FIN4006 Chap.3 Parity, Arbitrage and Exchange-Rate Determination
Parity, Arbitrage and Exchange-Rate Determination
Define covered interest parity
The course material gives this chapter a concrete anchor: The parity materials construct borrowing, conversion, investment and forward conversion as one cash-flow loop.
That covered interest parity anchor controls how arbitrage is explained and how uncovered interest parity is tested in changed practice.
Parity, Arbitrage and Exchange-Rate Determination is a quantitative decision problem built from covered interest parity, arbitrage and uncovered interest parity.
The aim is to derive a no-arbitrage forward and test a quote; a numerical result earns meaning only when the variables, units, assumptions and comparison are all explicit.
Begin with covered interest parity: state what quantity it represents, the scale on which it is measured and the condition under which it changes.
Then map every symbol in the Parity, Arbitrage and Exchange-Rate Determination formula checkpoint to covered interest parity before calculation begins.
Next connect arbitrage to the calculation. Show the arbitrage transformation line by line, preserve units and signs, and make any denominator or baseline visible.
A arbitrage calculator output is not a method; the reader must be able to reconstruct why that operation answers the question.
Formula checkpoint: covered interest parity
For matching maturity and compounding, the domestic-per-foreign forward follows relative gross returns under no arbitrage.
Trace arbitrage
Use uncovered interest parity to interpret or stress-test the result.
Ask whether the uncovered interest parity magnitude is plausible, whether a boundary case behaves as expected and which conclusion would reverse if an assumption changed. This is where computation becomes analysis rather than arithmetic.
When the task is to derive a no-arbitrage forward and test a quote, separate inputs supplied by the problem from quantities you derive.
Then report the uncovered interest parity result in the language of the course and attach the relevant uncertainty, limitation or decision consequence.
Build a representation check before solving. Put covered interest parity, arbitrage and uncovered interest parity into a small symbol-and-units table, mark which values are observed and which are calculated, and predict the direction of the result before doing arithmetic.
A sign, scale or unit mismatch in covered interest parity then becomes visible at setup instead of being hidden inside a polished final number.
Run one sensitivity test after the baseline answer. Change the input most closely connected to arbitrage, hold the remaining assumptions fixed and recompute only the affected steps. Explain whether the movement in uncovered interest parity matches the mechanism.
This arbitrage sensitivity shows which assumption controls the conclusion and prevents a single scenario from being presented as universal.
Test with uncovered interest parity
Use a three-column covered interest parity error log for FIN4006: translation error, calculation error and interpretation error.
Record the exact line where the arbitrage solution first diverged, rewrite that line, and check it with a limiting case or an independent calculation.
Correcting the first failed arbitrage move is more useful than copying the complete solution again.
A complete response should make the task visible before the detail: identify what must be decided, define the relevant terms, connect the evidence to arbitrage, and use uncovered interest parity to test the result.
The final sentence about uncovered interest parity should answer the question actually asked rather than merely repeat the topic.
The controlling limit is specific: transaction costs, credit and capital constraints create practical bands.
Keep that uncovered interest parity limit beside the worked example, because it separates a careful FIN4006 answer from one that sounds confident but claims more than the task or evidence supports.
For revision, retrieve covered interest parity, arbitrage and uncovered interest parity without notes, explain their relationship aloud, then complete a changed version of the application: derive a no-arbitrage forward and test a quote.
Record the first failed arbitrage reasoning move and repair it before attempting another case.
What this chapter covers
- 01
Covered interest parity
- 02
Arbitrage
- 03
Uncovered interest parity
- 04
Applying covered interest parity
- 05
Limits of arbitrage and uncovered interest parity
Check a forward quote
- 1Define SGD as domestic quotation currency.
- 1Grow both currency investments consistently.
- 1Compute the covered-parity forward.
- 1Compare it with the dealer quote.
- 1Include costs before declaring arbitrage.
Key terms
- Covered interest parity
- No-arbitrage link among spot, forward and comparable interest rates with currency risk covered. In this chapter it establishes the object needed to derive a no-arbitrage forward and test a quote. Use this definition when the task is to derive a no-arbitrage forward and test a quote.
- Arbitrage
- Simultaneous transactions exploiting inconsistent prices without net market exposure under ideal assumptions. It becomes operational when the analysis must derive a no-arbitrage forward and test a quote. Use this definition when the task is to derive a no-arbitrage forward and test a quote.
- Uncovered interest parity
- Expected-return relationship using an anticipated future spot rate without forward cover. Its interpretation stays bounded because transaction costs, credit and capital constraints create practical bands. Use this definition when the task is to derive a no-arbitrage forward and test a quote.
Parity, Arbitrage and Exchange-Rate Determination FAQ
Which inputs and assumptions control the attempt to derive a no-arbitrage forward and test a quote?
Derive a no-arbitrage forward and test a quote. The parity materials construct borrowing, conversion, investment and forward conversion as one cash-flow loop. No-arbitrage link among spot, forward and comparable interest rates with currency risk covered. In this chapter it establishes the object needed to derive a no-arbitrage forward and test a quote.
What would be overlooked if a student ignored that transaction costs, credit and capital constraints create practical bands?
Transaction costs, credit and capital constraints create practical bands. Simultaneous transactions exploiting inconsistent prices without net market exposure under ideal assumptions. It becomes operational when the analysis must derive a no-arbitrage forward and test a quote.
If a student were to add a bid-ask spread, how should they identify whether the apparent arbitrage survives?
The benchmark forward is 1.35×1.04/1.02 ≈ 1.3765 SGD/USD; only a sufficiently different executable quote after costs supports arbitrage. Transaction costs, credit and capital constraints create practical bands.
Exam move
Reconstruct the relationship among covered interest parity, arbitrage and uncovered interest parity; complete the chapter application without notes; then test the result against this limit: transaction costs, credit and capital constraints create practical bands.
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