Parallel cartoons of fractal models of finance

Summary. Having been crafted to welcome a new scientific journal, this paper looks forward but requires no special prerequisite. The argument builds on a technical wrinkle (used earlier but explained here fully for the first time), namely, the authors grid-bound variant of Brownian motion B(t). While B(t) itself is additive, this variant is a multiplicative recursive process the author calls a cartoon. Reliance on this and related cartoons allows a new perspicuous exposition of the various fractal/multifractal models for the variation of financial prices. These illustrations do not claim to represent reality in its full detail, but suffice to imitate and bring out its principal features, namely, long tailedness, long dependence, and clustering. The goal is to convince the reader that the fractals/multifractals are not an exotic technical nightmare that could be avoided. In fact, the authors models arose successively as proper, natural, and even unavoidable generalization of the Brownian motion model of price variation. Considered within the context of those generalizations, the original Brownian comes out as very special and narrowly constricted, while the fractal/multifractal models come out as nearly as simple and parsimonious as the Brownian. The cartoons are stylized recursive variants of the authors fractal/multifractal models, which are even more versatile and realistic.This revised version was published online in January 2005 with corrections to the Cover date.     

Nonparametric prediction for the time-dependent volatility of the security price

In this paper we consider a continuous time model for the security price with the time-dependent volatility. It is shown that the non-normality and non-linear dependency of the short-term return, the major characteristics observed on many financial assets, can be incorporated into our model. In order to evaluate the option price formula on the model we propose a nonparametric predictor for the volatility function without reference to a specific functional form. We examine the so-called continuous record asymptotics and show that the proposed predictor is asymptotically minimax for a wide class of the volatility functions. One of the most important results is that the application of the Black-Scholes method can be justified by plugging the proposed predictor in the standard Black-Scholes formula even if the volatility changes over time.     

Determinants of stock market volatility and risk premia

Summary. We show the dynamics of diverse beliefs is the primary propagation mechanism of volatility in asset markets. Hence, we treat the characteristics of the market beliefs as a primary, primitive, explanation of market volatility. We study an economy with stock and riskless bond markets and formulate a financial equilibrium model with diverse and time varying beliefs. Agents states of belief play a key role in the market, requiring an endogenous expansion of the state space. To forecast prices agents must forecast market states of belief which are beliefs of others hence our equilibrium embodies the Keynes Beauty Contest. A market state of belief is a vector which uniquely identifies the distribution of conditional probabilities of agents. Restricting beliefs to satisfy the rationality principle of Rational Belief (see Kurz, 1994, 1997) our economy replicates well the empirical record of the (i) moments of the price/dividend ratio, risky stock return, riskless interest rate and the equity premium; (ii) Sharpe ratio and the correlation between risky returns and consumption growth; (iii) predictability of stock returns and price/dividend ratio as expressed by: (I) Variance Ratio statistic for long lags, (II) autocorrelation of these variables, and (III) mean reversion of the risky returns and the predictive power of the price/dividend ratio. Also, our model explains the presence of stochastic volatility in asset prices and returns. Two properties of beliefs drive market volatility: (i) rationalizable over confidence implying belief densities with fat tails, and (ii) rationalizable asymmetry in frequencies of bull or bear states.This research was supported by a grant of the Smith Richardson Foundation to the Stanford Institute for Economic Policy Research (SIEPR). We thank Kenneth Judd for constant advice which was crucial at several points in the development of this work. We also thank Kenneth Arrow, Min Fan, Michael Magill, Carsten Nielsen, Manuel Santos, Nicholas Yannelis, Ho-Mou Wu and Woody Brock for comments on earlier drafts. The RBE model developed in this paper and the associated programs used to compute it are available to the public on Mordecai Kurzs web page at http://www.stanford.edu/ mordecai.This revised version was published online in January 2005 with corrections to the Cover date.     

On the microstructure of price determination and information aggregation with sequential and asymmetric information arrival in an experimental asset market

Summary. Experiments were conducted on an asset with the structure of an option. The information of any individual is limited, as if only the direction of movement of the option value known for a single period without information of the value from when movement was initiated. However, if all information of all insiders were pooled, the value of the option would be known with certainty. The results are the following: (1) Information becomes aggregated in the prices as if fully informative rational expectations operated; and (2) The mechanism through which information gets into the market is captured by a path dependent process that we term The Fundamental Coordination Principle of Information Transfer in Competitive Markets. The early contracts tend to be initiated by insiders who tender limit orders. The emergence of bubbles and mirages in the markets are coincident with failures and circumstances that prevent the operation of the Fundamental Principle.The financial support of the national science foundation and the Caltech Laboratory for Experimental Economics and Political Science are gratefully acknowledged. The authors have benefited from helpful comments of David Grether, Kerry Back, Ivana Komunjer and Pete Kyle.     

Is the ‘Perfect’ Timing Strategy Truly Perfect?

In the presence of transaction cost, the perfect timing strategy which holds stocks in a period with positive excess return and holds cash in a period with negative excess return is not necessarily perfect. Using the optimal growth criterion, this paper derives the truly perfect timing strategy which can achieve the maximum long term growth. It is found that such a perfect timing strategy can achieve a much higher annual return than the perfect timing strategy under reasonable transaction cost. Also, it can achieve a return of over 80% when a review period is as short as a day and when transaction cost is low. Using the truly perfect timing strategy as a benchmark, the likely gains from imperfect timing can be more accurately assessed. For a less frequent review schedule, a market timer needs a very high correct prediction probability in order to be at par with the buy-and-hold strategy. However, the needed correct prediction probability is much less when the review schedule is more frequent. Also, the correct prediction probability needed to be at par with the buy-and-hold strategy increases with the transaction cost.     

Horizontal Inequity and Vertical Redistribution

Inequality of post-tax income among pre-tax equals is evaluated andaggregated to form a global index of horizontal inequity in the income tax.The vertical action of the tax is captured by its inequality effect on averagebetween groups of pre-tax equals. Putting the two together, horizontalinequity measures loss of vertical performance. The identification problem,which has previously been thought insuperable, is addressed by a procedurevalidating the banding of income units into close equals groups. Thehorizontal and vertical effects of a major Spanish income tax reform areevaluated. Lines for future investigation are suggested.     

Financial Distress and Bank Restructuring of Small to Medium Size UK Companies

We use a unique data set to study how U.K. banks deal with financially distressed small and medium-sized companies under a contractualist bankruptcy system. Unlike in the U.S., these procedures limit the discretion of courts to strict enforcement of debt contracts, without any dilution of creditors claims. We show that lenders and borrowers select a debt structure that avoids some of the market failures often attributed to a contractualist system. Collateral and liquidation rights are highly concentrated in the hands of the main bank, giving it a dominant position in restructuring or liquidating a defaulting firm. There is little litigation, and no evidence of co-ordination failures or creditors runs. However, there is some evidence that the banks dominance makes it lazy in monitoring, relying heavily on the value of its collateral in timing the bankruptcy decision.     

Environmental Taxes, International Capital Mobility and Inefficient Tax Systems: Tax Burden vs. Tax Shifting

This paper deals with the so-called double dividend of an environmental tax reform. In a model with only labor and a polluting input as factors of production, we find that society faces a trade-off between internalizing environmental externalities and raising revenues in the least distortionary way. However, if capital enters the production structure, an ecological tax reform may render the tax structure more efficient from a non-environmental point of view, thereby raising not only environmental quality but also private incomes.     

Information Monopoly and Commitment in Intermediary-Firm Relationships

A bank may use the private information that it acquires through monitoring to hold up borrowers. This information monopoly of the bank may inefficiently distort the borrowers investment decisions in environments where moral hazard is prevalent. The paper analyses how this problem is resolved within bank-firm relationships. In the benchmark case when the bank can contractually commit to future actions, the optimal contract turns out to be ambiguous in nature. When commitment contracts cannot be written, firms have an incentive to develop multiple banking relationships in order to decrease the inside banks bargaining power. However, with costly monitoring, this may defeat the initial purpose for contracting with a financial intermediary, namely information production. The paper argues that when contractual commitment is not feasible, bank size may serve as an alternative commitment device that prevents the bank from holding up borrowers in the future.     

Residual Income and Value-Creation: The Missing Link

This paper extends the residual income literature to provide a framework for the use of residual income in performance measurement, applicable in value-based management. It shows that, under a simple initializing assumption, an accounting-free measure of excess value created over a multi-period interval can be written entirely in terms of (i) within-interval realized residual incomes and (ii) end-of-interval expected future residual incomes, both appropriately adjusted for the time value of money. It also shows that, when the simple initializing assumption is relaxed, excess value created can be expressed in terms of excess residual incomes, measured by comparison with expectations as at the beginning of the multiperiod interval.     

Getting the Unemployed Back to Work: The Role of Targeted Wage Subsidies

This paper examines alternative approaches to wage subsidy programmes. It does this in the context of a recent active labour market reform for the young unemployed in Britain. This New Deal reform and the characteristics of the target group are examined in detail. We discuss theoretical considerations, the existing empirical evidence and propose two strategies for evaluation. The first suggests an ex-post trend adjusted difference in difference estimator. The second, relates to a model based ex-ante evaluation. We present the conditions for each to provide a reliable evaluation and fit some of the crucial parameters using data from the British Labour Force Survey. We stress that the success of this type of labour market programmes hinge on dynamic aspects of the youth labour market, in particular the pay-off to experience and training.     

Environmental Taxes and Pre-Existing Distortions: The Normalization Trap

The double-dividend hypothesisclaims that green taxes will both improve the environment andreduce the distortions of existing taxes. According to the earlierliterature on the double dividend the tax rate for pollutinggoods should be higher than the Pigovian tax which fully internalizesthe marginal social damage from pollution, in order to obtaina second dividend. On the contrary, Bovenberg and de Mooij(1994) argue that environmental taxes typically exacerbate, ratherthan alleviate, pre-existing distortions. The optimal pollutiontax should therefore lie below the Pigovian tax. This paper pointsout that there is no real contradiction between these apparentlyopposing policy recommendations. It will be shown that the differencein the results appears because, implicitly, different definitionsof the second-best optimal pollution tax are chosen.     

Two Games of Interjurisdictional Competition When Local Governments Provide Industrial Public Goods

In this paper we investigate two different games of interjurisdictional competition when local governments provide public goods that benefit industry. Governments play a game either in tax rates on mobile industrial capital or in public expenditures. Although the literature suggests that competition in public expenditures is more competitive than in tax rates, this is not necessarily true in the case of industrial public goods. Moreover, in the presence of industrial public goods interjurisdictional competition may also lead to overprovision of public services.     

Economic Effects of the 2003 Partial Integration Proposal in the United States

On January 7, 2003, President George W. Bush proposed a significant change in capital income taxation in the United States. In the context of a jobs and growth package, the President proposed to reduce substantially the double taxation of corporate-source income by eliminating investor-level taxes on dividends paid from earnings on which corporate tax had been paid. In addition, the Presidents proposal would have reduced the tax on retained earnings by allowing a basis adjustment for accumulated previously taxed retained earnings. Taken together, these proposals would have moved the U.S. income tax much closer to an integrated tax system along the lines outlined by the Treasury Department in President George H.W. Bushs administration a decade earlier.Putting together the impacts of the Presidents proposal on economic activity through greater capital accumulation and improved calculation, I estimate that the proposal, if it had been enacted in its original form, would yield a permanent increase of 0.48 percent in the U.S. economys potential output. This estimated gain does not include any gains made possible by improved corporate financial policy.At the time of the integration proposal, the author was Chairman of the Council of Economic Advisers.     

Modeling Spatial and Temporal House Price Patterns: A Comparison of Four Models

This research reports results from a competition on modeling spatial and temporal components of house prices. A large, well-documented database was prepared and made available to anyone wishing to join the competition. To prevent data snooping, out-of-sample observations were withheld; they were deposited with one individual who did not enter the competition, but had the responsibility of calculating out-of-sample statistics for results submitted by the others. The competition turned into a cooperative effort, resulting in enhancements to previous methods including: a localized version of Dubins kriging model, a kriging version of Clapps local regression model, and a local application of Cases earlier work on dividing a geographic housing market into districts. The results indicate the importance of nearest neighbor transactions for out-of-sample predictions: spatial trend analysis and census tract variables do not perform nearly as well as neighboring residuals.     

Exact Utilities under Alternative Monetary Rules in a Simple Macro Model with Optimizing Agents

We construct an optimizing-agent model of a closed economy which is simple enough that we can use it to make exact utility calculations. There is a stabilization problem because there are one-period nominal contracts for wages, or prices, or both and shocks that are unknown at the time when contracts are signed. We evaluate alternative monetary policy rules using the utility function of the representative agent. Fully optimal policy can attain the Pareto-optimal equilibrium. Fully optimal policy is contrasted with both naive and sophisticated simple rules that involve, respectively, complete stabilization and optimal stabilization of one variable or a combination two variables. With wage contracts, outcomes depend crucially on whether there are also price contracts. For example, if labor supply is relatively inelastic, for productivity shocks, nominal income stabilization yields higher welfare when there are no price contracts. However, with price contracts, outcomes are independent of whether there are wage contracts, except, of course, for the nominal wage.     

Global Trends and Issues in Value Added Taxation

Since the late 1960s, the VAT has become one of the mainstays of the tax systems in over one hundred countries. Apparently, its revenue raising and neutrality properties make it an attractive tax in a rapidly integrating, high-tax world. Following an overview of VATs throughout the world, this article examines various VAT structure and policy issues under the following headings: tax coverage features, tax base aspects, hard-to-tax sectors, rate structure issues, and interjurisdictional coordination problems. It is shown that the normative requirements of a good VAT are often met only in the breach.     

Diversified Portfolios in Continuous Time

We study a financial market containing an infinite number of assets, where each asset price is driven by an idiosyncratic random source as well as by a systematic noise term. Introducing asymptotic assets which correspond to certain infinitely well diversified portfolios we study absence of (asymptotic) arbitrage, and in this context we obtain continuous time extensions of atemporal APT results. We also study completeness and derivative pricing, showing that the possibility of forming infinitely well diversified portfolios has the property of completing the market. It also turns out that models where the all risk is of diffusion type are qualitatively quite different from models where one risk is of diffusion type and the other is of Poisson type. We also present a simple martingale based theory for absence of asymptotic arbitrage.     

Pension Plan Investment Management Mandates: An Empirical Analysis of Manager Selection

We examine the impact of several factors on the selection of portfolio managers for Australian pension plan mandates. Performance measures do not affect the probability of a mandate allocation. Pension sponsors tend to choose managers with top-quartile five-year performance who have recently beaten a market benchmark. Management expenses have a negative impact on a managers chances. A surprising result is sponsors tolerance for high portfolio trading costs. Mandates are spread across manager investment styles. The style and institutional attributes of preferred managers suggest trustees reputation and prudential concerns matter, particularly for the aggregate annual mandate allocations.     

Loan Portfolio Swaps and Optimal Lending

Theories on loan portfolio swap hedging are based on a portfolio-choice approach. This paper presents an alternative: a firm-theoretic model for bank behavior with loan portfolio swaps. Our paper derives the optimal loan rate and rate-taking loan amount of the banks portfolio, and relates them to the market loan rate, counterparty loan rate, swap default risk, capital-to-deposits ratio, and deposit insurance. We find that in the bilateral default risk approach, the comparative static results are generated by four factors: the banks risk magnitude about the equity market value, loan composition in the swap contract, the substitution effect in the loan portfolio, and the income effect from the swap transaction. The results imply that changes in the payoff asymmetry in the event of swap default and the banks regulatory parameters have a direct effect on the banks loan portfolio for lending and swap transactions.We would like to thank two anonymous referees for helpful comments and advice.