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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.