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.     

Decomposition of Japanese Yen Interest Rate Data Through Local Regression

Seven different Japanese Yen interest rates recorded on a daily basisfor the period from 1986 to 1992 are simultaneously analyzed. Byintroducing a new concept of short term trend, we decomposeeach interest rate series into three components, long termtrend, short term trend and irregular. It is obtained by atwo step lowess smoothing technique. After that, amultivariate autoregressive model (MAR) is fitted to the vectorvalued time series obtained by combining those seven irregularcomponents. The decomposition and MAR model fitting were quitesatisfactory. It enables us to understand well various aspects ofinterest rate series from the trends, the MAR (2) coefficientsand its residuals. The result is compared with the decompositionthrough sabl and the advantages of our procedure will bedemonstrated in relations to other parametric model fitting likeARCH or GARCH. Based on the decomposition we can have betterdaily prediction and more stable long term forecasting.     

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.     

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.     

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.     

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.     

Income Redistribution in an Economic Union: The Trade Off Between Inter- and Intra-National Redistribution

This paper studies the design of redistributive policiesbetween and within the member countries of an economic union.There are two types of countries, which differ in their proportionof high income individuals. Both the supra-national and the nationalgovernments attempt to redistribute income within their respectiveboundaries. However, the central government cannot observe anindividual countrys ability to pay; it only observes the aggregate(internal) redistributive effort of each country. We derive theoptimal incentive compatible tax-transfer policy of the centralgovernment and show that there is a tradeoff between inter- andintra-national redistribution. Specifically, to reduce informationalrents of the rich countries, the optimal policy induces a distortionin the poor countries (internal) redistributive policies. Interestingly,both insufficient as well as excessive redistribution can arise.     

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.     

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.     

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.     

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.     

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.     

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.     

Edokko Options: A New Framework of Barrier Options

In this paper, we will give a new framework of barrier options to generalize`Parisian Option' and `Delayed Barrier Option'. Take a stopping time asthe caution time. When occurs, derivatives are given `Caution'. After, if K.O. time =() occurs, derivative contractsvanish. We simply say that first `Caution' second `K.O.'. Using thisframework, designs of barrier options become more flexible than before and newrisk management will be possible. New barrier options in this category arecalled Edokko Options or Tokyo Options.     

Relative arbitrage in volatility-stabilized markets

Summary. We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets. These criteria postulate essentially that the excess growth rate of the market portfolio, a positive quantity that can be estimated or even computed from a given market structure, be sufficiently large. We show that conditions which satisfy these criteria are manifestly present in the U.S. equity market. We then construct examples of abstract markets in which the criteria hold. These abstract markets allow us to isolate conditions similar to those prevalent in actual markets, and to construct explicit portfolios under these conditions. We study in some detail a specific example of an abstract market which is volatility-stabilized, in that the return from the market portfolio has constant drift and variance rates while the smallest stocks are assigned the largest volatilities. A rather interesting probabilistic structure emerges, in which time changes and the asymptotic theory for planar Brownian motion play crucial roles. The largest stock and the overall market grow at the same, constant rate, though individual stocks fluctuate widely.We are indebted to Adrian Banner and Constantinos Kardaras for several helpful discussions; in particular, the computation of (4.27) is due to Adrian Banner. We are also grateful to Professors Chris Rogers and Marc Yor for their expert advice on the subject of planar Brownian motion, and to Professor Peter Bank for an observation that helped us correct an error in an earlier version of the paper.This revised version was published online in January 2005 with corrections to the Cover date.     

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.     

Redistributive Taxation in the Era of Globalization

This paper analyzes the impact globalization has on voting for redistributive policies in an increasingly integrated world. It explains why tax competition has so far not led to a significant decline in redistributive taxation. The voting process is considered for the two alternatives of direct democracy and representative democracy. In both regimes, globalization pushes down the scope for redistribution, but this effect is mitigated with political representation, since the electorate votes strategically for a slightly more left-wing politician with stronger preferences for redistribution. Moreover, voting polarizes twice, with respect to governments' preferences for redistribution and to equilibrium tax rates.     

Income Redistribution with Well-Informed Local Governments

This paper examines the problem of redistributing incomeacross jurisdictions and to mobile workers within jurisdictionswhen local governments have better information than the centralgovernment about local production conditions. Under the centralgovernments optimal policy, the subsidies or taxes that localgovernments provide to mobile workers normally depend on whetherthese governments are net recipients or net donors of interjurisdictionalincome transfers. Moreover, the public-input decisions of somelocal governments are distorted. The analysis demonstrates thatit may not be desirable to harmonize social policies across jurisdictions,even when the beneficiaries are quite mobile.     

Bid-ask bounce and speads in the foreign exchange futures market

This paper examines the intraday bid-ask bounce in Deutschemark and Japanese yen futures prices. The intraday Markovian bid-ask bounce process, which leads to a desirable equilibrium condition of reaching a bid or an ask transaction type with equal chances, is identified. A second-order Markov chain transition matrix model is used to derive a generalized estimator of bid-ask spreads in the foreign exchange futures market. It incorporates the conditional probabilities of a subsequent transaction being the same type as the current transaction's () and that of the next transaction being the same as the current type but different from the previous type (). The specification is {-Cov(P _t ,P _t+1 )/[(1–)(–)]}^1/2. The empirical results show that the average implied bid-ask spread is about $10, which is less than one tick's value of $12.50. It is also found that spreads are higher at the beginning and end of the trading day than the rest of the day, reflecting the uncertainty due to information flows and overnight inventory carrying costs, respectively.     

The Effect of Mortgage Price and Default Risk on Mortgage Spreads

Variations over time in mortgage yield spreads should reflect changes in the underlying prepayment option value; moreover, the relationship between mortgage yield spreads and interest rate dynamics should weaken as the value of the borrowers prepayment option declines. We verify this hypothesis through an empirical analysis of residential mortgage yield spread behavior, and we also present evidence that the strength of the relationship between mortgage spreads and interest rate dynamics weakens (strengthens) as the level of default risk increases (decreases). This result is consistent with the competing risks effect between a borrowers option to prepay or default. Our results demonstrate the importance of accounting for mortgage price discount to par as well as default risk when developing time series of mortgage yields.