# Covered interest rate parity: the forward contract is not risk free

Covered interest rate parity (CIRP or CIP) can be formulated as: $$(1+r_{f,Home})=\frac{S_0}{F_{0\rightarrow 1}} (1+r_{f,Foreign})$$ where $$r_f$$ are risk-free rates in the home and foreign countries, $$S_0$$ is the spot exchange rate at time 0 and $$F_{0\rightarrow 1}$$ is the forward exchange rate at time 0 for delivery at time 1.

CIRP should hold because one can invest risk-free at home and get $$r_{f,Home}$$ or one can exchange money in the spot market, invest risk-free abroad and then exchange money back according to a forward contract entered at time 0 for delivery at time 1 and get $$\frac{S_0}{F_{0\rightarrow 1}} (1+r_{f,Foreign})$$. Both alternatives are risk free, so their returns should be the same. If they were not, there would be an incentive to invest in one of the countries, say the foreign one. This would create demand for the foreign country's currency in the spot market and home currency in the forward market. This would bring $$S_0$$ down and $$F_{0\rightarrow 1}$$ up. It would also reduce demand for risk-free assets at home and increase demand for risk-free assets abroad, bringing $$r_{f,Home}$$ up (as the price goes down) and $$r_{f,Foreign}$$ down (as the price goes up). Consequently, the equality would start to hold.

I have a quibble with this argument. Forward contracts are not risk free. One could consider futures instead, but then one would be subject to margin calls due to fluctuations in the futures price between time 0 and time 1, and one would need to borrow money for that (if the futures prices is going in an unfortunate direction) or would have some free cash (if the futures prices was going in the other direction).

How does one tackle this in theory? Does CIRP simply assume away (by handwaving) the counterparty risk of the forward contract, or is there a smarter argument than that?

• The existence of the cross-currency basis indicates a violation of CIP. Also, physically settled FX forwards and NDFs are subject to variation margin under EMIR. Dec 2, 2022 at 12:01
• @AKdemy, my question is about the theoretical justification for CIRP. I am hoping the theory behind CIRP is based on more or less sensible assumptions, and I am concerned about the one I have identified as problematic. Does anything in your comment apply to that? (I am not that good with the acronyms. I can decipher CIP and FX but not the other two.) Dec 2, 2022 at 12:21
• What is the theoretical justification for perfect competition? All CIP says is that of the assumptions hold, there is this relationship. Empirically, it held quite well until 2007. Nowadays, markets are a bit different and my first comment applies. Dec 2, 2022 at 14:24
• @AKdemy, it has been a long time since I studied perfect competition, so I cannot answer the question. Now you say if the assumptions hold, there is this relationship. Well, the textbook that I was reading did not explicitly state the assumptions, hence my question. Dec 2, 2022 at 14:29