The Swiss Franc isn't the easiest example to step through because it's under negative interest rates, so let me use a fictional example with round numbers so it will be more intuitive. Let's say there is a currency called the Franconian Franc (FFF) that currently has a national interest rate of 1%. That means that a hedge fund or large financial institution could both borrow and lend at right around 1%. And lets say the US currently has an interest rate of 2%, meaning big financial players can borrow and lend at that rate. Let's say the USD/FFF currently trade at parity, 1 USD = 1 FFF. And the futures for 1 year from now are also at 1 USD = 1 FFF. If you were a financial player, you could borrow $100 in FFF at 1% interest rate. Immediately convert that $100 FFF to $100 USD. Then lend that $100 USD at 2% and simultaneously enter into a futures transaction for 1 year from now to exchange $102 USD into $102 FFF. At the end of the year, you would owe $101 FFF (you borrowed $100 FFF at 1% interest) and you would have $102 USD (you lent $100 USD at 2% interest). But your futures transaction would also be in play, it would immediately convert that $102 USD into $102 FFF. You would use the $102 FFF to pay off your $101 FFF loan and have a risk free dollar left over. If you were a large financial player you would do that to the tune of billions of dollars, until you arb'd the opportunity away. And how would you arb the opportunity away? The futures rate wouldn't stay at $1 USD = $1 FFF. Instead it would move to $1 USD = $.99 FFF. At that point, when you tried to do the arb position, you'd end up at the end with $102 USD that the futures transaction would convert to $101 FFF and you'd have no risk free money left over. The futures rate of $1 USD - $.99 FFF isn't random or the market's guess of the future price of FFF. It's simply the mathematically what it has to be in order to prevent a zero risk arb from happening. It's very possible that at the end of a year $1 USD = $1.05 FFF or $.93 FFF, but if you entered into the futures transaction on the first day of the year and the offsetting transactions I described, you would end up flat at the end of the year, as it has to be to satisfy the no arb condition. If you do the double negatives on the 5 year Swiss treasury rates and 5 year U.S. treasury rates compounding over 5 years, you'll see it come up to very close to the 5 year futures rate. Keep in mind that not always does the no arb condition hold, and if you look historically at the Swiss Franc they tried to maintain a band versus the Euro that distorted things. But generally, between two liquid, regularly traded currencies, that condition will hold pretty closely.
Sig, thanks so much! Your example is crystal clear, I follow it 100%. Two follow up questions. 1. The first one is just a small technical question. Taking your example, what is the specific mechanism that causes the FFF currency to rise? So the lender borrows in FFF, then lends in dollars. The lender is borrowing in FFF and converting said FFF into dollars (over and over again until the arb opportunity goes away). Just not clear in my mind right off hand the specific thing that is causing the FFF to rise in this scenario. I guess the lender is borrowing in FFF, creating a demand for FFF, but then it is also converting that FFF into dollars, I would guess increasing the amount of dollars? 2. More importantly, given that the futures prices of the two currencies generally have to follow this interest rate equation to avoid arb opportunities, does that mean there ARE ways to make money, for example, looking at the expected money supply increases between the two currencies? Taking your example, if the FFF futures are priced at $.99 FFF to a dollar, and the U.S. government tomorrow decided to double the amount of currency in circulation, and you had bought those futures, wouldn't you have made a killing because you could wait the year, acquire the FFF at $.99 cents per FFF, but the spot price then you have to (well, more likely me) closer to like $.495? Thanks so much!
On item 1, it's unlikely the borrowing or lending would impact national interest rates. Much more likely that entering into the futures contracts required to make the whole no arb situation work impacts the price of that futures contract toward the no arb price. For item 2, my hypothetical probably wasn't completely clear on this point but it assumed you were buying a 1 year bond, for example, and holding it to maturity or lending money for 1 year at a fixed rate. That's the only way it can be a no-arb situation, you lock everything at the point it's initiated. Your question is a good one because you could instead borrow or lend at a variable rate for one or more of the legs. In that case the true arb goes away and you've really just exposed yourself to a bet on what happens to interest rates during the year and if those changes happen early or late. There are probably better instruments to use to make those bets (like eurodollar futures), but certainly you could do that and it would be a valid strategy. Going back to the original question I think that's probably actually what you were getting at?
Thanks Sig! On option 1, I got it - the adjustment would just be taken into account in the futures price. Hence why futures price is (generally) spot + interest rate (cash and carry) adjustments over time, per your example. On option 2, my question was this (but I think I have it figured out now). If the futures prices were determined solely by reference to the spot plus the interest rate cash-and-carry adjustments as your example so perfectly demonstrated, would they not be pricing a future huge increase in the USD or FFF money supply. And if they did not, could you take advantage of that. But, thinking about it, I think the answer is that the SPOT forex rate should take into advantage potential huge increases in money supply - if people think that the USD money supply will increase 30% in short order, they are going to want to get out of the dollar, driving down is spot rate. That driving down in the spot rate will then drive down futures prices as well so that they meet spot + cash-and-carry interest rate adjustments per your example. How'd I do? Thanks Sig!!!
Yeah, I think you have that about right. That's why the spot prices diverge for the futures price over time and the futures price isn't actually a prediction of where spot will be at that point in time in the future. Now go take an grad level MOOC on forex, you'll really enjoy it!