Consideraciones finales

1. The stock market may be in one of three states: a fundamental state in which share prices (approximately) equal their fundamental values, a bull market in which prices exceed their fundamental value but the efficient market condition (1) holds, and a bear market where equation (1) does not hold and shares are overvalued.

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2. In the fundamental state shares may not exactly equal their fundamental values because of transactions and calculation costs. Shares may also be somewhat above their fundamental values because of the expectation (by rational agents) that the shares might enter a bull market or bear market state.

3. Bubbles can occur. In developing models of bubbles the extreme rationality assumptions that are often made in models of bubbles need to be relaxed; appropriate models of bubbles should hence be developed assuming a mixture of rational and irrational agents.

4. In a bear market, the marginal investor is irrational. It could be that all shares are held by irrational agents, with rational agents being unable to exploit the overvaluation because of short-selling constraints. But optimistic rational agents could hold shares in a bear market, provided that the marginal investor is irrational.

5. It is also important to consider the implications of assuming heterogeneous rational agents in the fundamental market.

What is new about the GTSM? Although most of the ‘ingredients’ of the GTSM are not new (e.g. the point about short-selling constraints giving rise to overvaluation goes back to Miller, 1977), we would claim the way in which the ingredients are combined to produce the overall theory is novel. We would point out that in the theory shares can be overvalued for two very different reasons. The first is that they are overvalued because they are expected to rise still further in price (i.e. there is a bubble). The second is that they are overvalued because they are held exclusively by irrational agents and rational agents cannot exploit the overvaluation because of short-selling constraints. The two states in which share prices are overvalued can be expected to behave in very different ways. In the first, share prices might be expected to rise on average over time and in the second they might be

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expected to fall. It is not clear that this possibility (that overvalued shares may behave in very different ways) has been recognised in the literature. We have also emphasised heterogeneity of investors’ expectations. Discussion of such heterogeneity is not of course absent from the literature. One important paper is De Long et al. (1990) who consider the interaction of irrational noise traders and rational arbitrageurs. Hong and Stein (2007) also survey much of the literature on investor heterogeneity. We would stress that this heterogeneity, which certainly exists, may affect the behaviour of the stock market in different ways in different circumstances. Again, it is not clear that this point has been recognised in the literature.

18. Conclusions

The paper has argued that the stock market can best be understood as being comprised of a mixture of rational and irrational agents. There are several possible outcomes for the way the stock market behaves. The behaviour of the stock market may be determined entirely by the behaviour of rational agents; alternatively, there may be circumstances where share prices are determined by the decisions of irrational agents and rational agents cannot exploit any overvaluation this may give rise to. It has also been argued that there may be heterogeneous rational expectations; such an assumption does not contradict any basic principle of economics and may play a role in explaining the behaviour of the stock market.

So the GTSM combines the insights of Fama, who argues for the efficiency of the stock market (it may be approximately efficient for much of the time under the GTSM) with the insights of Shiller (it can explain excess volatility, for example). There is plenty of room for behavioural economics to explain the behaviour of irrational agents, and the approach

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can potentially integrate the insights of behavioural economics into an overall theory of the stock market. It should be able to construct a model which explains the reaction of stock prices to (say) an expansion by the central bank of its quantitative easing programme, something which behavioural economics by itself does not seem able to explain, so hence providing a genuine alternative to the EMH, and meeting Fama’s point quoted above. The theory should be able to explain the anomalies which the EMH finds extremely difficult to explain (excess volatility, overvaluation, bubbles, momentum effects, overreaction and underreaction), but is also compatible with it being impossible to systematically beat the market and with the stock market reacting to news.

There is much work which needs to be done to develop such a theory, but we would claim that it does contain the essence of a satisfactory theory of the stock market.

APPENDIX I

An Example of Overvaluation

Consider a firm which has just announced the following results:

(1) In the year for which it is reporting results, it had revenues of £23.3m and a loss of £31.4m.

(2) In the previous year it had revenues of £14.84m and a loss of £5.17m. (3) It has net cash of £96m.

Also, it is regarded as a ‘world leader’ in a rapidly growing sector of the economy. Question: what would be a plausible estimate of the market value of the company?

According to the Efficient Markets Hypothesis (EMH), share prices are determined as in equation (3), which we repeat here for convenience:

38 0 0 1 [ (1 ) ] . i i i i E D r P F       _{ }  



Let us try to estimate a plausible upper bound on the market value of the company. Consider the following scenario:

1. In the next three years, the firm’s revenues grow to £100m., using its cash reserves which it exhausts at the end of the three years (so revenues double every 17 months or so in this period).

2. In the following four years, its revenues grow from £100m to £400m. (i.e., they double every two years.) Assume it finances its expansion by internally generated funds.

3. Thereafter, the firm’s revenues grow at 5% per year indefinitely, and it pays a dividend equal to 10% of its revenues (so its first dividend is £40m.)

Then it is not too difficult to calculate that the firm’s market value in 7 years’ time, using a discount rate of 10%, will be £800m. This means its current market value will be about £400m.

Is this credible?

The above calculations are based on some extremely favourable assumptions about the firm’s behaviour. For example, it is assumed that its average rate of growth of revenues will be about 35% over the next ten years. According to Chan et al., 2003, only 2% of firms have annual sales growth rates in excess of 22% over a ten-year period, and these figures are biased upward by survivorship bias. Also, assuming that the firm can pay dividends equal to 10% of revenues indefinitely after ten years seems very strong indeed.

So it would seem that £400m is a considerable overestimate of what the firm’s market value should be; indeed it would seem to be a considerable overestimate of the

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maximum plausible market value of the company, assuming that its price equals its fundamental value.

However, perhaps it can now be revealed the firm in question is one called Baltimore Technologies, and the figures are those for March 2000. At the time its market value was £4.48bn, that is about eleven times a value which was argued to far exceed its fundamental value! It seems very difficult to avoid the conclusion that Baltimore Technologies was (massively) overvalued.

APPENDIX II

On the Rationality and Heterogeneity of Expectations

We would make a number of contentions about expectations here. (1) There is often a huge amount of heterogeneity in expectations.

(2) For some decisions, an assumption that virtually all agents making the decisions have rational expectations is defensible. For many other decisions, it is reasonable to suppose that some agents have rational expectations and other do not. Furthermore, there are some decisions for which an assumption of rational expectations is much less plausible for any agent.

(3) It is plausible that those expectations, which may plausibly be regarded as ‘rational’, can differ between agents, sometimes massively.

(4) As far as investors in the stock market is concerned, many investors make buying and selling decisions that in no reasonable way can be considered rational.

To make a compelling case for these contentions would take a long time. The rest of this Appendix contains some discussion which is hopefully relevant although it may fall short of making a persuasive case.

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On contention (1), for evidence on heterogeneity of shareholder expectations, see Bagwell (1991) and Booth (1993), footnote 7.

As far as contention (2) is concerned, many decisions we make can plausibly be described as rational. For example, virtually everyone would pick up a £20 bill on the pavement (sometimes thought of as the archetypal rational decision). There are a number of well-established results in economics which hold because some agent can make a clear-cut unambiguous gain from acting in a particular way. One example is covered interest parity, which holds because some agents perceive and act upon opportunities to make riskless arbitrage profits. But for many other decisions, rationality seems much less plausible. Behavioural economists and psychologists have documented numerous biases and distortions in much of our decision making; Kahneman (2011) is the obvious reference.

However, there are some decisions where rationality is much less plausible for any agent, or only is a reasonable assumption for a handful of specialist and exceptionally well- informed individuals. Examples might include the level of rationality that each agent needs to possess if Ricardian equivalence is to hold, and the information some speculators need to possess and the calculations they need to do to rule out divergent dynamic paths in some optimizing macroeconomic models.

Contention (3), that there may be heterogeneity in rational expectations, may seem a strange idea, and has scarcely featured in the literature, but it may be justified by supposing that each agent may have idiosyncratic information. Alternatively, it might be that it is costly to gather information, and agents gather different amounts of information, and hence may

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have different expectations, because their costs of gathering information differ.6 At a casual level, we might note that many stockbrokers have widely differing recommendations on the same shares and it would be an uncontroversial statement that many well-informed people have radically divergent views on the same issues. To take the example that started the paper, Fama and Shiller are both outstanding academics who have spent their careers studying the stock market – if we do not consider them as ‘rational’ then who is? Yet they have very different views on how the stock market operates. This is surely one example of heterogeneous rational expectations.

As far as contention (4) is concerned there is plenty of evidence that many traders in the stock market can by no means plausibly be described as rational. Here are some possible candidates for irrational or noise traders:

(i) Managers of Index Funds. A considerable proportion of shares are held in index funds. Managers of index funds construct their portfolios so that the proportions of shares in these portfolios are the same as the weights of the shares in the index they are tracking, so if a particular share is given a weight of say 5% in the index, the fund will hold 5% of its portfolio in that share. Index funds are quite popular, and many funds that are not explicit index funds are believed to be ‘closet’ index trackers. Investing in tracker funds has an obvious attraction for believers in the EMH. If one cannot systematically beat the market, there is no point in wasting resources researching various shares - one may as well buy shares in an index fund, which hopefully can minimise transactions costs. However, this means that managers of index funds buy and sell shares for reasons completely unrelated to whether they are over- or under-valued by fundamental criteria; the sole consideration is replicating the index. So if

6 _{See Brunnermeier and Parker (2005) for one model in which agents may optimally have heterogeneous}

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a new company enters the index, the index fund has to buy the shares of that company even if its shares are overvalued.

(ii) Institutional Investors Motivated by Relative Performance Criteria. Institutional investors are very important in the stock market, and it is commonly believed that they are motivated by relative performance criteria – i.e. that what matters is not how well or badly they perform in an absolute sense but how well or badly they perform relative to other institutional investors. This means that they shift their portfolios towards stocks that comprise their benchmark index. (See Basak and Pavlova, 2013.)

(iii) Small Individual Traders. De Bondt (1998) presents survey evidence according to which many individual investors behave very differently from the way in which standard models predict.

(iv) Technical Analysts. Such analysts try to predict stock price changes on the basis of past patterns in stock prices. An elaborate vocabulary has grown up around technical analysis; terms such as ‘resistance level, ‘support level’ and ‘head and shoulders pattern’ are commonly used. Typically, economists have been quite sceptical about technical analysis, sometimes asserting that it has the scientific status of astrology. Yet technical analysis is widely used by financial market professionals; according to one survey: ‘At a forecasting horizon of weeks, technical analysis is the most important form of analysis.’ (Menkhoff, 2010, p. 2573.)

These may be the main categories of noise or irrational traders; there are undoubtedly others. We might ask whether traders who only review their portfolios periodically should be considered irrational. Ascertaining fundamental values may be quite difficult and costly, so it may be rational for many investors to gather information about

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their portfolios and whether their shares are over or undervalued periodically. But the archetypal rational investor needs to be constantly updating his or her information and be ready to trade when they perceive a mis-valuation. It is difficult to believe that many investors come anywhere close to doing this.

This Appendix is intended to make the case that for many decisions, including stock market investment decisions, there is a huge amount of heterogeneity. We may make a distinction for analytical purposes between rational and irrational traders, which may shed some insights, but even this distinction is simplistic. (We would expect many noise traders to act rationally in many situations, such as picking up £20 notes on the pavement.)

Characterising the heterogeneity of agents, and developing models of the stock market which incorporate this heterogeneity, is clearly no easy task. It needs to be an important part of the research agenda over the next few years.

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