Covered Interest Arbitrage When Forward Rates Exceed Parity
Summary
The document explains how a forward exchange rate above the level implied by spot and the two currency interest rates creates a covered interest arbitrage. The proposed trade borrows the foreign currency, exchanges it for the home currency at spot, invests the proceeds at the home rate, and sells the future home currency proceeds forward for foreign currency. The forward proceeds repay the foreign borrowing, leaving a surplus if the stated inequality holds.
The argument relies on the forward contract to lock in the conversion rate and remove exchange-rate uncertainty from the payoff. It illustrates covered interest parity as a no-arbitrage relationship and shows how a deviation suggests which side of the currency trade to take. The discussion is conceptual: it gives no numerical example and does not account for transaction costs, borrowing and lending spreads, collateral, or other market frictions that could reduce or eliminate the apparent profit.
Key ideas
- A forward rate above the level implied by spot and relative interest rates indicates a covered interest parity deviation.
- Borrow the foreign currency and exchange it into the home currency at the current spot rate.
- Invest the home currency and lock in its future conversion back to foreign currency with a forward contract.
- The locked-in foreign proceeds repay the borrowing, and the excess is the arbitrage payoff before costs.
Tags
Full text
# construct portfolio offering risk free profit
# construct portfolio offering risk free profit
Have trouble understanding this question, seems quite open ended.
Assume that $S(0)$ is the current rate of exchange for foreign currency. Assume that and $K_n$ and $K_f$ are rates of return on home and foreign currency if it is invested over a period $T$.
Assume that the forward rate of exchange $F > S(0)\frac{1+K_n}{1+K_f}$. Construct a portfolio that offers a risk free profit.
I'm not quite sure what I'm asked to do here...
## Answer by RandyF (score 2)
https://quant.stackexchange.com/a/24365
The question is asking if there is a way to create arbitrage by borrowing in one currency, exchanging at the current spot rate, lending in another currency and converting the future payments back to the original currency at the forward exchange rate.
Specifically, given the assumption above, if there were no arbitrage the inequality above could not hold. However, given the inequality, it would be optimal to borrow in the foreign currency at rate of $K_f$, convert that cash flow into the local currency at the spot rate, lend the local cash flow at $K_n$ and enter into a forward contract to convert the future local cash flows into the foreign currency to pay off the initial debt. This is because the true forward price (converting local currency into foreign currency) is more expensive than the synthetic forward price. Therefore, it is optimal to be on the side that is converting the foreign currency into local currency.
For more information, see: http://www.investopedia.com/terms/t/triangulararbitrage.aspShown 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.