6. Inbound Tourism Trends in South Korea
6.3. Temple Stay Program
As we have seen, mean reversion in expected returns is at odds with the hypothesis of efficient markets. Therefore, it is not surprising that many explanations of mean reversion in returns draw on investor psychology. Keynes’ (1936) famous
“animal spirits” that are supposed to drive investor’s decisions were put into a more scientific shape in the works of Tversky and Kahneman, for example in their (1981) article. Later, they developed a more economic explanation, the overreaction hypothesis.
Temporal dependence at some time scale that drives a return process back to the mean is often explained by the hypotheses of underreaction and overreaction.
The hypothesis of underreaction states that investors are slow in appreciating good news about a stock. The news are incorporated slower into prices than appropriate and this leads to further positive returns. That is, underreaction explains positive autocorrelation in returns at some time scale.
Contrary to that, overreaction means that once a run of good news occurs, that is, a consecutive sequence of good news arrives, investors believe that this trend prevails and consequentially bid the price up higher than the appropriate level. The first arrival of negative news then induces a large negative jump.
Overreaction thus corresponds to negative correlation of returns.
So which effect is prevalent, over- or underreaction? Griffin and Tversky (1992) argue that both can coexist and in fact explain the data. They distin-guish between the “strength” and the “weight” of a signal. For example, in financial markets, a run of positive earning announcements has great “strength”
but little “weight”. That is, it is “strong” in the sense that it is much noticed and commented in the markets and in the financial press. It is “light” in the sense that even in an i.i.d. random Bernoulli chain, the probability of the occur-rence of runs is surprisingly high. Thus, a run of positive earning announcements
provides little evidence that there is autocorrelation in the earnings process and that it is any more likely for the next announcement to be positive rather than negative. Contrary to that, a single positive earning announcement is “weak” in the sense that it is not much noticed and seen as a transitory bit of information but “heavy” in the sense that in fact this single piece of information has substan-tial weight for forecasting the level of earnings. The hypothesis is that investors tend to focus too much on “strength” and too little on “weight”. By that, they underreact to single positive earning announcements but overreact to runs. This creates positive autocorrelation on short scales between one month and one year and negative autocorrelation on long scales between three and four years, in line with the early findings of mean reversion in the 1980s that I will discuss in the following section.
Based on these concepts, Barberis, Shleifer and Vishny (1998) present their
“model of investor sentiment” and calibrating it with real data, they are able to explain a substantial fraction of the later excess returns of “loser” portfolios.
Another explanation of mean reversion, still more in the tradition of eco-nomics, is given by Poterba and Summers (1988). It posits that equilibrium required returns may be time varying and thus cause mean reverting behavior of stock prices and returns.
The starting point is that in equilibrium, the stock price is given by the sum of the expected future dividends, discounted with the required future returns.
S(t) =
∞ τ =t
e−˜rτ,t(τ −t)D˜τ,t, (2.3.13)
where ˜rτ,t :=E(rτ| Ft) and ˜Dτ,t :=E(Dτ| Ft).
Investor tastes for current versus future consumption and the stochastic evo-lution of investment opportunities result in
r˜τ,t = α˜rτ,t−1+ εt. (2.3.14) Let ˜Dτ,t be given by some function of today’s information and disturbance
D˜τ,t = f (Ft) + ηt, and assume
Eεtηt= 0.
Then, shocks to ˜rτ,thave no effect on expected dividends and as the ˜rτ,t’s are mean reverting, there is no influence on the long run expectations. The cumulative effect of a shock must hence be exactly offset by an opposite adjustment in the current asset price. Consider for example a positive shock to the required return.
The offsetting mechanism described above must result in a lower stock price and
hence negative returns today. Inasmuch as higher required future returns lead in fact to higher actual returns in the future, negative actual returns will be followed by positive actual returns.
Observe the difference to the statement (2.2.5). Here, we are considering the time series of the expectations of the return at a single point in time. This is to model required returns. Contrary to that, in (2.2.5) we considered the expectations of the returns time series itself, trying to model expected returns.
Therefore, (2.3.14) does not violate the efficient market condition, and (2.3.13) is a rational equilibrium model.
We model both required and expected returns by conditional expectations even though they are economically distinct objects. There may be a better way to do it. Fama’s statement is still valid:
But we should note right off that, simple as it is, the assumption that the conditions of market equilibrium can be stated in terms of expected returns elevates the purely mathematical concept of expected value to a status not necessarily implied by the general notion of market effi-ciency. (Fama 1970, p 384).
The autoregressive dynamics of required returns were not very well motivated in Poterba and Summers (1988) and their approach has therefore been refined to representative agent models that allow for mean reversion in fully rational equilibrium settings.
The basic idea in all of these models is that the agent maximizes his con-sumption over his complete life span whereas shocks to returns occur locally.
The result is a smoothing effect. When the expected returns increase, for in-stance because the economy is in a sustained boom phase, the agent will expect higher income and increase his consumption by selling stocks, thereby pushing prices and returns.
The key parameter is the relative risk aversion which also controls the in-tertemporal substitution of consumption. The higher the risk aversion, the smoother the consumption dynamics and the stronger the mean reversion ef-fect. Risk neutrality eliminates the consumption smoothing and hence the mean reversion effect. Fine examples of this class of models are Cechetti, Lam and Mark (1990) and Black (1990).
The state of the economy is assumed to be exogenous in these models and output fluctuations are captured in some reduced form manner, for example in a Markov chain indicating boom or recession. It is natural to extend the models to endogenously determined production and model changes in the state of the economy in the form of veritable output shocks. Examples of these type can be found in Basu (1993) and Basu and Vinod (1994). An excellent discussion of
representative agent models that accommodate mean reversion is presented in Bodmer (1996).