A short note on the problematic concept of excess demand in asset pricing models with mean-variance optimization

Referring to asset pricing models where demand is proportional to excess returns and said to be derived from a mean-variance optimization problem, the note formulates what probably is common knowledge but hardly ever made an explicit subject of discussion. This is an insufficient distinction between the desired holding of the risky asset on the part of the speculative agents, which is the solution to the optimization problem and usually directly presented as excess demand, and the desired change in this holding, which is what should reasonably constitute the excess demand on the market. The note arrives at the conclusion that in models with a market maker the story of the maximization of expected wealth should be dropped

On the Interpretation of Price Adjustments and Demand in Asset Pricing Models with Mean-Variance Optimization

With reference to the class of asset pricing models with a market maker and mean-variance optimization of speculative agents, the note seeks to clarify the concepts behind the price adjustment rule, which are often treated somewhat carelessly in this literature. Calling attention to the distinction between the agents? desired holding of the risky asset and the desired change in their position, the following conclusion is drawn. If market prices are said to adjust in the direction of excess demand, then the story of the maximization of expected wealth should be dropped. On the other hand, the story could be perfectly maintained if the market maker were assumed to adjust prices inversely to his accumulated inventory. --Expected wealth maximization,market maker,positions of speculative agents

Artificial Long Memory Effects in Two Agend-Based Asset Pricing Models

This note is concerned with two recent agent-based models of speculative dynamics from the literature, one by Gaunersdorfer and Hommes and the other by He and Li. At short as well as long lags, both of them display an autocorrelation structure in absolute and squared returns that comes remarkably close to that of real data at a daily frequency. The note argues that these long memory effects are to be ascribed to the stochastic specification of the price equation, which given the wide fluctuations in these models unduly fails to normalize the price shocks. Under an appropriate respecification, the long memory completely disappears. --Volatility clustering,Autocorrelations of returns,Fundamentalists and trendfollowers

A Proof of Determinacy in the New-Keynesian Sticky Wages and Prices Model

The paper is concerned with determinacy in a version of the New-Keynesian model that integrates imperfect competition and nominal price and wage setting on goods and labour markets. The model is reformulated with an explicit period of arbitrary length and shown to remain well-defined as the period shrinks to zero. The 4×4 constituent matrix of the model?s continuous-time counterpart is mathematically tractable and its determinacy results carry over to the period model at least if the period is sufficiently short. This being understood, it is proved that determinacy is (essentially) ensured if an extended Taylor principle requirement is met. --Determinacy,New-Keynesian wage and price Phillips curves,variable period length,continuous-time limit,Taylor principle

Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

In the framework of small-scale agent-based financial market models, the paper starts out from the concept of structural stochastic volatility, which derives from different noise levels in the demand of fundamentalists and chartists and the time-varying market shares of the two groups. It advances several different specifications of the endogenous switching between the trading strategies and then estimates these models by the method of simulated moments (MSM), where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. In addition to the standard version of MSM with a quadratic loss function, we also take into account how often a great number of Monte Carlo simulation runs happen to yield moments that are all contained within their empirical confidence intervals. The model contest along these lines reveals a strong role for a (tamed) herding component. The quantitative performance of the winner model is so good that it may provide a standard for future research. --Method of simulated moments,moment coverage ratio,herding,discrete choice approach,transition probability approach

Why a simple herding model may generate the stylized facts of daily returns: Explanation and estimation

The paper proposes an elementary agent-based asset pricing model that, invoking the two trader types of fundamentalists and chartists, comprises four features: (i) price determination by excess demand; (ii) a herding mechanism that gives rise to a macroscopic adjustment equation for the market fractions of the two groups; (iii) a rush towards fundamentalism when the price misalignment becomes too large; and (iv) a stronger noise component in the demand per chartist trader than in the demand per fundamentalist trader, which implies a structural stochastic volatility in the returns. Combining analytical and numerical methods, the interaction between these elements is studied in the phase plane of the price and a majority index. In addition, the model is estimated by the method of simulated moments, where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. A (parametric) bootstrap procedure serves to set up an econometric test to evaluate the model's goodness-of-fit, which proves to be highly satisfactory. The bootstrap also makes sure that the estimated structural parameters are well identified. --structural stochastic volatility,method of simulated moments,autocorrelation pattern,fat tails,bootstrapped p-values

A prototype model of speculative dynamics with position-based trading

To avoid the indeterminate and generally unbounded positions of the agents in financial market models with order-based trading, the paper considers the alternative of position-based strategies. To this end it extracts a prototype model from the literature, with fundamentalists, chartists, and a risk-averse market maker. The deterministic formulation of the model leads to a neutral delay differential equation of the price, whose mathematical analysis is non-standard. The stability conditions are nevertheless quite analogous to the order-based Beja–Goldman model. The effects of parameter variations are also studied in a stochastic setting, where special emphasis is put on the misalignment between price and the time-varying fundamental value, and on the differential profits of fundamentalists and chartists

Estimation of a microfounded herding model on German survey expectations

The paper considers the dynamic adjustments of an average opinion index that can be derived from a microfounded framework where the individual agents switch between two kinds of sentiment with certain transition probabilities. The index can thus represent a general business climate, i.e., expectations about the future course of the economy. This approach is empirically tested with the survey expectations published by the ZEW and ifo institute. The estimated coefficients make economic sense and are highly significant. In particular, besides effects from fundamental data like the output gap in the recent past, one can identify a strong herding mechanism within both panels, such that metaphorically speaking the agents do not just join the crowd but follow each single motion of it. In addition, the transition probabilities of the ZEW agents are found to be influenced by the ifo climate but not the other way round

On the Determinacy of New Keynesian Models with Staggered Wage and Price Setting

This paper shows that an analytical determinacy analysis of the baseline New Keynesian model with both staggered wages and prices developed by Erceg, Henderson and Levin (2000) is possible despite the high dimensional nature of this model. It is possible if the formulation of the model is translated from discrete to continuous time. Our findings corroborates in an analytical manner Galí's (2008) numerical findings regarding the determinacy frontier and the Taylor principle for this model type, where a generalized Taylor rule that employs a weighted combination of wage and price inflation is used as a measure for the inflation gap.Period models, continuous time, (in)determinacy.