Oil price, mean reversion and zone readjustments.

• Author: Hammoudeh, Shawkat

1. Introduction

   Observing OPEC's short-term price-output ceiling behavior during the late 1980s and 1990s, one can conclude that it attempts to stabilize the market price within a range of its announced target price by controlling the output ceiling.(1) If the price moves within four to five dollars below the target price, it usually reduces the output ceiling and assigns new quotas to its member countries to keep the price close to the target price. In reality, OPEC establishes a band for the market price positioned around the target price by basically choosing suitable upper and lower limits for the output or, at least in soft markets, it places a tolerance zone below the target price in order to restrict the discrepancy between the market price and the target price [8; 9]. The lower limit is particularly needed because it sets a price floor and ensures that the market price stays above the significantly lower marginal cost of oil production. If the limits of these zones are backed by a perfectly credible intervention policy, they can generate an expectations process that should turn the market prices around even before any intervention takes place.

   While OPEC in some sense observes the target zones for its prices, those zones are neither well defined nor vigorously defended. It can not always or may not be willing to maintain the price within the limits of the desired zone by cutting the output ceiling; it must sometimes readjust the target price and output ceiling, and thus create a new target zone to reflect the market's new fundamentals. This is particularly true now because OPEC is losing market share to the other oil producers and is contemplating to shift the current band.

   Actual readjustments in the target price can be so large, as in 1980 and 1985, that the new market price must jump as well. They can occur when both the market price is near the limits of the band as well as when it is inside the band but still further away from those limits. Therefore, OPEC's policy of defending the limits of a target zone for a given target price may be imperfectly credible.

   In this paper, I examine OPEC's oil market price behavior: First, when OPEC's policy is credible and the market price is limited within a given target zone; Second, when OPEC policy is imperfectly credible and the price reverts to the free market price due to speculative attacks triggered by "too large" output ceiling; and third, when OPEC has the chance of: either defending the current price or shifting the current target zone and declaring a new one.

2. The Basic Oil Model of Target Zones

   In this model there are marginal interventions by OPEC which occur when the market price hits the limits of the current zone while the target price remains unchanged. There are no intramarginal interventions that aim at returning the market price to the specified target price within the band (mean reversion).

   The equation that describes the oil price behavior inside the price's target zone is

   [Mathematical Expression Omitted]

   where [Mathematical Expression Omitted] is OPEC's output ceiling, [q.sub.2] is the cumulative inventory shock, E(dP)/dt is the expected rate of change in the price, [Gamma] is the speed of price adjustment [7; 10; 11]. Therefore, Equation (1) describes the price behavior inside the target zone as a function of OPEC's output ceiling, cumulative oil shock or inventory shock and market participants' expectations of changes in oil price. The ceiling [Mathematical Expression Omitted] is the intervention policy variable which is bounded by the announced upper and lower limits on the market price (i.e., the limits of the target zone). In this case [Mathematical Expression Omitted] will only change only if the market price reaches the maximum or the minimum defined by the band in order to bring it back to the interior of the target zone.

   The cumulative shock [q.sub.2], which is a shift factor, is assumed to follow a random walk with a trend drift independent of the oil price:

   d[q.sub.2] = [Eta]dt + [Sigma]dz (2)

   where [Eta] and [Sigma] are constants, dz is the increment of a standard Wiener process. The shock d[q.sub.2] could be a demand shock, a supply shock or the difference between the two. The differentiating factor is the sign. If d[q.sub.2] is positive then it must be that OPEC's production exceeded its output ceiling and the surplus was added to the inventories, [q.sub.2]. The opposite is true if d[q.sub.2] is negative. The sum [Mathematical Expression Omitted] is called the fundamental.

   The expectations term, E(dP)/dt, is a balancing item that matches the demand and supply of oil. If the demand falls short of supply then this term is negative in order to ensure that the demand matches the given supply. On the other hand, if demand exceeds supply the expectations term is positive.

   In the presence of perfectly credible policy, which sufficiently influences expectations, the target zone price differs from the price dictated by the fundamental q. As the price reaches the limits of the zone, market participants' expectations of future interventions by OPEC causes an expected turnaround in the price, which the market turns into an immediate change [14]. This effect renders the perfectly credible target zone to be inherently stable in the sense that the zone stabilizes the aggregate fundamental q by basically setting an upper and lower limit on it. Inside the target zone, all the changes in q are due to the changes in [q.sub.2]. But when q reaches its lower and upper limits, OPEC changes the output ceiling [Mathematical Expression Omitted] to maintain the price within the limits of the band. Moreover, there is a negative (decreasing) relationship between the limits on the price and the limits on the fundamental q.

   If the price is outside the band, intervention is considered passive or ineffective and the price will be determined by the fundamental forces of supply and demand.

   In order to understand the dynamics of the market price we need to find an explicit expression for the expectations term in equation (1). Let the general form of the solution be represented by P = g(q). The term E(dp)/dt can be derived by applying Ito's lemma:

   dP = g[prime](q)d[q.sub.2] + 1/2g[double prime](q)[(d[q.sub.2]).sup.2]. (3)

   Substituting equation (2) into equation (3) and taking expectations conditioned on current information yields

   E(dP)/at = g[prime](q)[Eta] + 1/2g[double prime](q)[[Sigma].sup.2]. (4)

   Again substituting this term into equation (1) gives

   P = g(q) = [Gamma]q + [Theta][g[prime](q)[Eta] + 1/2g[double prime](q)[[Sigma].sup.2]]. (5)

   The general solution to equation (5) is

   P = g(q) = [Gamma]q + [Theta][Gamma][Eta] + A exp[[[Lambda].sub.1q]] + B exp [[Lambda].sub.2q]] (6)

   where

   [[Lambda].sub.1] = [-[Eta] + ([[[Eta].sup.2] + 2[[Sigma].sup.2]/[Theta]).sup.1/2]]/[[Sigma].sup.2] [greater than] 0

   and

   [[Lambda].sub.2] = [-[Eta] + ([[[Eta].sup.2] + 2[[Sigma].sup.2]/[Theta]).sup.1/2]]/[[Sigma].sup.2] [less than] 0

   Then

   [Mathematical Expression Omitted]

   Equation (6) describes a family of solutions for the oil price. Any selected solution should satisfy the boundary conditions appropriate to target zone models. The constants A and B are determined by those conditions.

   If the intervention policy is passive and [Mathematical Expression Omitted] is expected to remain unchanged at its initial level the oil price may take on any value. However, it should not deviate arbitrarily far from the fundamental level as [q.sub.2] takes on large values or it may asymptotically approach this level as [q.sub.2] tends to infinity. Thus, in this case we may assume that A = B = 0 and the general solution of the model represented in equation (6) can be reduced to the free fundamental solution(2)

   [Mathematical Expression Omitted] (8)

   which is a combination of the output ceiling, the inventory shock, the time trend, the sensitivity to changes in expectations and the market speed of adjustment.

3. The Price solution within a Given Target Zone

   Marginal Interventions

   OPEC pursues marginal (infinitesimal) interventions in the output ceiling at the limits of the target zone in order to turn the market price around as it hits those limits, without changing the target price. Figure 1 plots the within-band solution form of the target zone model for this case (the curve labeled 1). If there is no intervention, [Mathematical...