Academic journal article Economic Inquiry

Risky Arbitrage, Limits of Arbitrage, and Nonlinear Adjustment in the Dividend-Price Ratio

Academic journal article Economic Inquiry

Risky Arbitrage, Limits of Arbitrage, and Nonlinear Adjustment in the Dividend-Price Ratio

Article excerpt

MARK P. TAYLOR (*)

I. INTRODUCTION

The present value model of stock prices has generally been rejected on U.S. data, as in Campbell and Shifler (1987, 1988a, 1988b). (1) While this may be taken as evidence against the efficient markets hypothesis, an alternative view would be that the instantaneous arbitrage assumed in the simple present value model is too restrictive. In recent arbitrage models developed by, inter alios, Grossman and Miller (1988), De Long, Shleifer, Summers, and Waldmann (1990) and Campbell and Kyle (1993), arbitrage is generally less than perfect because arbitrageurs face either fundamental or noise trader risk. In particular, given that the actions of noise traders may lead to greater fundamental mispricing of an asset, perceived deviations of asset prices from their fundamental values represent risky arbitrage opportunities, as in Shleifer and Summers (1990). (2) Thus, small deviations from fundamentals may not be arbitraged because the perceived gains may not be enough to outweigh this risk. Given, however, a distributio n of degrees of risk aversion across smart traders, arbitrage will increase as the degree of fundamental mispricing increases, so that arbitrage is stabilizing and becomes more stabilizing in extreme circumstances. Traditional arbitrage models, therefore, imply a degree of nonlinearity in asset price dynamics, for example, as in Chiang, Davidson, and Okunev (1997). We term this broad approach the "risky arbitrage" hypothesis.

This approach may be contrasted with the more recent "limits of arbitrage" hypothesis, suggested by Shleifer and Vishny (1997), in which arbitrage activity is viewed in an agency context. In the Shleifer-Vishny model, arbitrageurs (the agents) have access to funds mainly from outside investors (the principals), who will generally gauge the ability of arbitrageurs--and hence decide on the amount of funds to allocate to them--based on their past performance. Since the track record of smart arbitrageurs is likely to be poorest when prices have deviated far from their fundamental values, the implication of the limits of arbitrage hypothesis is that arbitrage is likely to be least effective in returning prices to fundamental values when investor sentiment has driven them far away. (3) That is, "[w]hen arbitrage requires capital, arbitrageurs can become most constrained when they have the best opportunities, i.e., when the mispricing they have bet against gets even worse" (Shleifer and Vishny [1997, 37]). In contra st, the risky arbitrage models are without agency problems and arbitrageurs are more aggressive when prices move further from fundamental values.

In this article we provide a simple test of these two alternative views of arbitrage activity by nonlinear time series modeling of the aggregate log dividend-price ratio, such that adjustment towards equilibrium varies nonlinearly with the size of the deviation from equilibrium.

The remainder of the paper is set out as follows. Section II presents a simple test of the risky arbitrage hypothesis against the alternative of the limits of arbitrage hypothesis using the logarithmic present value model and recently developed techniques in parametric nonlinear modeling. The procedure for selecting the appropriate modeling of the log dividend-price ratio is outlined in section III. Section IV describes the data and presents the empirical results. Section VI extends the earlier empirical results to allow for a time-varying returns in the present value representation. Section VI concludes the study.

II. THE LOG DIVIDEND-PRICE RATIO, NONLINEARITY, ARBITRAGE, AND ADJUSTMENT

The loglinear present value model can be expressed as:

(1) [y.sub.t] = [d.sub.t] - [p.sub.t] = -[summation over ([infinity]/j=0)] [[rho].sup.j][E.sub.t][DELTA][d.sub.t+1+j] + [k.sup.*]

where [p.sub.t] and [d.sub.t] are the log of real stock prices and real dividends, respectively, [rho] = [(1+R). …

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