fin-PRESENT.DOC

Finance 567. Presentation on 20.5.93 by Sanjeev Sabhlok DO STOCK PRICES MOVE TOO MUCH TO BE JUSTIFIED BY SUBSEQUENT CHANGES IN DIVIDENDS? by Robert J. Shiller, American Economic Review, 1981

INTRODUCTION: THE EFFICIENCY PUZZLE: The term "efficient market" was introduced into the literature by FFJR (1969). There are three types of efficiency which are usually tested (Fama, 1970): a) In the weak form, share prices are thought to fully reflect all past information. This form of efficiency has now been re-christened by Fama (1991) as Return Predictability. The current paper by Shiller has been classified by Fama as a test of this form of efficiency. b) In the semi-strong form, share prices are assumed to reflect all past, plus all publicly available information. This form of efficiency is now called Event Studies by Fama (1991). c) The strong-form assumes that share prices reflect all known information (including privately held, or insider information). Fama (1991) now calls this form "Tests for private information". The Ball (1990) review shows that the concept of efficiency, the research designs for testing this concept, and the evidence

thereupon, are anomalous, and puzzling.

Various research designs have been constructed, with

different criticisms of these methods. We look into a design called

VARIANCE BOUND TESTS, devised by Shiller (1981), and Stephen LeRoy

and Richard Porter (1981). In this procedure, the bounds of

different variances are determined by theory, and then data is

tested for these bounds.

Shiller's study involves comparing the volatility of stock

prices implied by the volatility of dividends to observed stock

price volatility (Martin:279). "Consider the following

simplified stock valuation model. Define stock price, P(t), as

the present value of future expected dividends, E(Divk).

_ E(Divk)

P(t) = ð ------- Eqn. i

k=t+1 (1 + R)k

where R s the market's required rate of return (discount

rate) for the stock.

Changes in P(t) over time can result from a) variations in expected future dividends and/or b) changes in the discount rate used in valuing them. Shiller focused his tests on the former, treating R as a constant." (Martin)

SHILLER'S PAPER: DATA SETS USED: For his empirical study, he uses two different

Stock Price indices: Data set 1: Standard and Poor's Annual series from 1871- 1979. Data set 2: Modified Dow Jones annual Industrial average from 1928-1979. (details in given in the Appendix of Shiller's paper) Shiller is interested in finding out what explains the movements in real stock prices. Can these movements be explained by new information about subsequent real dividends? He starts

off by the assumption that the expected real returns for the aggregate stock market are constant through time (or approximately so).

PART I: KEEPING REAL DISCOUNT RATES CONSTANT: VERSION I OF Efficient Markets model: Generalising equation i,

_

Pt = ð Et Dt+k Eqn. ii.

k=0 (1+r)k+1

where Pt is the real price of a share at the beginning of

time period t, r is the constant real interest rate, Et is

the expectation conditional on information available at time

t, and Dt+k is the real dividend paid at time t+k. E(D) is

therefore the expectation of the real dividend. Here, the

return from holding the stock for one period is r, the real

interest rate.

Writing Ó = 1/(1+r), we get

_

Pt = ð Ók+1 Et Dt+k where 0

k=0 (Eqn. 2)

where Ók+1 is the constant real discount factor.

VERSION II: Detrended version of Eqn. 2: Dividends are expected to grow (at a rate g) in the future. However, if they are expected to grow perpetually at a rate higher than the real interest rate then the present value of the expected future dividends would sum to infinity (Statement A). Let equal 1/(1+g). This is the long-run growth factor of the stock. Now divide both sides of (2) by t-T, and multiply the numerator and denominator on the RHS by k+1.Putting Ó= Ó, _ pt = ð Ók+1 Et dt+k k=0 (Eqn. 3) where pt and dt are respectively the proportion of the price and dividend discounted by the long-run growth factor. By this process we have removed the growth trend from the series in Eqn.2, or have de-trended the series. Now, Ó = (1+g)/(1+r). If g>r, then Ó>1 and the series in Eqn.3 sums to infinity. Therefore Ó <1 (this proves the above Statement A). The discount rate appropriate for the pt, dt series (Eqn.3) is given by Ó = 1/(1+r). VERSION III of EM model: The above two versions can also be written as follows, since the real stock price is equal to the present value of rationally expected or optimally forecasted future real dividends discounted