Dynamic portfolio adjustment and capital controls: a Euler equation approach.

• Author: Broer, D. Peter

1. Introduction

   Empirical papers on (intertemporal) portfolio balance models fall into two categories. The first category assumes that asset holdings can be changed instantaneously and without cost. Asset demand is then determined by the expected returns and the covariance matrix of the returns and the attitude towards risk. Or, written in the form of an asset pricing relation, the expected returns depend on asset supplies, risk aversion, and the return covariance matrix. The empirical work, which often focuses on asset pricing relations, is geared toward testing the mean variance (MV) restrictions implied by the model. These papers typically estimate the structural parameters governing the portfolio problem, i.e., the risk aversion parameter and the conditional return covariances, under the assumption of rational expectations. Recent research has incorporated time-varying conditional covariances into the portfolio model, usually by specifying them as a member of the autoregressive conditional heteroskedasticity (ARCH) family.(1) The MV restrictions are virtually always strongly rejected.

   The second body of literature abandons the idea of instantaneous portfolio adjustment and has established the lagged response of asset demand to permanent changes in expected returns as an empirical regularity, especially for less liquid financial assets. The dynamic specification is usually a variant of the multivariate stock adjustment model introduced by Brainard and Tobin (1968). According to that model, investors gradually adjust their asset positions to their desired levels implied by the static portfolio model. The papers in this vein all estimate reduced-form equations, usually do not assume rational expectations, and use interest rates as proxies for expected holding period yields. Moreover, they are only able to test some of the weaker implications of portfolio theory, like symmetry and positive definiteness of the matrix of return coefficients. Although several authors refer to quadratic adjustment costs to motivate their dynamic specification, they do not fully incorporate the theoretical restrictions in their empirical specification. Adjustment costs merely serve as an expedient to justify the appearance of lagged variables in the econometric specification.(2) From a choice-theoretic point of view, this is unsatisfactory because it remains unclear how the reduced form estimates should be interpreted in terms of structural parameters. The plausibility of the coefficients obtained is therefore hard to judge.

   Zietz and Weichert (1988) demonstrate the importance of a correct dynamic specification of asset demand systems for testing hypotheses implied by portfolio theory. In the static version of their asset demand model, homogeneity and symmetry of the matrix of return coefficients were rejected, while in the dynamic version these hypotheses were accepted. This finding, in combination with abundant evidence that lagged asset holdings have statistically significant effects, strongly suggests that tests of MV restrictions based on structurally estimated models should also take dynamics into account if these tests are to be dependable. Unwarranted neglect of lagged portfolio adjustment may lie at the root of the rejection of MV efficiency because of misspecification bias in the parameter estimates. A similar argument applies with respect to capital controls, which were maintained in many OECD countries in the 1970s and part of the 1980s.

   This paper aims to contribute to the two strands in the literature mentioned above. First, we examine the empirical validity of MV restrictions in an asset demand system in the presence of dynamic adjustment and capital controls. Second, because we estimate the structural parameters of the portfolio problem, we can judge the plausibility of the parameter estimates. In particular, we investigate whether adjustment costs, which are often thought to be rather low, can plausibly explain the observed lagged portfolio adjustment. Third, we explore the potential of existing capital controls and adjustment costs to explain the "home bias" observed in portfolios in industrialized economies, that is, the empirical observation that foreign assets are greatly underrepresented in portfolios as compared to an optimal portfolio selected on the basis of observed returns in a simple MV framework (see French and Poterba 1991).

   Our multiasset dynamic portfolio model is explicitly derived from the optimization problem of a risk-averse consumer who maximizes an intertemporal utility function in consumption under uncertainty, capital controls, and quadratic adjustment costs. We derive the consumer's portfolio allocation rule as well as the consumption rule. We estimate the model's structural parameters, using quarterly observations on the portfolio of the German private sector in the period 1975.I-1990.II. We assess the effects of capital controls and adjustment costs, and also address the question of whether the empirical results are consistent with MV efficiency.

   The remainder of the paper is organized as follows. In section 2 we give a short description of the relevant data. In section 3 we set out the model. Section 4 is devoted to empirical application issues, and section 5 presents the empirical results. The paper ends with a summary and some conclusions.

2. Data

   We analyze the portfolio behavior of the German private sector in the period 1975.I-1990.I. Net wealth is allocated among three assets: assets from the U.S., the Rest of the World (RW), and Germany itself.(3) As Figure 1 shows, the German portfolio has become much more internationally diversified over time, especially since the early 1980s. The share of U.S. assets roughly tripled between 1975 and 1990, rising to approximately 7% in 1990, and the share of assets from the Rest of the World experienced an almost six-fold increase from 8 to 47%. The share of German assets steeply declined from 89 to 46%. However, the German portfolio still displays a considerable "home bias": its composition is a long way from the internationally completely diversified portfolio (world market portfolio) implied by simple theoretical portfolio models (Dumas 1994). Investors in other industrialized countries also exhibit a substantial home asset preference, as French and Poterba (1991) and Tesar and Werner (1992) show.

   In Figure 2 we plot the time series of the (realized) total returns of the three assets, and in Table 1 we list some summary statistics.(4) The quarterly total return on the foreign assets displays far greater variability than the return on German assets, because these returns are dominated by exchange rate changes. For a German investor, holding a U.S. security is riskier than one from the Rest of the World because the latter is a composite asset, which is naturally more diversified. The American return does not seem to display the conventional risk-return trade-off: the average return is the lowest, while the variability is the largest. The return on RW assets follows a normal pattern: Investors have on average earned more on RW assets than on German assets as a compensation for greater exposure to risk.

   Because there are no persistent trends in the three-return series, we need to introduce extra variables into the model to explain the observed international diversification. An obvious candidate is the worldwide liberalization of international capital movements that has taken place over the past two decades. Institutional barriers to cross-border capital flows were brought down on a massive scale, especially in the 1980s. The U.K. abolished all exchange controls at a stroke in 1979, and Japan liberalized from 1980 onward. The drive for greater European unity created a boost for the complete liberalization of intra-EC capital movements. OECD (1990, pp. 3234) gives a concise historical overview of the liberalization process. Because both the U.S. and Germany traditionally have had liberal regulatory regimes concerning international capital movements, the cause for the diversification must primarily lie with the liberalization in the Rest of the World.

   Measuring the level or intensity of existing capital controls necessarily involves ad hoc methods. We base our capital control index on the extent countries comply with the OECD Code of Liberalization (OECD 1990, pp. 63-72). All OECD countries are signatories of this Code, which prohibits restrictions on cross-border financial flows. However, countries are allowed to lodge general derogations and full and limited reservations on individual items covered by the Code for both capital inflows and outflows. Our index is defined as the number of derogations and full reservations lodged by RW countries, expressed as a fraction of the total number of items under the Code.(5)

   Table 1. Summary Statistics of Returns for German Investors Mean Standard Deviation Total Return U.S. 0.0143 0.0602 Total Return RW 0.0181 0.0293 Total Return Germany 0.0155 0.0064 Total Return Portfolio 0.0157 0.0112 [Delta] Exchange Rate U.S. -0.0060 0.0579 [Delta] Exchange Rate RW -0.0060 0.0282 Interest Rate U.S. 0.0203 0.0070 Interest Rate RW 0.0241 0.0047 Interest Rate Germany 0.0155 0.0064 Inflation Germany 0.0080 0.0062 Quarterly rates. Sample period: 1975.I-1990.I. Figure 3 shows the development of our measure of capital inflow and outflow controls in the Rest of the World. Both indices gradually decrease until the mid-1980s, after which the decline accelerates. The majority of the remaining restrictions at the end of the sample period were in force in Greece, Ireland, Portugal, and Spain, which have a minor influence on international capital flows. Capital outflows (purchase of foreign securities by domestic agents) are more heavily regulated than capital inflows (sale of domestic securities to foreign agents). This reflects to a large extent prudential considerations on the part of the authorities, who want to...