The big picture
A large interest-rate difference looks attractive until currencies, funding and trading restrictions are included. Global macro research studies these relationships, but a carry position is not automatically arbitrage. This topic develops matched cash-flow comparisons, covered interest parity, currency-regime analysis and a practical risk review. All numerical rates and exchange rates below are hypothetical teaching assumptions, not current market quotes or offers. Product access, borrowing, hedging and remittance permissions must be verified for the actual investor through authorised channels.
Core concepts
Learning objectives
- Calculate an unhedged carry outcome in a consistent funding currency.
- Derive a matched-maturity theoretical forward rate.
- Explain why a quoted basis is not freely accessible profit.
- Build an eligibility, liquidity and stress checklist before considering implementation.
Write the complete two-currency balance sheet
1.1 Choose the quote convention and funding unit
Let S mean PKR perUSD. A rise in S is rupee depreciation against the dollar. For a hypothetical one-year position, borrowingUSD10,000 at4% creates a repayment obligation ofUSD10,400. Converting at an assumed S0=280 producesPKR2,800,000. Investing at an assumed12% givesPKR3,136,000 at maturity before costs and taxes. The terminal dollar amount is3,136,000 divided by S1. Comparing12% with4% alone therefore omits the variable that can reverse the outcome.
1.2 Separate yield from the eventual currency conversion
At S1=280, the asset converts toUSD11,200 and leavesUSD800 after repayment. At S1=308, it converts to approximatelyUSD10,181.82 and leaves aUSD218.18 loss. Neither result includes spreads, credit loss, tax or funding fees. These are arithmetic scenarios, not probability estimates. Always reconcile opening principal, investment proceeds, debt service and closing residual in the same currency. Leverage increases the effect on the investor’s own equity and can require additional cash before maturity.
Step-by-step method
- Write the exchange quote and every cash-flow date.
- Convert terminal investment proceeds into the funding currency.
- Subtract principal, interest and all relevant costs.
A learner initially labels the12% minus4% spread a guaranteed8% profit. The depreciation scenario shows why this is wrong: the investment earned its assumed local interest but did not cover the foreign-currency obligation.
Derive covered interest parity carefully
2.1 A no-arbitrage comparison under restrictive assumptions
With S expressed as PKR perUSD and matched one-year simple rates, the ideal covered parity relation is F=S0×(1+rPKR)/(1+rUSD). It assumes comparable credit, executable borrowing and lending, enforceable conversion, matching maturity and no relevant frictions. Using the same hypothetical12% and4% rates gives F=280×1.12/1.04≈301.5385PKR perUSD. Selling thePKR3,136,000 proceeds forward at that rate yieldsUSD10,400, exactly matching the debt repayment before costs.
2.2 Hedging the terminal proceeds
The higher local yield has been offset by the forward conversion; a forward is not a free insurance add-on. A real hedge may cover the wrong amount if an investment defaults, pays at a different date or changes principal. Actual quotes have bid-ask spreads, credit terms and collateral requirements. Use the correct executable side for each leg rather than combining favourable mid-prices. A forward price is a contract conversion rate, not a reliable forecast of the future spot exchange rate.
Step-by-step method
- Match currency, credit, maturity and cash-flow convention.
- Calculate the theoretical relation as a diagnostic benchmark.
- Recalculate with executable quotes, hedge amounts and costs.
In the teaching example a perfectly matched parity hedge removes the assumed currency uncertainty and also the apparentUSD800 windfall. Additional fees would make the modelled residual negative. An actual investor cannot infer access to these fictional rates or instruments.
Understand basis, funding and implementation limits
3.1 A pricing discrepancy can reflect constrained balance sheets
Observed prices can deviate from a simple parity benchmark because funding is not equally available to every participant. Bank balance-sheet capacity, credit exposure, collateral, regulation and hedging demand can affect pricing. The cross-currency basis describes part of the difference between funding through currency markets and a benchmark cash-market comparison. Its sign depends on the quoting convention, so document which leg carries the spread instead of interpreting a positive number in isolation.
3.2 Liquidity can fail before a trade converges
A relative-value position may be economically hedged at maturity yet face daily mark-to-market cash calls, collateral haircuts and a withdrawn credit line. Short funding against a longer asset adds rollover risk. The relevant return is after realistic funding, capital and execution costs, not the gross pricing gap. Test whether the actual investor can borrow and lend at the assumed rates and maintain both legs through stress. A discrepancy visible on a screen may not be simultaneously executable at useful size.
Step-by-step method
- Obtain institution-specific funding and collateral terms.
- Map interim liquidity and rollover dates.
- Stress spread widening, haircut increases and forced liquidation.
A hypothetical desk expects a basis to narrow over six months but its lender can withdraw weekly funding. Even if the long-run pricing argument is sound, the desk may have to close at a loss. Convergence timing and survival funding are separate research questions.
Analyse currency regimes and capital flows
4.1 A peg is a policy arrangement, not a guarantee
Fixed, managed and floating exchange arrangements create different adjustment mechanisms. A stable observed rate can coexist with reserve pressure, external funding needs or restrictions on conversion. Study the policy framework, reserves and external obligations with their data dates; do not infer convertibility from a quiet historical chart. Foreign portfolio inflows can support local funding conditions, while reversals may pressure both asset prices and currency liquidity. These relationships are conditional, not a mechanical trading signal.
4.2 Carry unwinds can change correlations
Carry strategies can share crowded exposures: investors borrow similar funding currencies and own higher-yielding assets. A funding shock may trigger simultaneous reductions, making a currency hedge more expensive and diversification weaker when it is most needed. The BIS discusses how leveraged carry unwinds can amplify exchange-rate responses to policy. Build scenarios for risk-off outflows, a regime change and delayed repatriation rather than extrapolating a short period of low volatility.
Step-by-step method
- Describe the exchange regime and actual conversion rules.
- Track dated reserves, debt service and capital-flow evidence.
- Stress simultaneous currency, asset and funding shocks.
An investor sees months of a stable hypothetical peg and models no currency loss. A better adverse case includes an adjustment in the exchange rate plus a temporary difficulty converting proceeds. The exercise does not predict a change in any country’s regime.
Apply a legal, economic and risk gate
5.1 Eligibility comes before an execution plan
Pakistan-related cross-border activity requires the applicable SBP foreign-exchange framework, account route, authorised-dealer process and current circulars to be checked. Chapters on forward facilities, loans, remittances and securities address different activities. Eligibility for one account or security does not authorise unrestricted foreign borrowing, speculative forwards or offshore trading. Confirm investor residence, purpose, documentation, permitted instrument, tax treatment and settlement route with the relevant institution and qualified advisers.
5.2 Compare a trade with doing nothing
Produce a go/no-go memo with a funding-currency cash-flow sheet, executable quotes, counterparty limits, margin reserve and an exit plan. Include normal and stressed returns after tax and costs, and explain which risks remain unhedged. Compare the proposal with an unleveraged lawful alternative and a cash benchmark. Reject a strategy if access or funding is unresolved; a spreadsheet cannot supply permission. Record expected behaviour and review triggers so an attractive narrative can be challenged after new evidence.
Step-by-step method
- Verify legal access and written counterparty terms.
- Reconcile base and adverse cash flows after all costs.
- Approve only with adequate liquidity and an executable exit.
A research memo may conclude that the theory is educational but implementation is unsuitable because the client cannot obtain a matched permitted hedge. That is a completed analytical result, not a reason to improvise an unauthorised route.
Hypothetical terminal assets versus debt
| Measure | Value |
|---|---|
| Assets at S1=280 | 11,200 USD |
| Debt repayment | 10,400 USD |
| Assets at S1=308 | 10,181.82 USD |
Reference table
| Item | Assumption or calculation | Meaning |
|---|---|---|
| Borrowing | USD10,000 at4%; repayUSD10,400 | Funding liability |
| Local investment | PKR2,800,000 at12% becomesPKR3,136,000 | Before costs and tax |
| Unchanged spot | 3,136,000/280−10,400=USD800 | Unhedged teaching profit |
| Depreciated spot | 3,136,000/308−10,400≈−USD218.18 | Unhedged teaching loss |
| Parity hedge | F≈301.5385; terminalUSD10,400 | No gross residual before costs |
Glossary of key terms
- Arbitrage
- A pricing strategy designed around offsetting exposures; real implementation can retain costs and risks.
- Carry trade
- A position seeking a yield difference while often retaining exchange-rate and funding risk.
- Covered interest parity
- The ideal matched-currency relationship between spot, forward and interest rates.
- Cross-currency basis
- A quoted adjustment reflecting a difference between currency-market funding and a benchmark funding comparison.
- Forward
- An agreement to exchange a specified amount on a future date at a contracted rate.
- Funding currency
- The currency in which borrowing and repayment obligations are measured.
- Haircut
- A reduction in the recognised collateral value used for lending or margin.
- Rollover risk
- The risk that maturing financing cannot be renewed on workable terms.
Frequently asked questions
Is a high local yield a guaranteed carry profit?
No. Currency changes, default, costs and funding can outweigh it.
Does a forward forecast the future spot rate?
No. It is an agreed conversion rate influenced by funding and market conditions.
Does a hedge eliminate every risk?
No. Amount, timing, credit, collateral and legal risks can remain.
Can a Pakistani investor automatically borrowUSD and buy local assets?
No. The investor, purpose and routes require verification under applicable rules.
Common pitfalls
| Common mistake | A better approach |
|---|---|
| Subtracting two yields and ignoring currency | Model terminal cash in the funding currency. |
| Mixing mid-market and executable prices | Use consistent bid-ask sides and actual capacity. |
| Calling a basis free profit | Include funding, balance-sheet and collateral constraints. |
| Assuming a peg or hedge ensures liquidity | Stress conversion, margin and forced-sale scenarios. |
Your learner task
Reproduce the assumedUSD10,000 example, then add separately labelled hypothetical transaction costs. Calculate the theoretical matched forward, an unhedged depreciation outcome and a mismatched-hedge case. Prepare an access checklist, collateral calendar and stressed exit memo. Keep every assumption distinct from a dated verified quote; do not execute a position as part of this exercise.
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.
- BIS · Covered interest parity lost,2016 ↗
Primary research on funding constraints and cross-currency basis; not evidence of retail access or a current PKR trading opportunity.
- BIS · Bulletin124,6May2026 ↗
Research on carry unwinds and state-dependent exchange-rate transmission; scenarios here are independently constructed teaching arithmetic.
- SBP · Foreign Exchange Manual ↗
Official entry point for forward facilities, loans, remittances and securities rules. Verify applicable chapters and later circulars with an authorised dealer.
Editorial review: 22 October 2026