How Cross-Rate Errors Could Affect Covered Interest Parity Tests
Summary
The document raises a measurement concern for historical tests of covered interest rate parity (CIP). It notes that interbank forward quotes are commonly expressed against the US dollar, with a stated exception, and asks whether inconsistencies between directly quoted exchange rates and rates implied through a common currency could distort calculated CIP deviations.
It illustrates triangular arbitrage: if a direct currency quote differs from the cross rate implied by two other quotes, converting funds around the three rates can produce a residual profit in the example. It also describes deriving a CHF/JPY swap by triangulating USD/CHF and USD/JPY outright rates, then subtracting the CHF/JPY spot rate to obtain forward points. These examples show how quote construction can matter for cross-currency calculations. The document does not establish that such errors occurred in the historical data or quantify their effect on CIP estimates; bid-ask spreads, timing, and market conventions would also matter in an empirical analysis.
Key ideas
- A cross rate is implied by combining two exchange rates that share a common currency.
- Inconsistent direct and implied quotes can create apparent triangular arbitrage opportunities.
- Cross-currency swap points may be derived by triangulating dollar currency legs.
- Quote construction may influence measured covered interest parity deviations.
- The document identifies a possible data issue but does not test its historical impact.
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Full text
# Possible interference of Cross-Rate inaccuracy and CIP Deviations # Possible interference of Cross-Rate inaccuracy and CIP Deviations I am currently attempting to calculate historical deviations from covered interest rate parity between 2013 and 2018. I recently read that: > "Unlike the interbank spot market, in the interbank forward market, every currency is quoted always against USD (except for EUR/GBP)" http://www.londonfx.co.uk/forwards.html Accordingly, my concern stems from possible deviations of directly quoted exchange rates from their cross rates with a common currency. What I am referring to here is what textbooks use as the classical example of triangular currency arbitrage.My question, therefore, is whether it is possible that said potential mispriced rates could influence the deviations I am planning to calculate? Example of a what I mean by triangular cross currency arbitrage: > The two indirect quotes being €0.8778/\$ and €1.4373/Pound. Then the cross rate refers to 1.4373 / 0.8778 = \$1.6355/Pound. Assuming 3 exchange rates above and the indirect exchange rate of $/Pound: 1.6365, an investor endowed with 1.000.000 Pound could earn a risk free profit by: first exchanging his money for \$1.636.500 then exchange this for Euros using €0.8788/\$ and obtain €1.438.156 The final step is then to exchange back to Pound from Euro € 1.4373/Pound, which leaves the investor with 1.000.596 Pound and therefore a riskless profit of 596 Pounds Example of what I mean by triangulating a swap: > To calculate a CHF/JPY swap, a forward trader must calculate each leg of the swap by triangulating USD/CHF and USD/JPY outright rates. The CHF/JPY spot rate is then subtracted from the resultant CHF/JPY outright rates to give CHF/JPY forward points. Whereas the second example can also be found at the page linked above.
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