Appendix 2: Models of Asset Price Determination
(See Section 3 (a) (ii) Noisy Asset Values.)
(a) Market Structure and the Dissemination of Information.
There is a large and diverse literature analysing how information is processed in financial markets. The modern literature has its antecedents in a series of articles beginning with Grossman and Stiglitz (1980), Hellwig (1980), and Diamond and Verrecchia (1981), which developed rational expectations models of how traders with diverse information about the value of an asset trade, and how this information is reflected in the price of the asset. In these models prices have two roles: they clear markets, by equilibrating supply and demand, and they provide information which agents use to formulate their beliefs and hence their demands. Consequently, agents form demand schedules which are conditioned on price; if prices are high, for instance, they increase their demand because they interpret a high price as evidence that other agents have information which means the asset is worth more than they expected unconditionally.
Two key points emerged out of this work. First, Grossman and Stiglitz famously pointed out that an equilibrium could not be perfectly efficient, for if it were there would be no incentive to collect information. For an equilibrium to exist there had to be a certain amount of noise, generated by “liquidity” traders who are assumed to trade for reasons independent of any information about the value of the asset. This independent demand masks some of the demands of information traders. In turn, this means that the equilibrium price will be different to that which informed traders believe should prevail, so they will trade and make expected profits sufficient to cover the cost of information. Secondly, it became apparent that the model’s lack of market micro-structure was not innocuous. These initial models assumed that there was a walrasian auctioneer taking orders and working out the equilibrium prices, and that agents were price taking, not price making. Neither assumption seems particularly realistic.
Both of these assumptions have been tackled in subsequent work, in a variety of different ways that is intended to reflect the actual structure of different markets. For instance, many models of share or bond markets have followed Kyle (1985) in postulating a specialist trader or market maker who accepts orders from informed and uninformed traders, and who holds some of the asset to clear the market. Informed traders submit different sized bids according to their information, taking into account the influence on price they expect their bid to have. Models such as these are aimed at representing the actual institutions of the markets, and are increasingly being tailored to the institutions prevailing in exchange rate markets.
Different streams of the literature have analysed how agents use current prices to update their beliefs about future prices. Agents do this because information gathering is costly, so even those agents who gather some information will not have full confidence in their own views and will wish to incorporate “information” from prices into their information set. One theme that has emerged in the literature is how price crashes and herding behaviour can occur (see the review by Bikchandani, Hirshleifer and Welch (1998)). For instance, Gennotte and Leland (1990) show that if some agents have unobserved hedging instruments (such as stop-loss positions or portfolio insurance), huge swings in prices can occur because uninformed agents mistake a hedge sale for an informed sale and falsely revise their opinions as to the underlying value of an asset on this basis. In this case, the volatility of the asset price will be much greater than the volatility of the underlying fundamentals.
A different approach is that by Romer (1993). He develops a model in which agents gain information and make inferences about the precision of other agent’s information over time. Random liquidity trades will move prices around by a small amount, and traders deduce from the response of prices how confident others are in their beliefs. This process can lead to big changes in asset prices at times when no new information is otherwise released into the market. As he writes:
“ Uncertainty about the quality of other’s information can cause investors who in fact possess the best available information to place some weight incorrectly (but rationally) on the market price and little weight on their own information in attempting to estimate value; alternately, it can cause investors who have inferior information to place excessive weight on that information. As market developments (e.g. market responses to buy and sell orders arising from liquidity needs) reveal information about others’ uncertainty, it becomes clearer whose information is superior. The best available information therefore becomes reflected more fully in asset prices.”
(Romer 1993 p 113)
