Interest Rate Parity with FX Settlement Delays

Summary

The document asks how covered interest rate parity should be applied when spot foreign-exchange trades settle after a delay. Its starting point compares investing domestic currency at the domestic rate and converting at a forward rate with converting into foreign currency at spot and investing at the foreign rate. The question focuses on very short investment horizons, where the usual simplified argument may seem to ignore the time before spot currency is delivered.

It proposes adjusting the foreign investment period by subtracting the spot settlement lag, then asks whether that captures the effect. No answer or derivation is included, so the proposed adjustment is not established by the document. The practical issue it raises is that parity calculations must align cash flows, value dates, and investment accrual periods. Resolving the question would require specifying trade and settlement dates and how the forward contract's delivery date relates to those dates; the text supplies no examples, evidence, or general formula for doing so.

Key ideas

• Covered interest parity compares domestic and foreign investment routes linked by spot and forward exchange rates.
• Spot FX settlement introduces a timing gap between a trade and the delivery of foreign currency.
• For short horizons, settlement and investment dates need to be aligned when comparing cash flows.
• The suggested reduction in the foreign investment period is posed as a question and is not validated in the document.

Tags

# How does interest parity work with settlement dates?


# How does interest parity work with settlement dates?












Interest rate parity is typically proven as follows.

Given one unit of a domestic currency, one can either convert it into $S$ units of the foreign currency and invest at the foreign risk free rate $r_f$ for time period $T$, to obtain $S e^{r_f T}$. Alternatively, one can invest at the domestic rate $r$, and then convert to foreign currency at the FX forward rate $F$ to obtain $Fe^{r T}$. To be arbitrage free, these quantities must be equal.

I'm interested in how to use this in practice, and how this can be complicated by settlement dates. For example, FX spot settlement does not occur immediately, but instead typically takes two days. So it seems like this would break down for short time spans.

So suppose the time period invested $T$ above is less than the number of days it takes to settle an FX spot transaction. Then the above argument does not work, since the time it would take to convert to foreign currency is non-trivial compared to time invested. How to prove that IR parity holds in this case?

Additionally, it would seem that given the settlement period, there should be some small adjustment to IR parity, and it would be something like

$F e^{rT} = S e^{r_f T'}$, where $T' = T -$ ($2$ days),

since we would not be able to invest the $S$ amounts of foreign currency until it is delivered after 2 days. Is this correct?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.