss and cash-call budgets consistent with the mandate, review dates and thesis-invalidating evidence. A stop instruction cannot guarantee an exit price in an illiquid bond market.
5.2 Attribution after implementation
If an authorised strategy is implemented, reconcile actual fills, accrued interest, collateral and financing daily or at the frequency required by its risks. Attribute results to carry, curve movement, spread movement, convexity, costs and residual effects. A profitable outcome does not prove the initial mispricing claim was correct. Compare realised exposure with the model and document changes, including the decision to exit when funding assumptions no longer hold.
Step-by-step method
- Write base, adverse and combined-stress outcomes with cash needs.
- Set authority, position limits and a documented exit process.
- Reconcile realised performance with predicted risk drivers.
A hypothetical spread converges as expected, but funding costs increase and both legs execute poorly. The final report may show a loss despite a correct curve view. It should identify execution and funding failures rather than label the strategy risk-free arbitrage.
Net carry is a small residual before price risk
| Measure | Value |
|---|---|
| Assumed annual income | 1,400,000 PKR |
| Assumed funding cost | 1,200,000 PKR |
| Other assumed costs | 100,000 PKR |
| Net carry | 100,000 PKR |
Reference table
| Risk | Research test |
|---|---|
| Parallel yields | DV01 and full-repricing shocks |
| Curve twists | Maturity-specific sensitivity |
| Convexity | Larger moves and curvature mismatch |
| Funding and collateral | Higher rates, haircuts and cash calls |
| Liquidity and access | Executable sides, legal borrowing and exit |
| Credit and settlement | Issuer, counterparty and payment arrangements |
Glossary of key terms
- Basis point
- One-hundredth of a percentage point, or0.0001 in decimal yield.
- Carry
- Holding-period income less relevant financing and other costs.
- Convexity
- Curvature of the price-yield relationship under a specified convention.
- DV01
- Approximate currency sensitivity to a one-basis-point yield change.
- Dirty price
- Settlement-price measure including accrued interest where applicable.
- Modified duration
- First-order proportional price sensitivity to yield.
- Roll-down
- Conditional price effect of ageing along an assumed unchanged yield curve.
Frequently asked questions
Is a higher PIB yield than a bill yield arbitrage?
No. Maturity, duration, liquidity and funding differences can explain it.
Does DV01 matching eliminate risk?
No. It mainly addresses small parallel shifts under model assumptions.
Can a retail investor assume access to swaps or repo?
No. Verify eligibility, documentation and actual dealing access first.
Can positive carry coexist with a loss?
Yes. Adverse price moves, funding changes and liquidation costs can exceed carry.
Common pitfalls
| Common mistake | A better approach |
|---|---|
| Matching nominal instead of sensitivity | Compare DV01 and maturity-specific exposures. |
| Ignoring accrued interest | Reconcile clean, dirty and settlement values. |
| Calling a relative-value trade risk-free | Model convergence, funding, liquidity and counterparty risks. |
| Treating the curve as a certain macro forecast | Explain alternative drivers and test adverse scenarios. |
Your learner task
Prepare a paper-only two-security comparison using dated SBP or verified market evidence. Record terms and conventions, estimate duration and DV01, construct a hypothetical sensitivity-matched package and calculate net carry. Stress parallel and non-parallel shifts, funding increases and a liquidity freeze. List access constraints; do not assume any short or derivative leg is available.
Sources & verification
Use the linked documents to check the factual and regulatory context. Source dates and limitations are stated where relevant. Educational examples and analytical frameworks are not personalised recommendations.
- SBP · Financial markets and investor guides ↗
Official government-security guides and market framework. Verify product terms, dealing access and current notices separately.
- SBP · PIB investor guide ↗
Official government-security investment context; confirm current terms and provider procedures before dealing.
Editorial review: 22 October 2026