# Global Liquidity and Foreign Exchange

## International Transaction in 19th Century

Suppose we have a surplus country which is selling goods and receiving bills of exchange (the promise to pay in 90 days from a deficit country) as payments. On the other side of the trade, the deficit country buys the goods and issuing the bill of exchange.

However, the bill is not money and, the surplus country wants to convert it into money. That’s where we bring in the City of London, where there are tons of banks in the discounting business. The surplus country can take the bill to a bank and discounted it.

The bank will accept the bill and pay out notes. The surplus country winds up getting paid, even though the deficit company has not actually paid yet. When the bill comes due, the deficit country will pay the bill by paying off some notes. Banks are managing very carefully their inflow and outflow of notes.

Now the point, the surplus and deficit country’s domestic currency are not pound sterling. At some point they are going to have transfer that domestic currency into sterling notes in order to repay this bill. Now foreign exchange dealers come into play. They stand ready to buy or sell the domestic currency for the international currency which is the pound sterling notes.

Surplus country’s foreign exchange dealer is acquiring sterling notes from and paying out domestic currency to the surplus country.

On the other side, 90 days later when the bill is due, the deficit country is buying notes and paying domestic currency.

Here we have 2 different FX dealers, and the two domestic currencies of two countries are obviously different, but the one thing they have in common is that they’re both exchanging with the international currency, here it is the pound sterling. Both FX dealers use these notes issued by Bank of England as their international reserves..

### Treynor’s Model for Foreign Exchange

Let us assume the deficit country in previous example is the U.S., and under the gold standard both the dollar and sterling have mint pars against gold: \$1 = x ounces of gold, and ยฃ1 = y ounces of gold. Then the exchange rate `ยฃ/\$` at time zero is `S(0) = x/y`.

But the real exchange rate is not necessarily equal to that, because what holds that exchange rate in place is the movement of gold, and it costs something for gold to move. So the exchange rate is actually `x/y - ฮด < S(0) < x/y + ฮด`, where ฮด is determined by the cost of shipping gold. This is like an outside spread, there is a Treynor’s model in the background. Foreign exchange dealers are doing business inside that spread.

`````` FX rate |                                      |
|โ๏ธ                                     | \
|      โ๏ธ                               |  \
x/y+ฮด โ|โ๏ธ - - - - - - โ๏ธ - - - -               |   \ outside
x/y   โ|      โ๏ธ                | โ๏ธ            |   / spread
x/y-ฮด โ|- - - - - - - โ๏ธ - - - -| inside โ๏ธ     |  /
|                       | โ๏ธ spread     | /
|                       |        โ๏ธ - - | floor by central bank
----------------------------------------
short              0                 long
liquidity risk``````

In our example, the deficit country is the U.S. and the FX dealers are in a long position of the domestic currency, and selling (shorting) the international currency (the sterling), i.e. they’re taking on liquidity risk because they’re losing reserves. The dealer is moving the exchange rate quotes within these bounds `x/y - ฮด < S(0) < x/y + ฮด`, to sell pound sterling and take on domestic currency positions (here is U.S dollar), only if the dollar is cheap enough, i.e. `x` is small enough, then `x/y` is small enough.

Dealers are willing to accumulate more dollars with the thought that “maybe the dollar will in the future snap back”, and when it snaps back they can sell them at a higher price. It is impossible that the dollar keeps going down, because dealers can always take the domestic currency to the central bank and get gold for it. The central bank is putting a floor on the liquidity risk that the dealers are taking.

### Central Banks: Defense of Domestic Exchange

When the deficit country’s FX dealer thinks that it is holding too much deficit country’s domestic currency, it wants to reduce its liquidity risk, it can go to the deficit country’s central bank to get gold, that means the central bank has to sell gold or notes and buy the domestic currency. This is basically doing what the deficit country’s FX dealer is no longer willing to do.

Domestic currency is a liability of the central bank, so really what is going on here for the central bank is a shrinking of their balance sheet. However central bank has limited amount of gold (reserves), so this can not go on forever. The central bank could either borrow reserves from other central banks, or sell treasure bills to acquire more reserves. But selling more and more treasure bills may lead to the falling of its price, and so in fact the interest rates are going to be rising.

### Bank of England: Defense Against Internal Drain and External Drain

Now think about the City of London, the banks are discounting bills, watching liquidity flow, and taking on liquidity risk because they are not going to get money for 90 days. They are acting like dealers, but in interest rate space.

`````` interest|                                      |
rate |                                     โ๏ธ| bank rate
|                               โ๏ธ      |
|- - - - - - - - - - - โ๏ธ -            โ๏ธ|
|             โ๏ธ           |     โ๏ธ      |
|- - - โ๏ธ - - - - - - - โ๏ธ -|            |
|             โ๏ธ           |            |
|      โ๏ธ                  |            |
----------------------------------------
short              0                 long
liquidity risk``````

#### Internal Drain

Where as the disjuncture between banks’ cash inflow and their cash outflow gets worst, market rate is bid up, and eventually hit bank rate which is the rate that the Bank of England quotes. The FX dealers can go to the Bank of England to replenish their liquidity getting some notes or taking deposit, using some of the bills they are holding.

#### External Drain

Recall we previously talked about outside spread in the Treynor’s model: when deficit country’s currency gets bid down, there is a floor set by the central banks (it is the U.S in our example). However the other side of the outside spread, it is the Bank of England.

`````` FX rate |                                      |
BoE- - -|โ๏ธ                                     | \
|      โ๏ธ                               |  \
x/y+ฮด โ|โ๏ธ - - - - - - โ๏ธ - - - -               |   \ outside
x/y   โ|      โ๏ธ                | โ๏ธ            |   / spread
x/y-ฮด โ|- - - - - - - โ๏ธ - - - -| inside โ๏ธ     |  /
|                       | โ๏ธ spread     | /
|                       |        โ๏ธ - - | gold point, floor by
----------------------------------------  central bank
short              0                 long
liquidity risk``````

When the surplus country’s FX dealer thinks it has too many notes (sterling) and wants gold for them. Bank of England has to sell gold and take the notes. Actually Bank of England is defending pound sterling.

Similar to other central banks, the Bank of England has no unlimited gold. It can try to acquire additional reserves by raising bank rate (equivalent to raising interest rate in the world in our model), or suspending payment (dangerous).

### A Theory of Exchange Without the Gold Standard

Under the gold standard, there’s the outside spread caused by:

1. the gold point which is creating balance that is giving the dealers room to work in
2. the bank rate created by the central bank, which gives the private banking system a range to work in

When we’re moving away from the goal standard, we’re moving away from both of those things.

## Foreign Exchange in Modern World

Recall the 3 important equations, where F is forward exchange rate, S is spot exchange rate, R* is foreign interest rate, R is domestic interest rate, E is expectation:

There are links between these three equations.

### Economics of the Dealer Function

The matched-book dealer and the speculative dealer are willing to expand their book in order to help countries that are doing business, as long as there’s some expectation of profit in doing so.

#### Speculative Dealer

In the Treynor’s model, a speculative dealer is exposed to price risk.

When is it that the speculative dealer is going to be willing to take on a trade? The issue is really about the relationship between:

1. the forward exchange rate that you’re locking in today, and
2. what you think the expected spot exchange rate is going to be at maturity.

The profit in this kind of trade comes from buying low and selling high, that is to say locking in an forward exchange rate now that is lower than what it’s going to be in the future.

`````` FX rate |โ๏ธ                                     |
|      โ๏ธ                               |
|โ๏ธ - - - - - - โ๏ธ - - - - - - - - - - - | Expected spot rate
|      โ๏ธ                - โ๏ธ - - - - - -|   โ๏ธ profit
|              โ๏ธ        |        โ๏ธ     | Forward rate
|                       | โ๏ธ - - - - - -|
|                       |        โ๏ธ     |
|                       |              |
----------------------------------------
short              0                 long
liquidity risk``````

Speculative dealer is prepared to take the exchange rate risk that the matchbook dealer is trying to get rid of. That’s basically what you’re doing. You’re getting paid to take that risk off of this matchbook dealer’s hands.

#### Matched-book Dealer

Matched-book deal is also a profit-making person but it has a different strategy. It is willing to enlarge his book in its liquidity exposure.

The larger his book (the larger his liquidity exposure), the higher he’s going to want that `F/S` ratio to be, meaning paying less for the spot position (S) relative to the forward position (F).

``````     F/S |                                      |
|                                     โ๏ธ| โ R*
|                               โ๏ธ      |
|- - - - - - - - - - - โ๏ธ -            โ๏ธ|
|             โ๏ธ           |     โ๏ธ      |
|- - - โ๏ธ - - - - - - - โ๏ธ -|            |
|             โ๏ธ           |            |
|      โ๏ธ                  |            |
----------------------------------------
short              0                 long
liquidity exposure``````

Note we don’t have gold points and bank rate, which only existed under the gold standard in 19th century. If now central banks are not setting the outside spread, who are doing these? The key point is the Covered Interest Parity. The dealers are willing to expand their balance sheets, in doing so, the `R*` term rates in the deficit country get bid up.

Most central banks don’t set term interest rates, but they set overnight interest rates. Expectations Hypothesis of the Term Structure has set a link between them: term rates are just the expectation of the rollover of the overnight rate. If the central bank moves the overnight rate, and is completely credible about that, that should also move the term rate.

### UIP and EH Fail

From the matched-book dealer’s perspective: in order to facilitate this imbalance in payments (between surplus and deficit countries), term rates `R*` are bid up above that what you would expect from the expectations hypothesis (EH). It is exactly what we can observe in the real world. It’s creating an incentive for dealers, who have to make profit in order to make markets. This is where the profit comes from.

From the speculative dealer’s perspective, if the Uncovered Interest Parity (UIP) is true, no dealer would do the trade. Dealers would only do the trade if the forward rate `F` is different from the expected spot rate `E(S)`. That is to say, UIP must be false.

The failure of Uncovered Interest Parity, and the failure of the Expectations Hypothesis of the term structure, are sort of the same thing. Both of the failures are coming from the need to mobilize profit making dealers of two different kinds (matched-book and speculative) to handle the imbalances in payments internationally.

## Central Bank as FX Dealer of Last Resort

The central bank comes in when the private dealers are done – when the private dealers have enough risk and they don’t want to do deal any more. As before we have surplus country and deficit country, and their corresponding central banks, it starts with an swap:

1. deficit country central bank borrows reserves \$10 term (at R*Gov) from the surplus country central bank
2. deficit country central bank deposits the \$10 dollar in the surplus country central bank

Then deficit country central bank can sell the \$10 spot (at SGov) to their domestic residence. Once the domestic residence has the dollar, it can pay them to the surplus country.

The consequence for the surplus central bank is that there is an expansion of their balance sheet, therefore of money supply domestically. But the surplus central bank could reverse that just by selling treasury bills (sterilizing). Deficit central bank could also do the equivalent sterilization, what it is actually doing is like a speculative dealer, taking a naked forward position in its own currency, but without a profit motive.

Central bank is acting as a back stop for the foreign exchange market, as the same time as a consequence of its commitment to peg overnight interest rates. In poorer countries or countries where there aren’t very well developed foreign exchanged dealer markets, central banks usually act as the FX dealer of last resort.

Exchange intervention might sometimes be efficiency improving, because the private dealer system needs profit, it needs profit in order to and, and that means that prices get pushed away from their efficient levels.

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