(b)  Exchange Rate Models

In the last decade, there has been considerable interest in applying some of these models to the foreign exchange market. This work has two distinct aspects. One set of research has investigated and documented the actual workings of foreign exchange dealers and markets. The leading example is Lyons (1995, 1996) who examined the dealings of a single and large New York bank trader in the deutsche mark/dollar market in a single week in 1992.[46] This example is very informative because of the exceptionally high quality of the data, including both the time, quote quantity, bid and offer quotes, and the value and volume of trade if a transaction was made.[47] Lyons shows that the dealer had a very short horizon, typically closing out all positions at the end of the day; that he was risk averse in the sense of changing prices in response to the private position (or inventory of holdings) he built up during the day; that he changed his prices in response to order flows that might contain private information; and that there was a “hot potato” quality of many trades, as parts of a large order were rapidly unloaded to other dealers.

The second aspect of the work is the adaptation of asset price models to foreign exchange markets; for example Osler (1998) and Carlson and Osler (1996). Osler (1998) develops a model in which there are liquidity traders and risk averse speculators. The liquidity traders buy and sell foreign exchange in order to settle current account transactions. The size of the net current account transactions depends on the exchange rate, but also contains a random component. In each period the exchange rate adjusts to match the liquidity trader demand with the speculator supply and thus clear the market. The price the speculators quote is such that the expected gain they make from the speculation compensates them for the risk they undertake. This price is fully rational, taking into account how the exchange rate affects the non-random component of the current account position and the effect of their subsequent unloading of the position on the evolution of the price. Speculation is stabilising in the face of current account shocks - the variance of the exchange rate is reduced - although in the process the exchange rate deviates from the fundamental value.

The deviation of the exchange rate from the risk neutral position is in effect the cost of requiring the speculators to hold large net foreign exchange positions. This cost is related to the accumulated stock of the position, not just the current flow, even though this model equates foreign exchange rate flows in each period. As the number of speculators increases the responsiveness of the exchange rate to a shock decreases and the exchange rate appears to follow a random walk in response to purely random innovations.

The model developed in Carlson and Osler is similar but more interesting. In this model there are the same liquidity traders, but the speculators also take into account the short term interest differential between currencies. As previously, speculation is stabilising in the face of current account shocks. Speculation is destabilising in the face of interest rate shocks, however. Consider the effect of an interest rate increase in one country. Investors chasing the higher returns bid up the price of the currency, obtaining a return comprised of the higher interest rate minus the expected depreciation as the currency is expected to return to its long term value. (As the exchange rate increases, the current account position turns temporarily negative, becoming less negative as the exchange rate returns to its long term value.) The larger the number of speculators - or the less risk averse each speculator is - the greater the total demand for the high yielding currency, and consequently the larger the change in the exchange rate necessary to provide the current-account exchange rate flows. Consequently, the exchange rate becomes more volatile not less volatile as the number of currency speculators increases.

This story is similar but subtly different from the standard risk neutral arbitrage story. In the standard risk neutral story, the exchange rate will immediately rise by the accumulated difference in the two countries’ yield curves, and then start depreciating[48]. The total quantity of currency purchases is not clearly apparent, however. There is a similar mechanism in the risk averse story, but in this case the speculators are compensated for the risk they undertake. A 1 percent increase in interest rates will not lead to an immediate 1 percent increase in the exchange rate followed by a steady 1 percent depreciation; rather, the exchange rate will fall more slowly so that the expected return from holding the high yielding currency is greater than the expected return from holding the low yielding currency. These higher returns reward the speculator for the additional risk undertaken from holding a larger foreign exchange position. The exchange rate will eventually return to its long run equilibrium value (so that the expected depreciation is zero), but interest rates will have to remain high to keep it at this level, compensating the speculators for the risk they undertake holding a large position in the high yielding currency.

A notable feature of this model is that the risk premium is determined endogenously. In particular, the required compensation is a function of the holding that each speculator is required to take, so that countries which have large accumulated current account debt will be required to pay an interest rate premium[49]. A country running a tight monetary policy for an extended period, incurring a large accumulated current account position in the process, will have difficulty lowering interest to world levels (without causing a large exchange rate depreciation) because speculators demand high real returns in order to hold the accumulated position.

(c) Keynes, and the Noisy Traders of De Long, Shleifer, Summers and Waldmann

A different approach to asset price volatility has been taken by De Long, Shleifer, Summers and Waldmann in a series of articles that have modelled how misinformed agents can affect asset prices. They sought to model an insight of Keynes that well informed investment professionals spent relatively little time seeking and trading upon fundamental information but rather spent most of their time estimating the future demand for the assets.

De Long et al formulate a model in which there are “noise traders” as well as fully informed traders, and explore the limits of arbitrage designed to exploit noise trader’s misperceptions when arbitrageurs are risk averse and have short horizons. In these models a noise trader is someone who believes he or she has special information about the future value of an asset, or someone who has excessive certainty about their beliefs. Noise traders would include people who believe in and act upon broker’s tips, or who listen to investment gurus. While rational arbitrageurs take positions to exploit the beliefs of noise traders, they only take limited positions because of the risk that they will lose money because of a change in the fundamentals or because of a change in the beliefs of the noisy traders. This lack of arbitrage means that asset prices become much more volatile than they would have been in the absence of the noisy traders. When noisy traders are optimistic, they hold more of the asset and the price rises; rational traders lower their holdings but do not take extremely large short positions because of the chance that the noisy traders will become even more optimistic in the subsequent period. Conversely, when noisy traders receive a bad signal, they sell down the asset and its price falls. This additional volatility in the price of the second asset means that the average price of the second asset is lower than the price of the first asset, providing the average excess returns.

The results they derive are much stronger than this, however. Because noise traders induce greater volatility into asset prices, they reduce the desirability of holding the assets unless their average returns increase. This means that noise traders, who hold greater quantities of these assets than rational arbitrageurs, can make greater expected profits than rational arbitrageurs.[50] In equilibrium they are not driven out of the market even though they destabilise prices, because they make more profits than the stabilising speculators. This result is quite extraordinary, as the authors note (De Long et al, (1990), p 706)

“This result is more interesting than the point that if noise traders bear more fundamental risk they earn higher returns: our point is that noise traders can earn higher expected returns solely by bearing more of the risk that they themselves create. Noise traders can earn higher returns from their own destabilising influence, not because they perform the useful social function of bearing fundamental risk.”

The importance of this work is that the authors show that the process by which markets aggregate information will not necessarily cause good information to dominate bad information, and that merely the existence of bad information (rather than its particular content) will affect markets. They also derive some strong empirical predictions, and claim reasonable empirical support for their model. This evidence gives additional grounds for believing that something about the microstructure of asset markets generates additional short term volatility, and leads to prices that can deviate from fundamentals for reasonably long periods.

This idea has recently been incorporated into theoretical microeconomic models of exchange rate determination by Jeanne and Rose (1998). They develop a model with rational traders and noise traders in which there are multiple equilibria in the foreign exchange market, with one equilibrium associated with a large number of noise traders and excessively volatile exchange rates. The existence of these multiple equilibria enables them to argue that monetary policy can be used to lower exchange rate volatility without altering macroeconomic fundamentals.