CHAPTER 6
Foreign Exchange Forwards
Money often costs too much.
—Ralph Waldo Emerson
INTRODUCTION TO FORWARDS AND FORWARD PRICING
In some ways, the financial markets involve transactions that are similar to more mundane experiences. While on a trip, I may need a place to sleep. I could simply attempt to locate lodgings as my bedtime approaches, but that could prove problematic. I may not be able to find a vacancy, but, even if I could, I would have no idea what I would have to pay (and would probably feel like I was being taken advantage of, upon hearing that there are vacancies, but that I would have to pay $400 for that evening’s stay). In short, many of us who travel tend to arrange for our hotel/motel accommodations in advance. That way, we are ensured that we can get what we would like—at a price that we feel is reasonable. A large number of foreign exchange trades are done in this fashion. If you arrange a currency trade, locking in a price (an exchange rate) and a quantity in advance, this is known as a “forward contract,” a “forward transaction,” a “forward trade,” or, simply, a “forward.”
There is no reason why you should expect the price in a forward trade to be the same as the price in a spot transaction. Would you expect the price of bananas to be the same in Helsinki as in Honduras? No. These prices would differ because the trades would occur at different points on the globe. An FX forward trade will generally involve a different price than a spot trade; these transactions take place at different points as well—different points in time (and, as you may have heard, time is money)!
Let me start this section by asking you a question or two (and, to try to make the point, let’s get away from FX for the moment). Could I ever convince you to voluntarily agree to buy a stock today for S = USD 50 (a spot transaction) and simultaneously get you to agree to sell that stock in a week (a one-week forward transaction) for F = USD 48? Stop and think about it. It doesn’t sound good, does it?
I would venture to say, though, that if I offered to make an additional side payment to you of USD 5, you might willingly agree to do both of these trades. (This brings up the notion of “payment” or “premium” and will be revisited when we talk about off-market forwards and options.) But what if I do not offer you any “side compensation”? Is it possible to envision a scenario under which you might still willingly agree to both of the trades mentioned above? Have you seen it yet?
What if the stock itself pays you something? Stocks have been known to pay dividends. A dividend is a payment from the company to the registered owner of the share(s). If the stock were to pay you a dividend of USD 5 per share over the course of this week, this pair of trades would now look relatively attractive.
Finally, what if I am not offering to pay you anything (on the side) and the stock doesn’t pay any dividends. Could I convince you to buy the stock today in the spot market for S = USD 50 and to sell the stock in a week (sell the stock forward) at a price of F = USD 50? At least this looks a little better than our earlier numbers, but you shouldn’t fall for it. What you would lose is the interest on your money. In general, if there is no benefit from owning and “carrying” an asset, you should insist on being compensated for tying up your money (with the result that you’d expect the forward price to be higher than the spot price). On the other hand, if the benefit of “carrying” the asset (in the earlier instance, the dividend) is large enough, you’d willingly agree to sell that asset in the future at a forward price that is lower than the current spot price. Forward pricing is all about costs and benefits!
In general, the forward price (F) will be based on the spot price (S) grossed up by “the cost of carry” (in our example, by the cost of money or the interest cost) and reduced by “the benefit of carrying the asset” (in our example, the dividend). Perhaps it is easier to write the following:
(6.1)
Using a little notation, in this case of a dividend-paying stock, we could write
Where
(6.2)
F = the forward price S = the spot price
r = the (annualized) interest rate
t = the time (in years)
Div = the dividend
r = the (annualized) interest rate
t = the time (in years)
Div = the dividend
FORWARD EXAMPLE
If a stock is trading at S = 40.00, interest rates are r = 5.00%, we are thinking about a three-month time frame (t = 1/4 = .25), and, in two months and three and a half weeks, this stock will pay a (confirmed) dividend of Div = 1.50, where would you guess the three-month forward price would be quoted?
F = 40.00 + 40.00 × (.05) × (1/4) – (1.50) = 39.00
For simplicity, we sweep the couple of days of interest on the dividend under the rug (i.e., we will simply ignore it here).
FORWARD EXERCISE #1
If a stock is trading at S = 100.00, interest rates are r = 4.00%, we are thinking about a one-year time frame (t = 1), and, over the course of the year, this stock will pay a quarterly dividend of Div = 0.25, where would the one-year forward price be quoted?
FOREIGN EXCHANGE FORWARDS AND FORWARD PRICING
Let’s now attempt to bring this concept back to foreign exchange. It will be easiest to choose a currency pair, like USD|CHF, and think through what this spot-forward relationship would look like in FX. Assume USD|CHF S = 1.2500 (that is, USD 1 = CHF 1.2500). With this quote, the U.S. Dollar is the underlying asset, and the price of that asset is quoted in Swiss Francs. Let’s start with the benefits. Are there benefits to buying and holding Dollars (the underlying asset)? Of course. Unless you put the USD in your pillowcase or a safety deposit box in a Swiss bank, you will receive interest on your Dollars. What about the cost? To answer that question, we have to think about perspective. From whose perspective is this price quoted? This is the Swiss (European) perspective. If a Swiss individual wanted to buy and carry USD 1 (because, perhaps, they want to go to Disneyland—again, the real Disneyland, not Euro Disney), they would either have to take their Swiss Francs out of their Swiss bank savings account (forgoing interest) or borrow the Swiss Francs (in order to purchase the Dollars). It will always be easier to think of the latter; in this case, there is an actual and explicit cost associated with borrowing CHF and buying USD; that cost is the Swiss interest rate incurred as a result of the borrowing. At this point, we might try to fit these elements into our earlier relationship (using USD 1 as the notional magnitude of our transaction):
(6.3)
There’s only one problem here. You’re adding apples and oranges (or, really, Swiss Francs and Dollars). The cost of buying USD 1 is in Swiss Francs, but the benefit of “carrying one USD” is the interest you would receive—presumably in Dollars. Putting units on these terms, we get:
(6.4)
Since spot is quoted as CHF per USD 1, you would think the forward should be quoted in the same way, so the only problematic term here is the last one. If we want everything in terms of CHF (which makes sense, as that is how spot is quoted), one might propose multiplying the last term by the spot price. After all, that would convert those USD into CHF, would it not?
This would give us (using our earlier notation)
or more simply, now that everything is in Swiss Francs,
or
(6.5)
(6.6)
(6.7)
If you ask almost anyone who works in foreign exchange why the spot price and the forward price differ, they will respond with these three words:
“interest rate differentials.”
You can see it. If the costs and benefits are the same (that is, if Swiss interest rates and U.S. interest rates are equal), then the spot price and the forward price will be the same.
This is definitely the right intuition, but careful consideration might convince us that this isn’t really right. After all, the interest that we would get on USD 1 would be realized only in the future, so, really, the spot price applied to the U.S. Dollar interest shouldn’t be the spot price today; it seems as if it should actually be the spot price at the end of this time period (which, unfortunately, we do not know today). Sounds like we’re back to square one, but not really. We could ask, “Is there a price that we can observe today at which we could exchange USD for CHF at some point in the future?” The answer, of course, is yes. That is the forward price. Returning to our relationship, it would now look like this
or
or
or, finally,
F = S + SrCH t – F 1 rUSt
F = S(1 + rCH t) – F rUSt
F(1 + rUS t) = S (1 + rCH t)
This is the “correct” relationship.1 It may seem odd (using F in our definition of the forward price—kind of like defining “constitutionality” as “of or relating to the Constitution”), but indeed this is the relationship that must hold—otherwise an arbitrage would exist.
FORWARD EXAMPLE
Currency pair (Dollar-Swiss): Spot USD|CHF S = 1.2500
Using a one year (t = 1) time horizon with rUS = 5.00% and rCH = 3.00%, calculate the one-year forward price.
The one-year USD|CHF forward price should be F = 1.2500(1.03)/(1.05) = 1.2262 (rounded to the fourth decimal place).
FORWARD EXERCISE #2
If USD|JPY is trading in the spot market at S = 110.00, Japanese interest rates are rJ = 1.00%, U.S. rates are rUS = 5.00%, then where would you expect to see the one-year USD|JPY forward price quoted?
Let’s try to arrive at this FX spot-forward relationship in another way: If USD|CHF S = 1.2500, this means that CHF 1.2500 = USD 1 today in the spot market. These amounts of money are in some sense equal, or equivalent, or of the same value. Now if CHF 1.2500 today = USD 1 today, then, one would think that these would be expected to be equal at any given point in time in the future as well, but we can’t forget that money grows over time. This would mean that, in one year, what was previously equal (USD 1 and CHF 1.2500) should still be equivalent, but USD 1 will have grown into USD 1.05 and CHF 1.2500 will have grown into CHF 1.2875. On a per Dollar basis, this implies USD 1 should = CHF 1.2262. This is most easily seen diagrammatically (see Figure 6.1).
FIGURE 6.1 Example of Interest Rate Parity
Further, this can be depicted generically (again, using a European spot quote). See Figure 6.2. This spot-forward FX relationship is known as Interest Rate Parity. Three technical points:
FIGURE 6.2 Generic Interest Rate Parity
1. Rewriting the general spot-forward relationship in foreign exchange:
(6.9)
I am often asked, “Does the U.S. interest rate go on the top or the bottom?” Good question. Let me explain. In the case of USD|CHF, the spot price is quoted in terms of CHF. It therefore makes sense (does it not?) that the rate on top (in the numerator) should be the Swiss interest rate (the rate that goes with CHF). This next statement may sound hokey, but it always “works.” In USD|CHF, the U.S. Dollar is the UNDERlying asset; for that reason, the U.S. Dollar interest rate goes UNDERneath (in the denominator). If we were to quote EUR|USD, the spot price is quoted in USD, so the U.S. interest rate goes on the top in our formula; the EUR is the UNDERlying asset, so the EUR interest rate goes UNDERneath. Possibly lame, but hopefully now easy to keep straight.2
2. For those strange individuals who would rather use continuous interest conventions, the spot-forward FX relationship would look like this
(6.10)
While mathematicians, “quants” (or quantitative analysts), and computers may like this interest convention, one has to be careful not to simply insert market interest rates (quoted annually using noncontinuous compounding) into this formula. The one nice thing is that we again see that if interest rates are the same in the two countries, the spot price and the forward price will be the same.
3. One might think we should consider compounding the interest (that is, using a compounding convention, as opposed to the simple interest convention, which we have built into Equation [6.9], but, in practice, the vast, vast majority of forward trades are done under a year (most under six months), and so it is appropriate to employ the money market convention of using simple interest.3
INTEREST RATE PARITY (COVERED INTEREST ARBITRAGE)
Before moving on, let’s think once more about the intuition here—from an economist’s perspective. Spot is spot. There is a price in the market today for USD 1 and it is CHF 1.2500. Interest rates differ in the United States and Switzerland. U.S. Dollars are growing at 5% and Swiss Francs are growing at 3%. In relative terms, USD are growing faster than CHF. They taught me in economics classes at the University of Chicago that when supply goes up, the price goes down. That is what is happening here. S = 1.2500 today and F = 1.2262 in one year. The price of a Dollar is expected to fall because the Dollars (compared to Swiss Francs) are becoming relatively more abundant. (See Figure 6.3.)
Let’s take another stab at it. Why are interest rates in Switzerland different from interest rates in the United States? Both Switzerland and the United States have well-educated populaces; both have stable political and financial systems; both have access to world-class technology; both have solid economic infrastructure. Why are interest rates different? The most likely reason that nominal or market interest rates differ is not because real interest rates differ (though they may), but because the two countries have different rates of inflation, which is primarily the result of their monetary policies. The nominal or market U.S. interest rate of 5% might be made up of a 2% real rate of interest (as described in Chapter 3) plus 3% (expected) inflation. The nominal or market Swiss interest rate might be composed of a 2% real rate of interest plus 1% (expected) inflation.
FIGURE 6.3 Interest Rate Parity: Graphical Explanation of Interest Rate Parity as a Special Case of Supply and Demand
What is inflation? A general increase in the level of prices. What causes inflation? At the University of Chicago, as graduate students in the Department of Economics, we were taught to chant, “Inflation is always and everywhere a monetary phenomenon.” In other words, prices rise if monetary growth exceeds the rate of growth in the real economy. Inflation is a direct result of the government printing and spending. In general, you will see inflation (or possibly even hyper-inflation) when a government simply prints and spends (again, to be precise, at a greater rate than the real rate of growth in the economy). Inflation is a particularly sneaky form of taxation; the government gets to spend the valuable currency before all the citizens realize that the money they are holding is worth less than it was a short time before, since there is now more of it around relative to the supply of goods and services. This explains the popularity of expansionary monetary policy. As the U.S. Dollar is being debased relative to (or printed faster than) the Swiss Franc, one would expect the relative value of the USD to fall. S = 1.2500 and F = 1.2262.
We have said that this pricing relationship is known as interest rate parity. Parity implies an equivalence or equality between two things. Obviously interest rates in the United States and Switzerland need not be the same (nor do they have to “converge” in any sense), but, if a wealthy Swiss individual thought about converting CHF today into USD (in order to capture the higher interest of 5% in the United States, relative to the Swiss rate of interest of 3%) and also attempted to convert those Dollars back into Swiss Francs using the forward market (because, after all, this person is Swiss), they would end up with the same amount of CHF as if they had simply invested it directly in their Swiss bank at a rate of interest of 3%. They also taught me at the University of Chicago that there’s no such thing as a free lunch; interest rate parity is just another way of stating that fact.
Interest rate parity goes by other names. It is sometimes referred to as “covered interest arbitrage,” which would suggest doing trades (e.g., selling forward and covering it by buying spot) if the markets are out of line in some sense. Let’s consider spot-forward arbitrage in FX by showing the cash flows associated with an arbitrage situation.
FX SPOT-FORWARD ARBITRAGE
EXAMPLE
USD|CHF: S = 1.2500 t = 1 rUS = 5.00% rCH = 3.00% and F = 1.2000
If these were all market quotes (i.e., we could buy or sell USD in the spot market for CHF 1.2500, we could borrow or lend U.S. Dollars for 1 year at 5%, we could borrow or lend CHF for 1 year at 3%, and we could buy or sell Dollars one year forward at CHF 1.2000), it would appear that something is wrong or out of line.
In the financial markets, “out of line” sounds like an arbitrage opportunity (and indeed there is one here). Earlier, we figured out that the 1-year USD|CHF forward should be quoted/trading around F = 1.2262. Here, the quoted forward price in the market is too low. Remembering perhaps the most important adage in the financial markets: “Buy Low, Sell High,” what trades would you do? Think about it before reading on.
By comparing where the forward price IS quoted in the market (F = 1.2000) and the value at which you believe (based on interest rate parity) the forward SHOULD BE trading (F = 1.2262), it appears too low in the market. To be more precise, it seems as if the market price of a Dollar (quoted in terms of CHF) is too low in the forward market, so BUY USD FORWARD.
Once you have arrived at this point, the rest becomes mechanical.
If you are BUYING USD FORWARD, then you must be buying them with something. BUYING USD FORWARD = SELLING CHF FORWARD. If you stop here, you are simply betting that the Dollar will strengthen, or at least not weaken below CHF 1.2000; this is not an arbitrage. You are doing these trades, though, because something is out of line. Spot-forward arbitrage requires that you do the opposite trade in the spot market. SELL USD SPOT = BUY CHF SPOT.
In order to see how to turn a profit, let’s work out the cash flows. To begin, we must decide how big to play; in other words, you have to decide on a certain notional in one of the two currencies on which to base your cash flows. Let’s do this on USD 100,000,000, which might sound like a large amount, but is certainly not unprecedented in FX trading.
In the spot market, we said you’d want to Sell USD and Buy CHF (remember, this is one trade). Where do we get the Dollars to sell? Let’s assume we borrow them, and in this example, we are going to borrow USD 100,000,000 (for 1 year at a rate of 5%). Now you can Sell USD 100,000,000 and Buy CHF 125,000,000. Putting these CHF in a Swiss Franc account, you will receive 3% interest. Now what? Nothing, until a year goes by. At this point you will OWN CHF 128,750,000 and OWE USD 105,000,000. Where’s the profit? Well, we have to close out these positions in the forward market to realize the gain associated with the opportunity we identified. Presumably we locked in the forward price of 1.2000 (allowing us to buy USD 1 by selling CHF 1.2000). If we convert all of the CHF that we OWN to USD (and doing so would result in our obtaining USD 107,291,666.67) and then pay back the USD we OWE (that is USD 105,000,000), we will end up with a profit of USD 2,291,666.67. Not bad for a couple of trades, huh? It may help to review these trades in diagrammatic form (see Figure 6.4) remembering our two legs:
and the notional size of the (spot) transaction: USD 100,000,000. Look familiar? It should. It is simply interest rate parity at work.
BUY CHF SPOT = SELL USD SPOT
SELL CHF FORWARD = BUY USD FORWARD
SELL CHF FORWARD = BUY USD FORWARD
A number of questions.
1. What if you wanted to realize your profit in CHF? Could you do that? Of course. In this case, you would only want to convert enough of the CHF that you own in one year in order to cover the USD that you’ve borrowed (plus the interest on those Dollars, of course). Using our numbers, this would involve selling CHF 126,000,000, which at the forward price of F = 1.2000 would turn into USD 105,000,000. This would leave a profit in Swiss Francs of CHF 2,750,000. 
FIGURE 6.4 FX Spot-Forward Arbitrage
2. Does it matter how you choose to realize your profit? No and yes. A U.S. Dollar-based trader or institution might choose to realize their profit in USD; a Swiss bank might prefer to obtain their profits in CHF. A hedge fund might not care, unless, that is, they have a view on the future spot price (that is, USD|CHF in one year), if they thought that USD|CHF spot, because of the massive U.S. trade deficit, was going to be around 1.1600, then even if they are USD-based, they would prefer to realize their profit in CHF—with the expectation that these CHF will translate into even more USD in the spot market in 1 year than they might have been able to lock in if they had chosen up front to realize their profit in USD.
3. More importantly, though, when you enter into the forward contract, you agree to transact at the forward price (that is, you lock in the price), but you also have to agree on a notional quantity. You can’t just say, “I’d like to sell CHF = buy USD in 1 year at F = 1.2000.” You have to say, “I’d like to buy USD 105,000,000 for the forward price of F = CHF 1.2000 per USD,” which, of course, is the same as saying, “I’d like to sell CHF 128,750,000 in one year at the forward exchange rate of CHF 1.2000 per USD 1.” In other words, when you enter into a forward, you have to agree on a forward price and a quantity (or face or notional) in at least one of the two currencies.
4. Trivial pursuit. Your profit in Dollars was USD 2,291,666.67. Your profit in Swiss Francs was CHF 2,750,000. If we were to form the ratio of CHF to USD, what do you think that number (or really, that exchange rate) would be? Try it. Not surprisingly, it is 1.2000 (the forward price), because that was the rate at which you exchanged CHF for USD in the future.
5. Could you have realized your profit today? The answer is yes. You could either spend some of the USD you borrowed today and still have everything work out nicely, with neither a profit nor a loss in one year or you could spend some of the CHF that you purchase today, with the same result. Why not try to figure out how many of your Dollars you could spend today and still have everything work out in one year’s time?
6. Finally, does your profit figure look reasonable? As with our triangular arbitrage example in the spot market, it is good to do a reality check. In this case, we thought the forward should be quoted at F = 1.2262, whereas it was actually quoted in the market at F = 1.2000. The ratio of these two (1.2262/1.2000) gives us 1.0218333. How much did we expect to make? About 2.2%. How much did we make? Well, based on our original spot notional of USD 100,000,000, we made almost 2.3%. Close enough? Unlike spot triangular arbitrage, where our profit margin aligns exactly with our price-to-value ratio, here we are a little bit off because, when all is said and done (i.e., in one year), we didn’t end up doing this trade on only USD 100,000,000. Nevertheless, as a quick and dirty check, we should find some comfort in the fact that we made a profit of a little more than 2%.
Hopefully this example has served to reinforce the notion that interest rate parity will generally hold in the market in a fairly hard and fast way, unlike purchasing power parity. Any significant deviation of the market forward price from the forward value as derived from interest rate parity (Equation [6.9]) and traders would quickly jump in and arbitrage any differences away.
One last point. In all of our forward calculations, we have input interest rates. Which interest rate should one use? Textbooks have sometimes suggested that one use the “risk free” rate of interest (e.g., the rate of interest relevant to a riskless or default-free market participant, such as the U.S. government), but this would be wrong. The U.S. government, while they may intervene in the FX market, is generally not in the business of turning an arbitrage profit. On the other hand, banks—and more precisely their FX trading desks—would pursue such low-risk trading opportunities. In this case, both the associated cash flow funding and forward valuation will involve the interest rates relevant to that particular institution (and the better money-center banks usually fund themselves at or around LIBOR). To the extent that the spread between the three-month U.S. Treasury rate versus the three-month U.K. government rate probably correlates well with the difference between three-month USD LIBOR and three-month GBP LIBOR, it may look as if the market is using these “risk free” rates, but it is your cost of money (if borrowing) and your return on money (if depositing), which would include a bid-ask spread in rates that you would have to consider before entering these trades.
At the end of this chapter, we give you the opportunity to try your hand at a foreign exchange spot-forward arbitrage problem on your own. As with spot triangular arbitrage, these are intended less as practice in how to profit from trading FX and more as exercises in working with FX forwards, in gaining a deeper understanding of the spot-forward relationship in FX, and in becoming familiar with the cash flows associated with these trades.
FX FORWARD PRICE QUOTES AND FORWARD POINTS
Now, how does it work in the real world?
With USD|CHF S = 1.2500, t = 1 year, rUS = 5% , rCH = 3%, if you were to call an FX bank or dealer and ask for an indicative (midmarket) one-year forward quote (midmarket serving to set aside the bid-ask spread), you’d probably hear 238. What?
Let me briefly explain how forwards are quoted. If you were to request a forward outright or a forward outright price (which is what you probably had in mind a few seconds ago), a dealer/trader/salesperson might have said the following, “1.2262, no wait, 1.2260, just a second, 1.2265, no, no, . . . 1.2264, hold on, 1.2259, no, 1.2263, . . .”
What is that all about? Why is the forward price moving around like that? Because spot is moving around. A forward is a derivative and as such has a value that is derived from the underlying spot price. Every time the spot price moves, the forward moves. They are linked. How to avoid this when quoting forward prices? Dealers tend not to quote the forward price directly (or what we have referred to previously as the forward outright). They quote the difference between the forward price and the spot price (typically in pips, and often ignoring the numerical sign). It might sound confusing, but it really does make life easier.
In our previous example, recall that S = 1.2500 and F = 1.2262. Because F < S, some would say that the Dollar is trading at a discount (to the spot) in the forward market. If the forward price had been higher than the spot price, they would say that the Dollar is trading forward at a “premium.” The difference between F and S is – .0238 or – 238 pips. And what is this difference? It is the difference between forward and spot or the “carry.” It is driven by those interest rate differentials (and the time frame or time horizon under consideration). These are referred to as “forward points.” Although the forward outright can change very quickly, the forward points might be good for the better part of the afternoon, and so quoting forward points gives marketmakers a way to provide a more stable (if somewhat convoluted) forward price quote to a counterparty.
Of course, once the client “deals” the forward, the spot is observed and the forward price is “locked in.”
To see examples of forward points (without a bid-ask spread) in USD|JPY for a range of different maturities as well as for many of the major currencies (limited to one-month, three-month, and one-year maturities), look at Figures 6.5a and 6.5b.
In the professional interbank market, it is common when two banks do a forward trade, to see them do an accompanying, “offsetting” (i.e., opposite) spot transaction. In so doing, the banks are minimizing their FX risk and effectively “locking in” the “carry” or interest rates. This is typically referred to as an FX swap and explains why “forward points” are also known as “swap points.” More on FX swaps in Chapter 8.
Some have joked that quoting conventions involving forward points is simply an attempt on the part of FX dealers to preserve their job security. FX dealers also often drop the negative sign from the forward point quote (assuming that the counterparty knows whether the forward is higher or lower than the spot price). This is just another instance of needing to know the language of foreign exchange.
When incorporating a bid-ask spread in both the spot price and the forward points, the market has tended to summarize the possibilities in the way shown in Figure 6.6.
FIGURE 6.5a Foreign Exchange Forward Points in USD|JPY
Source: © 2006 UBS Investment Bank. Reprinted by permission.
Source: © 2006 UBS Investment Bank. Reprinted by permission.
FIGURE 6.5b Foreign Exchange Forward Points in the Majors
FIGURE 6.6 Generic FX Forward Point Screen
FORWARD PRICE/FORWARD POINTS EXAMPLE
Using Figure 6.6, find the three-month EUR|USD forward market.
Start with EUR|USD spot: 1.2500-05 or 1.2500 – 1.2505.
Now, to get the forward quote, you line up the forward points (found in Figure 6.6) with the spot quote (remembering that these are pips):
Now, to add or subtract? If the forward points are lined up lower-to-higher, one would then add to the spot price. If the forward points are lined up higher-to-lower, one would subtract them from the spot price. The FX traders have an expression they use to keep it straight:
Ascending, Add.
Descending, Deduct.
Descending, Deduct.
In this case, since the forward points are quoted “62.00 – 23.00” and so are ascending, add them to the spot price to get the forward market: 1.2562 – 1.2568.
Does this make sense?
What was the bid-ask in spot? 5 pips.
What was the bid-ask in the forward points? 1 pip.
Do you think it’s riskier to trade spot or forward? Forward.
So which bid-ask spread should be wider? The bid-ask in the forward will generally be wider than the bid-ask spread in the spot.
FORWARD PRICING/FORWARD POINT EXERCISES #3
Using Figure 6.6,
1. What is the one-year forward outright market in Cable (GBP|USD)?
2. What is the six-month forward market in USD|JPY?
3. What is the one-month forward in USD|CHF?
4. If you wanted to sell USD 10,000,000 in one month, how many CHF would you get?
TIMING
The extent of the subtlety associated with the timing of spot FX trades lies in recognizing that settlement dates do not coincide with trade dates and that generally settlement will take place on the spot date two good business days later (“T + 2”).
Forward trades also have their own unique timing conventions, but they are a bit more convoluted. For the record, say today is Monday, August 1. This means that the spot date is Wednesday, August 3. Everything in FX revolves around spot. When would a one-week trade settle? The timing convention for “weekly” trades (one week, two weeks, three weeks) involves going from “day of the week” to “day of the week”—in our example, from Wednesday to Wednesday. In short, if we do a one-week forward trade on Monday, August 1, we’d expect that trade to settle on Wednesday, August 10. On the other hand, if one does a “monthly trade” (one month, two months, three months, six months), then the convention is that these trades involve going from “date” to “date.” If you do a three-month forward trade on Monday, August 1, then spot is Wednesday, August 3, and that forward trade would involve settlement (the exchange of currency) on November 3 (assuming that day is not a holiday or a weekend, i.e, assuming the banks are open). In the event that this is not a good business day, the general rule of thumb is to roll that trade forward to the next good business day (unless this involves leaving the month, in which case you usually roll it back).
The most liquid forward quotes on any given day are usually the one-week, two-week, one-month, two-month, three-month, and six-month maturities. One can request a two-month, one-week, and four-day forward trade, but this would be relatively uncommon; this would be referred to as a “broken date.” Since one-month forwards are traded every day, and since forwards often result in delivery, there are exchanges of currencies every day as a result of maturing forward contracts.
EXAMPLE OF AN FX FORWARD TRADE
As with a spot transaction, one must indicate the currency pair (say, USD|CHF) and the size of the trade (in terms of one of the currencies, say, USD 10,000,000); with a forward, one must also specify a maturity (say, three months). Given this information (and armed with knowledge about the interest rates in the two countries), the forward price can be determined. Usually this is not done by hand. An example of an “e-tool” purchase of USD = sale of CHF in three months can be seen in Figure 6.7.
Although spot prices have historically been quoted in terms of pips or, in this case, four decimal places (S = 1.2972), note that here (and in general) the forward price is quoted out further (F = 1.286792).
Nondeliverable Forwards or NDFs
There are times when someone may like to trade a currency (whether for hedging purposes, to implement a speculative view, or as part of an investment strategy), but they cannot. Perhaps trading in that currency is restricted by the government, or perhaps they are not allowed (according to their fund’s prospectus) to trade that currency. There are a number of reasons why a currency trade may not be permissible, but if one still wished to gain exposure to that currency, there are contracts through which one can acquire the economic exposure to the foreign exchange rate movement without the need of “physical delivery.” One of these would be a nondeliverable forward (NDF).
FIGURE 6.7 Example: Long Three-Month USD|CHF Forward Trade
Source: © 2006 UBS Investment Bank. Reprinted by permission.
As an example, let’s say you believe the Russian Ruble will strengthen, but you are not allowed, for one reason or another, to trade the Ruble directly. You could agree to sell 10 million U.S. Dollars forward and buy Ruble forward (in 3 months) at a forward price of USD|RUB F = 28.50. Your view may be that Dollar-Ruble will, in three months time, be trading at a spot price of S = 25.00. This forward transaction would typically involve the following exchange of currencies in three months:
but, with a nondeliverable forward, the exposure is simply cash-settled in a currency that is tradable. If you were exactly correct in your assessment of where USD|RUB was headed, then, at the settlement date of the forward, you would consider where this exchange should trade (with, in this example, S = 25.00):
and effectively do an “unwind” so that there is no transfer of the Russian Ruble.
USD 10,000,000 out and RUB 285,000,000 in
USD 10,000,000 versus RUB 250,000,000
This should result in a “profit” of RUB 35,000,000, which, with a nondeliverable forward contract (and a spot exchange rate of S = 25.00) would terminate with a positive Dollar cash flow of USD 1,400,000 (= RUB 35,000,000/25.00).
In recent years, there’s been a great deal of interest in nondeliverable forwards on Chinese Yuan/Renminbi. Spot USD|CNY is not “accessible,” but there are many market participants with financial interests in the movement of this currency who’ve used NDFs. Of course, liquidity is always an issue with a controlled or restricted currency.4 There are also non-deliverable options.
OFF-MARKET FORWARDS
Now that the pricing of FX forwards is hopefully clearly understood, I’d like to ask one further question. Let us use the numbers from our earlier USD|CHF example:
USD|CHF. S = 1.2500 t = 1 rUS = 5.00% rCH = 3.00% and so F = 1.2262
As a forward marketmaker, what would you say to a client who telephoned and said, “I would like to purchase USD one-year forward at a price of F = CHF 1.1000.” You might be inclined to respond, “So would I!” because clearly that price is too low. If the client persisted, you might say, “Okay, I will sell you USD in one year at a forward price of F = CHF 1.1000 but only if you do something.” What would you ask your client to do?
Since this price is too low, you might ask your client to make a payment to you to compensate you for that difference. More precisely, you would probably want to be paid before you handed over such a forward contract involving too low a purchase price for your client. How much would you need to be paid and when would that payment take place? Let’s say we would like to know the magnitude of the required payment today. The difference between the correct forward value (1.2262 for a transaction in one year) and the wrong or off-market forward (1.1000 for a transaction in one year) is CHF .1262 (in one year). Presumably if the client agreed to pay you that amount (per USD 1) in one year, this would effectively make this an “on-market” forward. More likely, the client would be asked to pay the present value of that amount today (properly discounted at the Swiss interest rate) = CHF .1225 per USD 1. If the client wanted to buy this off-market forward on USD 20,000,000, the up-front payment would be around CHF 2,450,000.
In general, off-market forwards are not traded often in the market, but as a transition topic, we simply note that if you understand FX forwards (especially off-market forwards), then you are halfway to understanding FX options.
FOREIGN EXCHANGE FORWARDS IN THE REAL WORLD
With a firm grasp of the issues involved in the valuation of forward contracts, I ask one last question. What do you think would happen to, say, the three-month USD|CHF forward price today if the Federal Reserve Bank were to raise U.S. interest rates today?
If the spot price and Swiss interest rates are unchanged, then, mechanically, we know that the three-month U.S. interest rate would go in the denominator of this currency quote
and we would expect the three-month USD|CHF forward to fall. But there is a huge presumption here, namely that spot will not change. If everyone expected the Federal Reserve to raise interest rates by 25 basis points (.25%) and that is what the Fed does, then that new higher return associated with the U.S. Dollar will have already been priced into the spot price, the spot price should not jump, and the three-month forward will probably fall. On the other hand, if the Fed raised rates by more (more precisely, by more than the market anticipated), the return from holding U.S. Dollars will be unexpectedly higher, and we would expect to see the spot price go up (as people bid up the price of the Dollar given its new, more attractive interest rate return). In this case, the ultimate effect on the three-month USD|CHF forward is not certain, and, depending on expectations, it may very well go up. For better or worse, the real world FX forward price quotes may not move in a perfunctory manner, given changes in the interest rates that drive them.
FOREIGN EXCHANGE FORWARD EXERCISES #4
1. Undertake a spot-forward arbitrage in the following circumstances:
EUR|USD S = 1.2940 t = 1 year rUS = 3.00% and rEU = 4.00% and the one-year EUR|USD F = 1.2750
Do this on a spot notional of EUR 100,000,000 and check your answer.
2. What could you say about Turkish interest rates versus U.S. interest rates if the forward points in USD|TRY are positive?
3. What can you say about the forward points for USD|CHF if the respective (zero) interest rate curves in the respective countries’ currencies look like this (Figure 6.8):
FIGURE 6.8 U.S. and Swiss Zero Interest Rate Curves
4. If GBP|USD three-month forward is F = 1.7568, U.S. interest rates are 4.00%, U.K. interest rates 7.00%, and we assume three months involves 91 days, then
• What is the GBP|USD spot price?
• What do you think would happen to this forward price if the Bank of England raises interest rates?
• How much would you have to pay (today) for a three-month off-market forward of F = 1.7200 on a notional of GBP 10,000,000?
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