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Covered Interest Arbitrage When the Forward Rate Is Too Low

Article Quant Q&A · Author: Ethan S
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Summary

The document addresses the reverse of the familiar covered interest arbitrage example in which a forward exchange rate is too high. Its GBP/USD illustration explains that when the quoted forward is below the rate implied by covered interest parity, an investor can borrow the currency with the higher interest rate, invest in the other currency, and use a forward contract to lock in the exchange back. A second answer summarizes the equivalent idea as combining a short position in the underlying currency with a forward purchase.

The discussion stresses that textbook arbitrage assumes borrowing and lending access at comparable rates and few practical constraints. In real markets, available deposit and loan rates, bid–ask spreads, cross-currency basis, liquidity, and the ability to invest or borrow abroad affect whether the trade is feasible. Taxes, regulation, counterparty default, political risk, and exchange controls can also prevent an apparent pricing gap from being genuinely riskless. The example illustrates the direction of a trade, not a complete executable arbitrage calculation.

Key ideas

  • When a forward rate is below its covered interest parity level, the arbitrage direction reverses from the too-high case.
  • The illustrated strategy borrows the higher-rate currency, invests in the other currency, and hedges the exchange with a forward.
  • The equivalent construction can be described as shorting the underlying currency and buying it forward.
  • Actual funding rates, market spreads, and cross-currency basis affect the parity comparison.
  • Regulatory, tax, counterparty, and political risks can undermine the claim that a trade is riskless.

Tags

ForexArbitrageCarryRisk management
Full text
# Can you perform covered interest arbitrage when the forward rate is too low?


# Can you perform covered interest arbitrage when the forward rate is too low?












In covered interest arbitrage, if the forward rate is too high, you can (i) exchange domestic for foreign currency today (ii) invest at the foreign deposit rate (iii) exchange back to the domestic currency at the "too high" rate, and you have beaten the rate you could have gotten by just investing domestically. Mathematically, this is just $$ F > S\frac{1 + i_d}{1 + i_f} \implies 1 + i_d < \frac{F}{S}\frac{1 + i_f}{1 + i_d} $$ where $F$ is the forward rate, $S$ is the current exchange rate, $i_d$ is the domestic interest rate, and $i_f$ is the foreign interest rate.

How do you perform arbitrage if the forward rate is instead too low? All examples I have seen are for the "too high" case.

## Answer by AKdemy (score 2)

https://quant.stackexchange.com/a/63713

I do not like foreign and domestic. It frequently causes confusion, also by people who work in the market (@Ethan S, you use what is widely used, so excuse my rant).

I decide to demonstrate with GBPUSD (CCY1CCY2); GBP is foreign, USD domestic since it's quoted in units of domestic currency per unit of foreign currency. In other words, if S=1.4, one needs 1.4 USD to get one GBP.

Now, assume GBP interest is 2%, USD rate is 1% and the forward is 1.3. Fair FWD according to CIP is well above the actual market quoted forward.

Simple introductory textbooks assume borrowing and lending is at the same rate and there is no restriction to borrow abroad. Now, it is optimal to borrow in GBP, and invest in USD.

As @fesman points out; can you borrow abroad? Could just say it is always only one side of the pond that can do this arbitrage? Well, the actual question is, can you invest abroad? The answer is not so different really. From a retail investor side, the answer is probably not. That said more than one in five Polish mortgages was held in Swiss francs.

However, the FX and rates interbank market is something vastly different. There is strong competition and low regulatory burden, which results in very small spreads between interest rates at which banks are willing to pay for deposits and the interest rates that banks charge for loans. The Eurodollar market is very liquid. Moreover, there is a very liquid cross currency swap market. You should actually take this basis into consideration when doing the exercise.

One could argue this is all very much US centered thinking but even if the transaction is between COP and ARS, USD plays a role as one could always do the series of transactions via USD.

This is what professional tools computing this are doing. E.g. on Bloomberg, one can use `FXFA` to check CIP or imply any direction. It is displaying sided pricing (bid-ask), and flexible in terms of interest rates being used (LIBOR, OIS...).

Even if you were to find apparent arbitrage, it is likely that after considering all aspects (regulation in different countries, tax implications, default risk of counterparties, political risk, exchange controls..), this will quickly look unlikely to be riskless arbitrage. Ex-ante, you never know what happens...

## Answer by Randor (score 0)

https://quant.stackexchange.com/a/63771

Yes If forward is lower than the forward you can get via the strategy of shorting the underlying and investing the proceeds , then do that strategy and simultaneously buy forward and voila youve locked in profits :)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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