On mean-variance portfolio selection under a hidden Markovian regime-switching model

We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black–Scholes–Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the “true” state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem.     

An Experimental Study of Risk Aversion in Decision-making Under Uncertainty

This paper presents the findings of an experimental study of risk aversion in decision making under uncertainty. When presented with a series of gambles, subjects determined the certainty-equivalent wealth of each gamble. Risk aversion was measured by the Markowitz risk premium of the decision. The fixed effects regression model indicates the significant influence of the first three moments of a probability distribution in determining the risk premium. These results lend support to the rules of mean-variance and third-degree stochastic dominance. The extent of influence is also affected by the individual’s age, but not by gender, wealth or schooling.     

Mean-semivariance behavior: Downside risk and capital asset pricing

For over 30 years academics and practitioners have been debating the merits of the CAPM. One of the characteristics of this model is that it measures risk by beta, which follows from an equilibrium in which investors display mean-variance behavior. In that framework, risk is assessed by the variance of returns, a questionable and restrictive measure of risk. The semivariance of returns is a more plausible measure of risk and can be used to generate an alternative behavioral hypothesis, mean-semivariance behavior; an alternative measure of risk for diversified investors, the downside beta; and an alternative pricing model based on this downside beta. The empirical evidence discussed in this article for the entire MSCI database of developed and emerging markets clearly supports the downside beta and the pricing model based on it over beta and the CAPM.     

Increasing returns,entrepreneurship and imperfect competition

We study a simple bilateral oligopoly model in which individual agents, who are initially endowed with capital, decide sequentially (1) whether they want to act as producers (entrepreneurs) or as capital lenders (rentiers) and, then (2) which quantity of capital they would like to borrow or lend, though exchange of capital units against units of the produced good. Production takes place under increasing returns to scale. We show the existence of “natural equilibria”, at which wealthier capital owners become entrepreneurs while the remaining ones decide to be rentiers. We also study the efficiency of equilibria which is shown to increase by replication of the economy, but sometimes to decrease as a consequence of wealth redistribution.We thank an anonymous referee for his insightful comments     

Time-varying beta: a boundedly rational equilibrium approach

The conditional CAPM with time-varying betas has been widely used to explain the cross-section of asset returns. However, most of the literature on time-varying beta is motivated by econometric estimation using various latent risk factors rather than explicit modelling of the stochastic behaviour of betas through agents’ behaviour, such as momentum trading. Misspecification of beta risk and the lack of any theoretical guidance on how to specify risk factors based on the representative agent economy appear empirically challenging. In this paper, we set up a dynamic equilibrium model of a financial market with boundedly rational and heterogeneous agents within the mean-variance framework of repeated one-period optimisation and develop an explicit dynamic behaviour CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the two most commonly used types of investors, fundamentalists and chartists, into the model, we show that there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas. We also show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta.     

Aggregation, efficiency and mutual fund separation in incomplete markets

Summary. This paper studies the conditions for aggregation, portfolio separation and effective completeness of competitive allocations in general equilibrium models with incomplete markets where agents have general preference and endowment distributions. We show that these properties are distinct. Demands may aggregate yet may fail to exhibit fund separation and conversely. Fund separation implies effective completeness while aggregation does not. The implications of these properties for the structure of equilibria are discussed, and generalizations of the CAPM, the consumption CAPM and the CAPM with nonmarketed wealth emerge from the analysis. Received: September 12, 1996; revised version: November 7, 1996     

Covered Call Investing in a Loss Aversion Framework

In a mean-variance framework, the covered call investment strategy has been seen as an inefficient method of allocating wealth. Covered calls reduce the riskiness of the portfolio and therefore lead to lower portfolio returns. Recent debate has focused on the shortcomings of mean-variance efficiency as an accurate depiction of investor utility. Using alternative utility functions, we find mixed support for the use of the covered call investing strategy. Using loss aversion, however, we reexamine the covered call investment decision and find it significantly enhances investor utility relative to an index portfolio investment strategy. We conclude that loss aversion's more accurate depiction of investor preferences and behavior helps to explain the popularity of the covered call investment strategy.     

The capital asset pricing model in economic perspective

The capital asset pricing model (CAPM) is theoretically incomplete in its demand-side focus, risk-averse investors and internally inconsistent homogeneous beliefs; is not conclusively supported empirically; and yet it legitimizes a notion that investors can earn higher returns by bearing undiversifiable risk. Our article does not merely extend the CAPM with more realistic assumptions, it completes its original framework by including (1) risk-taking investors in the investor population, (2) investors who can have heterogeneous expectations or beliefs – an overlooked but required condition for the CAPM to be an internally consistent and meaningful model of competitive financial asset pricing under uncertainty and (3) a positive-sloped short-run supply curve based on a reasonable interpretation of the nature of financial asset trade. Upon a complete economic interpretation, it is shown that the equilibrium (systematic) risk-rate of return relationship depends on whose aggregate trading activity dominates, risk-averse or risk-taking investors’. There is no universal, or even general, positive relationship between systematic risk and rate of return. This has far-reaching implications for investors and investment advisors who serve them.     

Exact arbitrage and portfolio analysis in large asset markets

Summary. We provide a detailed portfolio analysis for a financial market with an atomless continuum of assets. In the context of an exact arbitrage pricing theory (EAPT), we go beyond the characterization of the existence of important portfolios (normalized riskless, mean, cost, factor and mean-variance efficient portfolios) to furnish exact portfolio compositions in terms of explicit portfolio weights. Such an analysis has not been furnished before in the context of the asymptotic arbitrage pricing theory (APT). We also characterize conditions under which a mean-variance efficient portfolio is a benchmark portfolio used in the EAPT to proxy essential risk. We illustrate our results with several examples of specific financial markets. Received: May 30, 2002; revised version: August 15, 2002 RID="*" ID="*"Some of the results reported here constituted part of Cowles Foundation Discussion Paper– No. 1139 circulated under the title “Hyperfinite Asset Pricing Theory”; additional results were obtained when Sun visited the Department of Economics at Johns Hopkins University during March 2002. This paper was presented at the Conference on Economic Design held at NYU on July 6–9, 2002 Correspondence to: M. A. Khan     

Generalized method of moments and present value tests of the consumption-capital asset pricing model under transactions costs: evidence from the UK stock market

In this paper we test for the inclusion of the bid–ask spread in the consumption CAPM, in the UK stock market over the time period of 1980–2000. Two econometric models are used: first, Fisher’s (in J Appl Econometrics 9:S71–S94, 1994) asset pricing model is estimated by GMM. We obtain plausible values of all the structural parameters and transactions costs. We subsequently test the robustness of our results by extending the VAR approach proposed by Campbell and Shiller (in Rev Financ Stud 1:195–228, 1988). This is achieved with the inclusion of the normalised bid–ask spread as an independent variable in the pricing equation. Overall, the statistical tests are unable to reject the bid–ask spread as an independent explanatory variable in the C-CAPM. In addition, in the VAR specification we find that both the normalised and the absolute bid–ask spread is a significant predictor of the dividend to price ratio. The paper’s main conclusion is that transaction costs should be included in asset pricing models, as they possess independent explanatory power.      

Consumption taxation, social status and indeterminacy in models of endogenous growth with elastic labor supply

In this paper, we examine the effects of consumption taxation on long-run growth in an infinitely lived representative-agent model of endogenous growth with endogenous labor supply in which the desire for social status induces private agents to care about others’ wealth or consumption levels. This analysis shows that the increase in consumption taxation raises (reduces) the long-run growth rate when the equilibrium path is locally indeterminate (determinate), provided the desire for social status is not too strong in the relative wealth model. By contrast, in the consumption externalities model, the same result holds, if the Frisch labor supply and labor demand curves have the ‘normal’ slopes at their intersection point, while the result is reversed if these two curves have the ‘wrong’ slopes.     

Strategic saving decisions in the infinite-horizon model

We study a mechanism that prevents the long-run distribution of wealth from becoming degenerate in the Ramsey–Cass–Koopmans model when households have different time-preference rates. This mechanism is based on the observation that price-taking behavior is no longer justified when all wealth is owned by a single household. Formalizing this observation, we obtain a model with a unique stationary equilibrium in which, depending on the parameter constellation, any number of households can own positive stocks of capital. We characterize this equilibrium and show for example that an increase in the dispersion of the time-preference rates across households unambiguously increases aggregate output. Whereas the main results are derived for a rather general class of production functions, we devote a separate section to the special case of the Cobb–Douglas technology for which the equilibrium conditions are particularly simple. The research reported in this paper forms part of the project “Economic Growth with Strategic Saving Decisions” supported by the Austrian Science Fund (FWF) under project number P17886. Comments from Robert Becker, Edward Green, Takashi Kamihigashi, David Levine, Fabrizio Zilibotti, anonymous referees, and participants at various conferences and seminars are gratefully acknowledged.     

Consumption,wealth and business cycles in Germany

This paper studies the long-run relationship between consumption, asset wealth and income—the consumption–wealth ratio—based on German data from 1980 to 2003. We find that departures from this long-run relationship mainly predict adjustments in income. The German consumption–wealth ratio also contains considerable forecasting power for a range of business cycle indicators, including the unemployment rate. This finding is in contrast to earlier studies for some of the Anglo-Saxon economies that have shown that the consumption–wealth ratio reverts to its long-run mean mainly through subsequent adjustments in asset prices. While the German consumption wealth ratio contains little information about future changes in German asset prices, we report that the U.S. consumption–wealth ratio has considerable forecasting power for the German stock market. One explanation of these findings is that in Germany—due to structural differences in the financial and pension systems—the share of publicly traded equity in aggregate household wealth is much smaller than in the Anglo-Saxon countries. We discuss the implications of our results for the measurement of a potential wealth effect on consumption. The views expressed in this paper are those of the authors and do not reflect the position of the Deutsche Bundesbank. We gratefully acknowledge comments and suggestions from an anonymous referee as well as from Heinz Herrmann, Helmut Lütkepohl, the editor, Baldev Raj, Burkhard Raunig, Monika Schnitzer, Harald Uhlig and Christian Upper. We also benefitted from comments by seminar participants at the ECB, the Deutsche Bundesbank, the CESifo Macro, Money and International Finance Area Conference 2005, the EEA 2005 annual congress and at the 2005 IAEA Meetings. Last but not least, we would like to thank Mark Weth for very useful information concerning the construction of the financial wealth data. Hoffmann’s work on this paper is also part of the project The International Allocation of Risk funded by Deutsche Forschungsgemeinschaft in the framework of SFB 475. Responsibility for any remaining errors and shortcomings is entirely our own.     

THE DISTRIBUTION OF BETAS IN PRESENCE OF NONTRADED ASSETS

This study considers a capital assets pricing model (CAPM) in an incomplete financial market wherein not all risky assets are traded and the risk from non‐traded assets is not orthogonal to that of the existing or traded assets. The model shows the extent of the divergence of the CAPM betas (true betas) from the traditional CAPM betas (perceived betas) in market equilibrium conditions in an incomplete market. Specifically, it implies that the more incomplete a financial market is, the wider is the discrepancy between the true and perceived betas, and the distribution of the perceived betas tends to centre more around 1 in an incomplete market than that of true betas. Empirical evidence in various settings support these results.     

Parametric characterizations of risk aversion and prudence

Summary. Our first main result says that whether one decision maker is more risk averse than another can be determined from their attitudes toward a given two-parameter family of risks. When all risks belong to this family, risk aversion can be compared even when initial wealth is random. Our second main result solves a long-standing problem in mean-variance analysis: what is the interpretation of the concavity of utility as a function of mean and variance? We show that in the case of normal distributions, this utility function is concave if and only if the agent has decreasing prudence. Received: July 29, 1996; revised: October 2, 1998     

Non-parametric and semi-parametric asset pricing

We find that the CAPM fails to explain the small firm effect even if its non-parametric form is used which allows time-varying risk and non-linearity in the pricing function. Furthermore, the linearity of the CAPM can be rejected, thus the widely used risk and performance measures, the beta and the alpha, are biased and inconsistent. We deduce semi-parametric measures which are non-constant under extreme market conditions in a single factor setting; on the other hand, they are not significantly different from the linear estimates of the Fama-French three-factor model. If we extend the single factor model with the Fama-French factors, the simple linear model is able to explain the US stock returns correctly.     

An examination of the economic significance of stock return predictability in UK stock returns

We explore the out-of-sample performance of domestic UK asset allocation strategies that use forecasts of expected returns from a linear predictive regression and those that are implied by asset pricing models such as the capital asset pricing model (CAPM) or arbitrage pricing theory (APT). Our findings suggest that using forecasts of expected returns from the predictive regression generate significant benefits in out-of-sample performance. We find the performance of the strategies using expected return forecasts implied by the CAPM or APT is lower than the predictive regression strategy. However, with binding investment constraints, the performance of the APT matches that of the predictive regression.     

A Reexamination of the Wealth Effect and Uncertainty Effect

In an influential article, [Romer, C. “The Great Crash and the Onset of the Great Depression,” Quarterly Journal of Economics, 105, 1990, pp. 597–624.] estimates the magnitudes of the uncertainty and wealth effects. She reports that before and after the Great Depression, the uncertainty effect has a large and statistically significant influence on durable good production, while the wealth effect is negative but negligible. When the authors of this paper change the specification of the model with respect to the amount of time necessary for stock returns to translate into changes in consumption, they reach the exact opposite conclusions that Romer does. Specifically, when the authors allow consumers 12 or more months to alter consumption behavior, rather than Romer's three, stock price uncertainty did not significantly affect the durable goods production before, during, or after the Great Depression. The authors also find that stock market returns from the previous year have a positive and statistically significant impact on the durable goods production, indicating the importance of the wealth effect.     

Market structure and the cost of capital

We contribute to the finance literature in two main ways. First, we present a theoretical capital asset pricing model (CAPM) to price assets in different market structures. Second, we use our model to analyze whether when markets are partially segmented using the local or the global CAPM yields significant errors in the estimation of the cost of capital for a sample of firms from developed and emerging countries.     

Post-earnings announcement drift: Spanish evidence

This paper analyses whether earnings announcements in the Spanish stock market are followed in subsequent months by a return drift in the same direction as the earnings surprise. Two alternative earnings surprise measures are used and they both provide strong post-earnings announcement drifts. In order to find an explanation for this anomaly we first make several unconditional adjustments, which include the CAPM, the Fama–French (J Financ Econ 33:3–56, 1993) three-factor model, a liquidity factor, controlling portfolios by size and book-to-market ratio, and controlling for the momentum effect. Second, we make a conditional analysis following two different approaches: (i) studying the relation with the business cycle and (ii) studying whether this phenomenon can be explained through a conditional version of the CAPM and the Fama-French model. None of these adjustments are able to satisfactorily capture the Spanish post-earnings announcement drift. A final analysis offers some slight evidence in favour of the limits-to-arbitrage explanation. A previous version of this paper is available in the Working Paper Series of FUNCAS (no. 221, 2005), who we thank for their collaboration in the research diffusion in Spain. We also acknowledge the financial support of the Ministerio de Ciencia y Tecnología (SEJ2005-09372/ECON), Conselleria d’Empresa, Universitat i Ciència (GV06/196) and University of Alicante (GRJ06-03). This version has benefited from interesting comments made by Gonzalo Rubio, Belén Nieto, Natividad Blasco, Renata Herrerías and Carina Sponholtz, as well as by various anonymous referees. Any remaining errors are the sole responsibility of the authors.