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.     

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.     

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.     

“Investor sentiment” and the closed-end fund puzzle: A 7 percent solution

Lee, Shleifer, and Thaler (1991) argue that the irrational noise trader model of DeLong, Shleifer, Summers, and Waldmann (1990) ... is consistent with the published evidence on closed-end fund prices. ... However, Lee, Shleifer, and Thaler provide no indication of how much of the variability of a closed-end fund's discounts and premiums is due to such investor sentiment. Using the signal extraction technique of French and Roll (1986) to measure noise, this article estimates that on average only 7 percent of the variance of a standardized measure of weekly changes in discounts and premiums can be attributed to noise-trading activity. Investor sentiment, therefore, seems to account for very little of a closed-end fund's discount and premium variability over time.     

Optimal Consumption Taxes and Social Security Under Tax Measurement Problems and Uncertainty

A representative individual lives for two periods; works when young and depends on savings and a government operated social security system when old—the returns on both sources of income, when old, are random. Due to administrative problems the returns to savings are observed with some measurement error. Two alternative consumption tax systems are considered; the Registered Asset Treatment (RAT) and the Non-Registered Asset Treatment (NRAT). The advantage of the RAT is that it can perform a social insurance role while the disadvantage is that it imposes measurement error risk. Correlation between the random return on saving and its measurement error can provide a risk-hedging role that can be further strengthened by the RAT version. The NRAT version neither provides social insurance nor imposes measurement error risk. Both tax systems hedge against the uncertainties in the social security system. The taxpayer engages in precautionary saving in response to future uncertainty.     

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.     

A General Theorem on the Comparative Statics of Changes in Risk

In this paper, the concept of absolutely riskier than is introduced to generalize Gollier's (Journal of Economic Theory, 66, 522–535) necessary and sufficient conditions for the comparative statics of a change in risk for risk averters. The restrictive assumption that the payoff function is monotonic in the risk is relaxed. The policymaker's choice problem, the newsboy problem, and a farmer's example are used to illustrate how easily the monotonicity assumption is violated. Finally, some important properties of the concept of absolutely riskier than, such as its relation with the concept of second-order stochastic dominance, are illustrated using the farmer's example.     

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.     

Time series models of mortgage choice: Evidence of lender influence

Unit root, co-integration, and Granger Causality are used to test specification of a generalized time series model of mortgage choice. Unit root tests determine that both the fixed-adjustable spread (FAsp) and the proportion of ARM originations (AP) are first difference stationary. The cointegrating vector between FAsp and AP was found to be weak, raising questions regarding their long-term relationship. Causality tests determined that ARM originations Granger causes the fixed-adjustable mortgage spread (APFAsp) rather than FAspAP. This result suggests that mortgage originators adjust the current FAsp spread based on last periods allocation. The coefficient vector for this specification was unstable and became increasingly negative during the 1980s.     

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.     

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.     

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.     

Dual VATs and Cross-Border Trade: Two Problems, One Solution?

In recent years, two distinct but related questions have been raised with respect to value-added taxes (VATs). Concern has been expressed over whether it is desirable or even possible for both national and subnational governments in federal countries such as India, Argentina, and Russia to impose VATs. One reason for thinking that such subnational VATs are unlikely to be workable on a destination basis is the problem of cross-border trade. Of course, this same problem also arises within the European Union, where there is no EU VAT. Drawing upon Canadian experience, we argue that not only is it possible to have two-tier or dual VATs on a destination basis in a single country but that the existence of dual VATs may help deal with some of the problems of cross-border trade.     

The Information Content of Bank Examinations

We identify three types of information from bank examinations—auditing information from verifying the honesty and accuracy of the bank's books, regulatory discipline information about the treatment of the bank by regulators, and private information about bank condition. We estimate these information effects by comparing the cumulative abnormal market returns associated with examinations in which the CAMEL rating remained unchanged, improved, and worsened. All three information effects are found to be greater for banks entering the examination process with unsatisfactory ratings from prior examinations. The only consistently strong effect found is that examination downgrades appear to reveal unfavorable private information about bank condition. The evidence also suggests that the information may reach the market in part through loan quality data released in quarterly financial statements.     

Performance Evaluation and Corporate Income Taxes in a Sequential Delegation Setting

We consider a setting where a firm delegates an investment decision and, subsequently, a sales decision to a privately informed manager. For both decisions corporate income taxes have real effects. We show that compensating the manager based on pre-tax residual income can ensure after-tax NPV-maximization (goal congruence) for each decision problem in isolation. However, this metric fails if both decisions are nontrivial, since it requires asset-specific hurdle rates and hence precludes asset aggregation. After-tax residual income metrics (e.g., EVA) allow the firm to consistently apply its after-tax cost of capital as the hurdle rate to its aggregate asset base. We show that existing tax depreciation schedules may explain why firms in practice use more accelerated depreciation schedules than those suggested by previous studies. Our findings also rationalize the widespread use of dirty surplus accounting for windfall gains and losses for managerial retention purposes.     

Corporate Real Estate and Stock Market Performance

An interesting question in corporate real estate literature is whether real estate can improve the stock market performance of property-intensive non-real estate firms. Using a data set comprising 75 non-real estate corporations that own at least 20 percent properties, this paper empirically assesses and compares the pair-wise return, total risk, systematic risk and Jensen abnormal return performance of composite (with real estate) and hypothetical business (without real estate) firms. We employed Morgan Stanley Capital International world equity index instead of a local market index to provide some insights into the performance of the local market relative to the global market during the 1997–2001 volatile periods experienced by many Asian countries. Our results suggest the inclusion of real estate in a corporate portfolio appears to be associated with lower return, higher total risk, higher systematic risk and poorer abnormal return performance. It is therefore likely that non-real estate firms own properties for other reasons in addition to seeking improvement in their stock market performance. Further research is needed to explore the main factors contributing to corporate real estate ownership by non-real estate firms.     

Do Market Makers Suffer from Splitting Headaches?

Studies of transactions surrounding stock split ex-dates often conclude that splitting firms either experience a decline or an improvement in their stock's liquidity, based on independent measures of trading costs and trading activity. In contrast, our evidence suggests that splits from outside into what often is deemed to be the optimal stock price range of $10.00 to $39.99 are nonevents for market makers: The spread-setting behavior of the market does not change after a split. Our analysis accounts for the interdependencies between bid-ask spreads and market microstructure effects and distinguishes between optimal and all other splitting firms.     

Failed delivery and daily Treasury bill returns

If the seller of a Treasury bill does not provide timely and correct delivery instructions to the clearing bank, the bank does not deliver the security. Furthermore, the seller is not paid until this failed delivery is rectified. Since the purchase price is not changed, these fails generate interest-free loans from the seller to the buyer. This article studies the effect of failed delivery on Treasury bill prices. We find that investors bid prices to a premium to reflect the possibility of obtaining the interest-free loans that fails represent. This premium is a function of the opportunity cost of the fail. We also find that the bid-ask spread varies directly with the length of the fail. We rule out that our results are due to liquidity premiums, or to a general weekly pattern in short-term interest rates or the bid-ask spread.     

Contracts for the sale of residential real estate

I propose a model where the terms of a real estate broker's contract influence both the broker's and theseller's choices. Given equal contract, higher quality, and thus higher priced on average, houses will sell in less time. Thus, simple conditions suffice to show that a competitively set commission rate should fall as the average price rises and, since a seller's cost of waiting are higher for higher quality houses, a cartel's commission rate should rise with the average price. Because this model studies the effects of alternate contracts on observable variables such as the price of a house and its time-till-sale, its implications are testable.