Tag Archives: models for foreign exchange

A Model for Foreign Exchange Rate Determination

A quick survey of the economic literature on foreign exchange rate determination will demonstrate the lack of success that economics has had in developing useful models. You know things are bad when leading academic articles in the area include titles such as “Exchange Rate Models are Not as Bad as You Think” (Engel, Nelson, West, 2007).

In this article, we shall discuss a new expectations-based model for foreign exchange rate determination. While the development of this model is quite complex, we will only focus on the key aspects of the theory.

It is important to start with the basics because this approach highlights the key problem with existing models of foreign exchange rate determination, namely that they don’t start with the right economic fundamentals. More specifically, current foreign exchange rate models don’t start with a comprehensive theory of price determination, nor do they start with a sensible theory of how money derives its value.

Rather than following the orthodox approach of thinking about what might influence a foreign exchange rate and then creating a model to backfill for this result, let’s begin by thinking about what a foreign exchange rate is and build a model one step at a time.

At the most basic level, a foreign exchange rate is a price. More specifically, a foreign exchange rate is the price of one currency in terms of another currency.

Every price is a ratio of two quantities exchanged. A foreign exchange rate is a ratio of two quantities of different currencies exchanged, for example, 1.2 US Dollars for every 1 Euro.

So, what determines this ratio of exchange? What determines the price of one currency in terms of another?

The immediate challenge faced by mainstream economics is that the current orthodoxy teaches that price is determined by “supply and demand”. So, if a foreign exchange rate is just a price, then shouldn’t it be determined by “supply and demand”? But in the case of an exchange rate, there is an obvious follow up question that needs to be asked: “supply and demand for what?”

Think about the USD/EUR exchange rate? Is this exchange rate determined by supply and demand for US Dollars, or supply and demand for Euros?

Mainstream economics can’t answer this basic question. Indeed, it ties itself in knots because the mainstream view is that supply and demand for money (i.e., supply and demand the US Dollar) determines “the interest rate”. But if the mainstream view is right (supply and demand for money determines the interest rate), then clearly it can’t determine the price of money in terms of another currency. So here is a price that isn’t determined by supply and demand!?

The view of The Money Enigma is that there is a simple answer to the question above. The USD/EUR exchange rate is determined by both supply and demand for US Dollar and supply and demand for Euros.

A foreign exchange rate is a relative expression of the market value of one currency in terms of another. It depends not on the market value of just one currency, but on the market value of both currencies.

In simple terms, the US Dollar per Euro exchange rate (the price of Euros in terms of US Dollars) can rise for one of two reasons: either the market value of the US Dollar falls (you need to offer more US Dollars per Euro because each US Dollar is worth less), or the market value of the Euro rises (again, you need to offer more US Dollar per Euro, but this time because each Euro is worth more).

The diagram below illustrates how every foreign exchange rate is determined by two sets of supply and demand. Supply and demand for the primary currency determines the market value of the primary currency. Supply and demand for the measurement currency determines the market value of the measurement currency. A foreign exchange rate, the price of one primary currency in terms of another measurement currency, is a relative expression (a ratio) of the market value of the two currencies.

Foreign Exchange Rate Determination

The key to this diagram is an understanding how the property of market value, which is possessed by both currencies, can be measured in both absolute and relative terms. A foreign exchange rate is a relative expression of the market value of two currencies. In the diagram above, supply and demand for each currency is plotted in terms of absolute market value, that is to say, in terms of an invariable unit of market value called “units of economic value” and abbreviated as “EV”.

How is a Price Determined?

Before we go further, let’s think about the concepts of “price” and “market value”. Most people believe that “price” and “market value” are synonymous, but price is just one form of measurement of the property of market value.

The view of The Money Enigma is that every price is a relative expression of the market value of two goods. In every transaction, both goods being exchanged possess the property of market value: the “price” of the transaction is a relative expression of the market value of the primary good in terms of the market value of the measurement good.

The property of market value, which is possessed by both goods being exchanged, can be measured in both absolute and relative terms. In our daily life, we measure the market value of all things in relative terms that we recognise as a “price”. But we can, at least theoretically, measure the market value of a good in absolute terms. In other words, we can measure the market value of a good in terms of an invariable measure of the property of market value.

Think about the property of “height”. We can measure height in absolute or relative terms. For example, we can measure the height of a tree in absolute terms, in terms of an invariable measure of height such as “inches” (the tree is 120 inches tall), or we can measure it in relative terms, in terms of some of other object, such as a girl (the tree is three times taller than the girl).

The problem with measuring the height of the tree in “girl terms” is that the height of the girl may change over time (her height is not a constant unit of measurement). While the challenge with relative measurement may not be such a big deal in the case of height (because heights change slowly over time), it is a big deal in the case of “market value” (the market value of a good or currency can change quickly).

The property of market value can be measured in terms of absolute or relative terms. Almost universally, we measure the market value of a good in relative terms (in terms a currency which itself possesses market value that is variable). However, we can, at least theoretically, measure the market value of a good in absolute terms, in terms of a theoretical and invariable unit of measure. The Money Enigma proposes a standard for the measurement of market value, called “units of economic value” or “EV” for short.

Once we this standard for the measurement of market value, we can use this on the y-axis to plot supply and demand for a good in terms of “absolute” market value, rather than “relative” market value (in terms of “price”).

Price Determination Theory

The diagram above illustrates how every price is determined by two sets of supply and demand. Every price is a relative expression of the market value of two goods: the market value of the primary good (good A), relative to the market value of the measurement good (good B).

We can apply this general principle to the determination of “money prices”. The price of a good, in terms of money, is a function of both supply and demand for the good, and supply and demand for money.

Price Determined by Two Sets Supply and Demand

Furthermore, we can also extend this general principle to the determination of “foreign exchange rates”, or the price of one form of money (one currency) in terms of another form of money (another currency).

Foreign Exchange Rate Determination

Take another look at the last three diagrams. Taken together, these diagrams represent a universal theory of price determination: a theory of price determination that applies to “good/good” prices (barter prices), “good/money” prices (the standard money-based prices we see in the stores every day) and “money/money” prices (foreign exchange rates).

It is the view of The Money Enigma that the primary reason that economics fails to deliver sensible models for foreign exchange rate determination is because it does not begin with a comprehensive microeconomic theory of price determination, such as that outlined above. It can not be the case that “good/money” prices are determined by one process, “good/good” (barter) prices are determined by another and “money/money” prices (foreign exchange rates) are determined by yet another random process. Either all prices are determined by supply and demand or none are. The view of The Money Enigma is that every price is a relative expression of market value and, therefore, every price is a function of two sets of supply and demand.

While a universal theory of price determination provides a good starting point, it does not provide us with a comprehensive model for foreign exchange rate determination. Recognising that the USD/EUR exchange rate is a function of two sets of supply and demand is a good start, but it doesn’t really help those who want to forecast foreign exchanges rates.

In order to say something really useful about foreign exchange rates we need to answer the question “why does money have value?”

Why Does Money Have Value?

We have already discussed this subject at length in previous posts. A few weeks ago, we discussed this issue in general terms in a post titled “Why Does Money Exist? Why Does Money Have Value?” More recently, we discussed this issue in slightly more complex terms in a post titled “Money as the Equity of Society”.

The view of The Money Enigma is that fiat money derives its value from its status as a financial instrument. Real assets derive their value from their physical properties: financial instruments derive their value from the contractual properties. Fiat money derives its value from an implied-in-fact contract that replaced the explicit contract that previously existed when fiat money was backed by gold.

Money derives its value from this implied-in-fact contract, the implied “Moneyholders’ Agreement”. Money is a liability of society, the ultimate issuer of fiat currency. More specifically, money is a proportional claim on the future output of society.

In the context of foreign exchange rate determination, this idea is interesting because it allows us the opportunity to create a valuation model for money, in much the way one might create a valuation model for a stock

In last week’s post we discussed some of the similarities between money (the monetary base) and shares of common stock. Shares represent a proportional claim on the future residual cash flows of the business that issues them. The monetary base represents a proportional claim on the future output of the society that issues it.

Money shares another common feature with traditional equity instruments: money is a long-duration asset. Just as the value of a share of common stock depends upon expectations of long-term earnings per share growth, so the value of money depends upon expectations of long-term (20 year plus) real output per unit of monetary base growth. The reasons for the long-duration nature of money are discussed at length in The Velocity Enigma, the final presentation in The Enigma Series.

Building a Valuation Model for Money

We can use the theory that money is a long-duration, proportional claim on the output of society (“Proportional Claim Theory”) to build a valuation model for money. In essence, the principle is the same as building any other valuation model: the present value of the financial instrument (one unit of the monetary base) is equal to the discounted future benefits that the marginal possessor of that financial instrument expects to receive from its future use.

Nevertheless, there are several complexities involved in doing building a valuation model for money. First, whereas a valuation model for common stock is expressed in money terms, the valuation model for money is expressed in terms of “units of economic value”, our invariable measure of market value. [Note: you can’t build a valuation model for money that is expressed in money terms, i.e. in terms of itself]. In our model, the present market value of money, as measured in absolute terms, is equal to the discounted future absolute market value of the goods that unit of money is expected to purchase.

Second, building a valuation model for money requires us to build a probability distribution for when the marginal unit of money demanded may be spent. A share of common stock entitles its holder to a stream of future benefits, but a unt of money only entitles its holder to a slice of future benefits (one dollar can only be spent once). In practice, resolving this problem is easier than it sounds because we can leverage the theory of intertemporal equilibrium to create this probability distribution.

A third complexity is that a unit of money can be invested before it is spent: these expected, risk-adjusted investment returns need to be included in our valuation model for money (they form part of the discounted expected future benefit of receiving one unit of money today).

The end result is a valuation model for money called “The Discounted Future Benefits Model for Money”. This model provides us with a framework for thinking about what factors drive the value of a fiat currency.

Valuation model for fiat money

The equation above states that the market value of money is a function of:

  1. The current levels of real output, qt
  2. The current level of the monetary base, Mt
  3. The current level of the general value level, VG,t
  4. The expected long-term growth rate of real output, g
  5. The expected long-term growth rate of the monetary base, m
  6. The expected long-term risk-adjusted nominal return on risk assets, i
  7. The real discount rate applied to future consumption, d

In simple terms, the equation above suggests that the market value of money depends critically upon the expected future path of the “real output/base money” ratio. If expectations about the long-term prospects of the economy become more pessimistic, i.e. slower output growth that is supported by higher base money growth, then the market value of money will fall.

We can put this in a more familiar context. The value of a share of common stock will fall if people believe that a company’s long-term cash flow growth will slow while share issuance will rise. Similarly, the value of money will fall if people believe that a society’s long-term output growth will slow while base money issuance will rise. In this sense, we can think of the monetary base as the “equity of society”.

Finally, we can apply this model to foreign exchange rate determination. As we discussed earlier, a foreign exchange rate is a relative expression of the market value of two currencies. The Discounted Future Benefits Model, developed in The Velocity Enigma, provides us with a model that determines the market value of an individual currency as measured in absolute terms. Therefore, all we need to do to convert this into a model for foreign exchange rate determination, (a model for the market value of a currency as measured in relative terms), is divide this model for one currency (the primary currency) by this same model for another currency (the measurement currency).

In mathematical terms, Price(EURUSD) = Value(EUR)/Value(USD), as per our earlier two sets of supply and demand diagram (notice the formula in the red box below).

Foreign Exchange Rate Determination

But now, by leveraging the concept that money is the equity of society, we have a model for determining the absolute market value of money that we can use to solve for both Value(EUR) and Value(USD) in the price equation above.

Value of Money and Long Term Expectations

In essence, our new model for foreign exchange rate determination states that a foreign exchange rate depends upon long-term (20 year plus) expectations of relative future output growth, relative monetary base growth and relative expected investment returns in the two respective countries. Current levels of the monetary base and real output also matter, but in the end, changes in these current variables tend to be overwhelmed by expectations of the future path of these variables.

The key aspect to this model is that it forces us to think about what drives the absolute value of a currency. This is an important idea. Nearly all economists start from the perspective of trying to determine what moves the relative value of a currency. This model describes what moves the absolute value of a currency, a notion that can then be easily applied to understanding what might move the relative value of a currency.

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On a personal note, I would like to take the opportunity to welcome our first child, James Robert John Heddle, who was born on Wednesday, 11th March 2015. Jocelyn and I are thrilled and James is doing well. I would ask readers to please bear with me if The Money Enigma weekly updates seem a little less coherent than usual over the next few weeks!