THE EFFICIENT MARKET, RANDOM WALK, AND THE OHLSON (1995) MODEL

0 http://ssrn.com/abstract=1524083

THE EFFICIENT MARKET, RANDOM WALK,

AND THE OHLSON (1995) MODEL

Samithamby Senthilnathan

Abstract: Though the efficient market and random walk are closely related to each other, the

gaining of risk free return (the result of risk free price change) indicated in efficient market

needs to be compromised with random walk. Ohlson (1995) demonstrates the price change

model, which illustrates that next period’s price change plus dividend is predictable with

current price. According to Ohlson (1995), if the results of current price as an independent

variable equals next period’s dividend, the next period’s price change is zero. This implies

that a shareholder obtains risk free rate profit as indicated in efficient market and the next

period’s price change (beyond dividend) is zero. In this context, Ohlson (1995) indicates that

equity price change in efficient markets is independent as indicated in random walk, and the

abnormal gain on the information associated with the historical equity prices seems not

realistic.

Key words: efficient market, random walk, equity price, price change, value relevance

JEL code: G12, M41

S. Senthilnathan is a senior lecturer in the Faculty of Commerce and Management, Eastern University, Sri Lanka. Your suggestions and advice are welcome to make this paper meaningful (e-mail: [email protected]).


THE EFFICIENT MARKET, RANDOM WALK,

AND THE OHLSON (1995) MODEL

1. INTRODUCTION

In the efficient market, equity price acts as the proxy for all information in the market, since

the equity price immediately incorporates new information that is useful to investors.

Therefore, the equity price is regarded as the best estimator of an investment value in a

portfolio (Fama, 1965). The efficient market implies as its main implication that the value of

equity represents present value of its future cash flows that can be discounted at a risk free

rate, i.e., an investment in an asset adds value that is equal to the risk free rate times the

investment value as a change in value.

Ohlson (1995, 2001) indicates that current equity price as the predictor of next period’s price

by utilising the risk free rate. But, the random walk theory indicates that the price change is

random and unpredictable.1 As the random walk indicates that next period’s price change is

difficult to predict and the efficient market indicates that an investment can gain risk free rate

as the change in price, it seems that there is an incompatibility between these two theoretical

explanations. However, some indicates that the efficient market and random walk are closely

related (e.g., Malkiel, 2003) and this raise questioning whether the random walk accepts the

price change that can be determined with the risk free rate. If the next period’s price change is

unpredictable, the explanation of the efficient market that an investment adds value with risk

free rate is verifiable. We provide some theoretical explanations that are available in theories,

their relationship to the Ohlson (1995) framework, and how the Ohlson (1995) model

compromises the efficient market with random walk.

1 The randomness of price change indicates the possibility of being a zero value.


The rest are organised as the efficient market and random walk, the Ohlson (1995) price

change model, compromising the efficient market with random walk, and conclusion.

2. THE EFFICIENT MARKET AND RANDOM WALK

Equity prices incorporate new information. When the equity prices responsively reflect the

same information, the market is efficient. Though many studies accept the inference of

efficient market hypothesis (e.g., Beechey, Gruen, and Vickery, 2000; Lee, 2001; Malkiel,

2003), the efficiency of the market is questioned over time (e.g., Finnerty, 1976; Grossman,

1976; Lo and MacKinlay, 1988 and 1999). Kihlstrom and Mirman (1975) question about the

extent to which the market equity prices reflect the insiders’ information. When the players in

the market are able to infer insiders’ information and expectation from the equity prices, the

market can be efficient. Failing to have this condition may dilute the robustness of market

efficiency. The efficient market hypothesis (EMH) is suspected when the share prices fail to

reflect an economy’s structure and trend. Malkiel (2003) indicates this by citing the market

crash in October 1987 as a result of the fiscal and monetary policy changes in the US.

Fama (1970) indicates that equity prices incorporate and reflect available information in

markets. As investors allocate capital among portfolios for maximising the return, the equity

pricing mechanism can only ensure the right allocation of investment in portfolios since the

optimum allocation of capital eventually depends on market prices of equity. The main

implication of informational efficiency of equity prices is the extent to which the equity

prices reflect the right information about the respective firms.


Fama (1970) attempts to describe the efficiency of the market into three forms:2

(a) Week form efficiency: This implies that the past prices of a share have already

incorporated the firm’s private information available to the market. Hence, the

current price of the equity is the unbiased and best estimator of the value of firm.

The investors do not earn an abnormal return in application of technical analysis as

they have already absorbed and reflected available private information;

(b) Semi-strong efficiency: This conceptualises that the share prices have incorporated

all publicly available information such as dividends, fiscal year-end financial

statements, news and reports on firms, and the data on the status of the economy and

industries. The investors with the information find hard beating the market

consistently to earn abnormal returns. The semi-strong efficiency lacks of firms’

insight information that is unpublished; and

(c) Strong form efficiency: This indicates that the share prices reflect all available

private and public information and investors cannot gain abnormal returns from their

portfolio investment. The existence of a strong form efficient market is unlikely

because many of the information that are mostly accessible and unpublished by the

directors of relevant firms cannot be incorporated in the share price as those

information are not publicly or privately available.

Notably, all three forms of market efficiency critically indicate that investors cannot gain

abnormal returns and there is a potential gain of a risk free rate of return. This implies that the

price would be adjusted only to the risk free rate. As the price change to new information

cannot be predictable and random, an investor cannot earn abnormal gain beyond the risk free

2 Fama (1970) viewed market efficiency with some basic assumptions similar to pure competition market. They

are: no transaction cost, availability of all information at zero cost for all market participants, no room to

influence market by any of the participants, and rational participants in the market with homogeneous

expectations.


rate. Fama (1970) categorically indicates that equity price change in an efficient market is

independent, and the abnormal gain on information associated with the historical equity

prices seems not realistic. Since the efficient market explores the independence of price

changes for new information, Malkiel (2003) indicates the close relationship of efficient

market to random walk.

The random walk theory indicates a notion that the equity price changes are random (e.g.,

Fama, 1995). Since information flow into the market at random, equity price reaction to the

new information is also random. Thus, predicting price change becomes uncertain and they

have no predictable opportunity. Malkiel (2003) also believes that technical and fundamental

analyses are not useful to gain abnormal gain by an investor. The random walk explanation

pinpoints a notion that the prediction of future value for a share does not have a significant

difference from its intrinsic value. Notable difference is that in the efficient market, an

investor can gain risk free return, which could be the result of the price change. Ohlson

(1995) also indicates a possibility of predicting next period’s price change as a function of

current equity price.

3. THE OHLSON (1995) PRICE CHANGE MODEL

Ohlson (1995) explains (see equation (6) on page 670 of Ohlson, 1995) the ratio of dividend

adjusted next period’s price (Pt+1 + Dt+1) over the immediate past fiscal year end equity price

(Pt) as3

t

t

t

t

t

tt

PPr

P

DP 1,221,1111.)1(

)1()(

(1)

3 Ohlson (1995) illustrates an equity valuation model by considering the dividend discount model and clean

surplus relations among accounting variables with the assumptions of (a) AR(1) dynamics for earnings and (b)

other earnings related information. His further illustration reveals (equation (5) on page 669 of Ohlson, 1995)

thatt

a

ttt vxbP 21 , where t is particular point of time, P is equity price, b is book value of equity, x is

earnings, xa

t = (xt –r.bt-1) abnormal earnings for period (t-1 to t), v is earnings related other information and 1

and 2 are parameters of earnings and earnings related other information (please refer to Ohlson (1995, 2001)

for further details).


where t = particular point of time,

P = equity price,

D = dividend,

r = risk free rate of interest,

α1 = parameter of earnings,

α2 = parameter of earnings related other information,

ε1 = error term of earnings, and

ε2 = error term of other information.

The above equation (1) can be rewritten as

(2)

(3)

and

(4)

Note that equation (4) explains the next period’s price change as risk free rate (r) time current

price (Pt) together with random error terms and next period’s dividend. Equation (4) also

explores the possibility of predicting next period’s price change as Ohlson (1995) considers

dividend irrelevance in his illustration. This is not consistent with random walk explanation,

but consistent with efficient market explanation that an investor can gain risk free return

(price change) in the market.

4. COMPROMISING THE EFFICIENT MARKET WITH RANDOM WALK

Notably, Ohlson (1995, 2001) smartly avoids using the terms “efficient market” and “random

walk” in his illustration of equity valuation, since his model has indirect link to both

explanations of efficient market and random walk. Rearranging equation (4) provides

(5)


Equation (5) explains next period’s price change (ΔPt+1) plus dividend (Dt+1) as a function of

current price (Pt), and error terms of earnings and other information (where risk free rate r is

the coefficient parameter of current price). In other form, in equation (5), the efficient input

value of current price (rPt) is the combined result of ΔPt+1 and Dt+1. If rPt equals Dt+1, the next

period’s price change (ΔPt+1) is zero, thus implying that (1) a shareholder obtains risk free

rate profit as indicated in efficient market and (2) the next period’s price change beyond the

dividend is zero, which is consistent with random walk. This implies that equity price

changes in efficient markets are independent as consistent with random walk, and the

abnormal gain on the information associated with the historical equity prices seems not

realistic.

In case, the next period’s dividend (Dt+1) accounts only a portion of rPt, the next period’s

price change (ΔPt+1) can be partially determined with rPt. Note that, in this context, the

current equity price (Pt) is efficient to consist of both the next period’s dividend (Dt+1) and

price change (ΔPt+1). If the next period’s dividend is value irrelevant, the next period’s price

change is predictable with current price. This implies that the random walk nature of equity

price is questionable (see Lo and MacKinlay, 1999; Senthilnathan, 2009).

According to Ohlson (1995), if an investor wants to sell a firm’s equity by the end of next

period, the next period’s dividend plays a benchmarking role together with risk free rate in

deciding the selling price, i.e., the change in price of the equity. When the investor believes in

random walk and constant availability of next period’s dividend, he/she may sell the equity to

Pt + Dt+1 (= Pt + rPt), thus implying that market is efficient as there is no information for the

price change. This implies that there is no use of predicting next period’s price change (ΔPt+1)

with current price (Pt). On the other hand, when the investor believes in non-random walk of

equity prices, the combined value of both next period’s price and dividend (Pt+1 + Dt+1)


becomes the function of current price. This indicates that the current price (Pt) is useful to

predict next period’s price change beyond the next period’s dividend information (Dt+1)

incorporated in it.

5. CONCLUSION

As equity price acts as the proxy for all information in the market and is useful to investors,

the equity price is regarded as the best estimator of an investment value in a portfolio.

Though the efficient market and random walk are closely related to each other, the gaining of

risk free return (the result of risk free price change) in the efficient market needs to be

compromised with random walk. Ohlson (1995) demonstrates the price change model, which

explains how the combination of next period’s price change and dividend is predictable.

Ohlson (1995) explains next period’s price change plus dividend as a function of current

price, error terms of earnings and other information. In other form, the efficient input value of

current price is the combined result of next period’s price change and dividend. According to

Ohlson (1995), if the results of current price as an independent variable equals next period’s

dividend, the next period’s price change is zero. This implies that (1) a shareholder obtains

risk free rate profit as indicated in efficient market and (2) the next period’s price change

(beyond dividend) is zero. In this context, Ohlson (1995) indicates that equity price changes

in efficient markets are independent as indicated in random walk, and the abnormal gain on

the information associated with the historical equity prices seems not realistic. Empirical

studies can be directed to verify whether the current price in the Ohlson’s (1995) price

change model is useful to predict the next period’s equity price change, dividend, or the

combined value of both.


References

Beechey, M., D. Gruen, and J. Vickery. (2000). The efficient market hypothesis: a survey.

Research discussion paper 2000-01, Reserve Bank of Australia.

Fama, E. F. (1965). The behavior of stock market prices. Journal of Business 38, 34-105.

Fama, E. F. (1970). Efficient capital markets: a review of theory and empirical works.

Journal of Finance 25, 383-417.

Fama, E. F. (1995). Random walks in Stock market prices. Financial Analysts Journal

(January – February), 75-80.

Finnerty, J. E. (1976). Insiders and market efficiency. The Journal of Finance 31(4), 1141-

1148.

Grossman, S. (1976). On the efficiency of competitive stock markets where trades have

diverse information. The Journal of Finance 31(2), 573-585.

Kihlstrom, R. E., and L. J. Mirman. (1975). Information and market equilibrium. The Bell

Journal of Economics 6(1) (spring), 357-376.

Lo, A., and C. MacKinlay. (1988). Stock market prices do not follow random walks:

evidence from a simple specification test, Review of Financial Studies 1(1), 41-66.

Lo, A., and C. MacKinlay. (1999). A Non-Random Walk Down Wall Street, Princeton.


Lee, C. M. (2001). Market Efficiency and Accounting Research. Journal of Accounting and

Economics 30, 233-253.

Malkiel, B. G. (2003). Efficient market hypothesis and its critics. Journal of Economic

Perspectives 17(1) (winter), 59-82.

Ohlson, J. A. (1995). Earnings, book values, and dividends in equity valuation.

Contemporary Accounting Research 11, 661-687.

Ohlson, J. A. (2001). Earnings, book values, and dividends in equity valuation: an empirical

perspective. Contemporary Accounting Research 18, 107-120.

Senthilnathan, S. (2009). The information perspective and usefulness of accounting

information. Working Paper (source: http://ssrn.com/abstract=1406788).

THE EFFICIENT MARKET, RANDOM WALK, AND THE OHLSON (1995) MODEL

Documents

Transcript of THE EFFICIENT MARKET, RANDOM WALK, AND THE OHLSON (1995) MODEL