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Papers marked with * are available on-line from main List of RPF Publications. Most papers are available in Acrobat .pdf format and require Acrobat Reader. Requests for recent papers are free to students and academics (limit of 5). There is a working paper fee of $5.00 (USA) or $7.50 (international) for businesses, corporations, and non-academic institutions. Checks should be payable to "Regents of University of California." Order Forms (Acrobat .pdf or Word.doc) available.

RPF-295 "On Adaptive Tail Index Estimation for Financial Return Models."

Niklas Wagner and Terry Marsh. November 2000.

Abstract: Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator's performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.

RPF-294 "Rational Markets: Yes or No? The Affirmative Case."

Mark Rubinstein . June 2000.

Abstract: This paper presents the logic behind the increasingly neglected proposition that prices set in developed financial markets are determined as if all investors are rational. It contends that realistically, market rationality needs to be defined so as to allow investors to be uncertain about the characteristics of other investors in the market. It also argues that investor irrationality, to the extent it affects prices, is particularly likely to be manifest through overconfidence, which in turn is likely to make the market in an important sense too efficient, rather than less efficient, in reflecting information. To illustrate, the paper ends by re-examining some of the most serious evidence against market rationality: excess volatility, the risk premium puzzle, the size anomaly, calendar effects and the 1987 stock market crash.

RPF-293 "Return-Volume Dependence and Extremes in International Equity Markets."

Terry A. Marsh Niklas Wagner. May 2000.

Abstract: This paper is an empirical study of the price-volume dependence in seven international equity markets. We fit a GARCH-M model to examine the overall return-volume relation under "normal" market conditions and a bivariate extreme value model to examine the relation under conditions of market stress. Using a pre-filtered stationary volume variable for each market, we find that: (i) volume explains a substantial amount of conditional return variance in most markets, and indeed for the U.S., GARCH effects are completely subsumed by the volume variable; (ii) above-average volume explains variation in conditional variance better than the entire set of volume observations; (iii) conditioning market return variance on volume provides a risk measure that is associated with a positive premium; (iv) for all markets but the U.S., negative return innovations relate to a larger increase in conditional return variance than positive return innovations; (v) the return variability-volume dependence is weaker, albeit mostly significant, in the tails -- i.e. for extremal return and volume observations -- where (vi) the dependence decreases for large extremal return and volume observations. We argue that our results are more consistent with a Genotte and Leland (1990) misinterpretation hypothesis for market crashes than with cascade or behavioral explanations which associate high volume with steep price declines.

RPF-292 "On the Relation Between Binomial and Trinomial Option Pricing Models."

Mark Rubinstein . May 2000.

Abstract: This paper shows that the binomial option pricing model, suitably parameterized, is a special case of the explicit finite difference method.

RPF-291 "Corporate Diversification and Agency." Benjamin E. Hermalin and and Michael L. Katz.

Abstract: Firms undertake a variety of actions to reduce risk through diversification, including entering diverse lines of business, taking on project partners, and maintaining portfolios of risky projects such as R&D or natural resource exploration. By a well-known argument, securities holders do not directly benefit from risk-reducing corporate diversification when they can replicate this diversification on their own. Moreover, shareholders should be risk neutral with respect to the unsystematic risk that is associated with many research projects. Some have argued that corporate risk reduction may be of value, or can otherwise be explained by, the agency relationship between securities holders and managers. We argue that the value of diversification strategies in an agency relationship derives not from its effects on risk, but rather from its effects on the principal's information about the agent's actions. We demonstrate by example that diversification activities may increase or decrease the principal's information, depending on the particular structure of the activity.

RPF290. * "Optimal Portfolio Management with Transactions Costs and Capital Gains Taxes." Hayne E. Leland. December 1999.

Abstract: We examine the optimal trading strategy for an investment fund which in the absence of transactions costs would like to maintain assets in exogenously fixed proportions, e.g. 60/30/10 in stocks, bonds and cash. Transactions costs are assumed to be proportional, but may differ with buying and selling, and may include a (positive) capital gains tax component.

We show that the optimal policy involves a no-trade region about the target stock proportions. As long as the actual proportions remain inside this region, no trading should occur. When proportions are outside the region, trading should be undertaken to move the ratio to the region's boundary. We compute the optimal multi-asset no-trade region and resulting annual turnover and tracking error of the optimal strategy. Almost surely, the strategy will require trading just one risky asset at any moment, although which asset is traded varies stochastically through time. Compared to the current practice of periodic rebalancing of all assets to their target proportions, the optimal strategy will reduce turnover by almost 50%.

The optimal response to a capital gains tax is to allow proportions to substantially exceed their target levels before selling. When an asset's proportion exceeds a critical level, selling should occur to bring it back to that critical level. Capital gains taxes lead to lower optimal initial investment levels. Similarly, it is optimal to invest less initially in asset classes that have high transactions costs, such as emerging markets.

RPF-289* "Credit Derivatives in Banking: Useful Tools for Managing Risk?" Gregory R. Duffee and Chunsheng Zhou. November 1999.

Abstract: We model the effects on banks of the introduction of a market for credit derivatives; in particular, credit-default swaps. A bank can use such swaps to temporarily transfer credit risks of their loans to others, reducing the likelihood that defaulting loans trigger the bank's financial distress. Because credit derivatives are more flexible at transferring risks than are other, more established tools such as loan sales without recourse, these instruments make it easier for banks to circumvent the "lemons" problem caused by banks' superior information about the credit quality of their loans. However, we find that the introduction of a credit-derivatives market is not necessarily desirable because it can cause other markets for loan risk-sharing to break down.

RPF-288* "Order Flow and Exchange Rate Dynamics" Martin D. D. Evans and Richard K. Lyons, August 1999.

Abstract: Macroeconomic models of nominal exchange rates perform poorly. In sample, R 2 statistics as high as 10 percent are rare. Out of sample, these models are typically out-forecast by a naïve random walk. This paper presents a model of a new kind. Instead of relying exclusively on macroeconomic determinants, the model includes a determinant from the field of microstructure-order flow. Order flow is the proximate determinant of price in all microstructure models. This is a radically different approach to exchange rate determination. It is also strikingly successful in accounting for realized rates. Our model of daily exchange-rate changes produces R 2 statistics above 50 percent. Out of sample, our model produces significantly better short-horizon forecasts than a random walk. For the DM/$ spot market as a whole, we find that $1 billion of net dollar purchases increases the DM price of a dollar by about 1 pfennig.

RPF-287.* "The Role of a Corporate Bond Market in an Economy - and in Avoiding Crises." Nils H. Hakansson, June 1999.

Abstract: While much attention has been focused on the optimal ratio of a firm's debt to equity, the "optimal" or best balance between bond financing and (longer-term) bank financing has scarcely been addressed. This essay examines the principal differences between an economy with a well-developed corporate bond market free from government interference and an economy in which bank financing plays a central role (as in East Asia). When a full-fledged corporate bond market is present, market forces have a much greater opportunity to assert themselves, thereby reducing systemic risk and the probability of a crisis. This is because such an environment is associated with greater accounting transparency, a large community of financial analysts, respected rating agencies, a wide range of corporate debt securities and derivatives demanding sophisticated credit analysis, and efficient procedures for corporate reorganization and liquidation. In addition, the richness of available securities will tend to enhance economic welfare, and the market forces at work on the wide array of bond prices are likely to have a strong spillover effect on the health of the banking system as well

RPF-286.* "Housing Return and Construction Cycles." Matthew Spiegel. January 1999.

Abstract: This paper presents a model that derives both housing returns and housing construction patterns from events in the real economy. The value of a home, unlike the value of many other financial assets, depends upon the care its owner exerts on upkeep. Within the model banks respond to this moral hazard problem by restricting the size of the loans they are willing to issue. As a result housing prices no longer follow a random walk, but rather are tied to changes in the endowment process which are both predictable and time varying. That is, in some states of nature homeowners expect to earn an above market return on their housing purchase while in others they expect to earn a below market return. evelopers in the model are fully cognizant of the housing price process and react accordingly. The result is a construction cycle that seems at odds with conventional wisdom. When endowments are growing quickly (a city with a rapidly growing economy) housing prices exhibit above market expected returns. However, since housing prices are expected to increase faster than the rate of interest, developers delay construction. Thus, during periods of rapid expected economic growth housing construction ceases until one reaches the crest whereupon development booms. In response housing supplies dwindle during economic booms (as homes deteriorate) and then increase when the boom ends.

RPF-285.* "Search Costs: The Neglected Spread Component."

Mark D. Flood, Ronald Huisman, Kees G. Koedijk, and Richard Lyons. October 1998.

Abstract: Dealers need to search for quotes in many of the world's largest markets (such as spot foreign exchange, US government bonds, and the London Stock Exchange). This search affects trading cost. We estimate the share of total trading cost attributable to search. Our experiments show that the share is large -- roughly one-third of the effective spread. Past work on estimating spread components typically omits the search component. Our estimates suggest this omission is important.

RPF-284.* "Valuation and Return Dynamics of New Ventures."

Jonathan B. Berk, Richard C. Green and Vasant Naik. September 1998.

Abstract: We develop and analyze a model of a multi-stage investment project that captures many features of R&D; ventures and start-up companies. An important feature these problems share is that the firm learns about the potential profitability of the project throughout its life, but that "technical uncertainty" about the research and development effort itself is only resolved through additional investment by the firm. In addition, the risks associated with the ultimate cash flows the firm realizes on completion of the project have a systematic component, while the purely technical risks are idiosyncratic. Our model captures these different sources of risk, and allows us to study their interaction in determining the risk premia earned by the venture during development. Our results show that the systematic risk, and the required risk premium, of the venture are highest early in its life, and decrease as it approaches completion, despite the idiosyncratic nature of the technical risk.

RPF-283.* "Predicting Excess Returns with Public and Insider Information: The Case of Thrift Conversions."

James A. Wilcox and Zane D. Williams. September 1998.

Abstract: We hypothesize that mutual thrifts often converted to stock ownership when the returns to conversion were predicted to be high. We show that excess returns on the initial public offerings (IPOs) of thrift conversions during the 1990s were predictable with publicly available data. The same conditions that predicted higher excess returns on thrift conversions also predicted that conversion was more likely. Higher predicted excess returns significantly raised the amounts of the IPOs that insiders at converting thrifts purchased. Data for insider purchases, which were publicly available before the first day of trading, further helped the public predict excess returns.

RPF-282. "The "Credit Crunch" and the Availability of Credit to Small Business"

Diana Hancock and James A. Wilcox. August 1998.

Abstract: We present estimates of how much bank loans and real activity in small businesses responded to changes in banks' capital conditions and other bank and aggregate economic conditions. Using data for 1989 through 1992 by state, we estimated the effects of those factors on employment, payrolls, and the number of firms by firm size, as well as on gross state product. In response to declines in their own bank capital, small banks shrank their loan portfolios considerably more than large banks did. Large banks tended to increase loans more when small banks were under increased capital pressure. Real economic activity was reduced more by capital declines and by loan declines at small banks than at large banks. Small banks were making "high-powered loans" in that dollar-for-dollar loan declines in their loans had larger impacts on economic activity than loan declines at large banks did. Capital declines at small banks produced larger changes in economic activity dollar-for-dollar than capital declines at large banks did. Aggregate economic conditions had smaller effects on small firms than on large firms and smaller effects on small banks than on large banks. The evidence hinted that the volume of loans made under Small Business Administration (SBA) loan guarantee programs shrank less in response to declines in bank capital than the volume of loans not made under the SBA loan guarantee programs.

RPF-281. "Dynamic Optimal Risk Management and Dividend Policy under Optimal Capital Structure and Maturity."

Michael P. Ross. July 1998.

Abstract: This paper examines the interaction between a firm's volatility and dividend policies and capital structure and maturity policies. The firm is permitted to costlessly and continuously select any asset volatility and dividend yield, within bounds. Simple and intuitive rules are derived for the firm's optimal dividend and volatility choices. It is found that the firm always optimally selects either the maximal or minimal dividend yield and asset volatility and that these decisions depend, respectively, only upon the delta and gamma of the firm's equity. These optimal dividend and volatility policies are then implemented within the context of the Leland and Toft (1996) capital structure model. It is found that firms will optimally select a low dividend yield and a low asset volatility over a greater range of firm asset values the shorter is the maturity of the firm's debt. Anticipating this behavior, bondholders will demand a smaller credit spread for short-term debt when the firm has great leeway in choosing its asset volatility. In turn, this may induce a firm to optimally issue short-term debt. It is also found that the better is a firm's ability to hedge, the more frequently it will refrain from paying dividends. This confirms the well-known result that risk management mitigates incentives for underinvestment. Here it is shown to apply ex-post as well as ex-ante.

RPF-280. "Corporate Hedging: What, Why and How?"

Michael P. Ross. July 1998.

Abstract: This paper explores the rationale for corporate risk management. Following Smith and Stulz (1985) and Mayers and Smith (1987), the assumption is made that firms can contractually commit to bondholders to maintain a particular risk management policy, or asset volatility. With that as a starting point, the essay derives the optimal hedge portfolio, examines this portfolio's robustness to variance-covariance misestimation, and proposes a new motive for corporate risk management; a firm that hedges its risk increases its optimal amount of debt and so realizes more tax benefits from leverage. Using the capital structure model of Leland (1994), three impacts of risk-reduction on shareholder value are measured: the increase in tax benefits, the reduction of bankruptcy costs and the reduction in the potential cost of the underinvestment problem. The essay's motivation is to serve as a guide to chief financial officers regarding the benefits of risk management and the sources of those benefits, so that risk management can be undertaken in a way that enhances shareholder value, rather than for its own sake.

RPF-279. "Pricing Derivatives the Martingale Way."

Pierre Collin Dufresne, William Keirstead and Michael P. Ross. July 1998.

Abstract: In recent years results from the theory of martingales has been successfully applied to problems in financial economics. In the present paper we show how efficient and elegant this "martingale technology" can be when solving for complex options. In particular we provide closed form solutions for several new classes of exotic options including the cliquet, the ladder, the discrete shout and the discrete lookback. We also provide a derivation of the price of an option on the maximum of n assets to demonstrate the power of the multi-dimensional Girsanov theorem. Although some of the results presented are well known, the treatment of the material in this paper is new in that it focuses on the application of the martingale technology to concrete problems in option pricing, methods that until now have mostly been used for purely theoretical purposes.

RPF-278 "Agency Costs, Risk Management, and Capital Structure" (text only .dvi)

Hayne E. Leland

Abstract: The joint determination of capital structure and investment risk is examined. Optimal capital structure reflects both the tax advantages of debt less default costs (Modigliani-Miller), and the agency costs resulting from asset substitution (Jensen-Meckling). Agency costs restrict leverage and debt maturity and increase yield spreads, but their importance is relatively small for the range of environments considered. Risk management is also examined. Hedging permits greater leverage. Even when a firm cannot precommit to hedging, it will still do so. Surprisingly, hedging benefits often are greater when agency costs are low.

RPF-277* "Applying the Grinblatt-Titman and the Conditional (Ferson-Schadt) Performance Measures: The Case of Industry Rotation Via the Dynamic Investment Model"

Robert R. Grauer and Nils H. Hakansson

Abstract: This paper applies Grinblatt and Titman's portfolio change measure and Ferson and Schadt's conditional performance measure to the problem of assessing the performance of the dynamic investment model applied to industry rotation over the period 1934-1995 as well as various sub-periods. The dynamic investment model used in the study employs the empirical probability assessment approach with a rear-view moving window, both in raw form and with adjustments for estimation error based on a James-Stein, a Bayes-Stein, and a CAPM-based correction. Both tests are unanimous in their conclusion that the excess returns attained by the (unadjusted) historic,, the Bayes-Stein, and the James-Stein estimators are (sometimes highly) statistically significant over the 1966-95 and 1966-81 sub-periods. This lends support to the idea that the joint empirical probability assessment approach based on the recent past, with and without Stein-based corrections for estimation error, contains information that can be profitably exploited.

RPF-276.* "Closed-End Fund Discounts in a Rational Agent Economy."

Matthew Spiegel. December 1997.

Nearly any standard financial model concludes that two assets with identical cash flows must sell for the same price. Alas, closed-end mutual fund company share prices seem to violate this fundamental tenant. Even when one considers several standard frictions, such as taxes and agency costs, classical financial models cannot explain the large persistent discounts found within the data. While the standard financial markets model may not explain the existence of large closed-end fund discounts, this paper shows that a rather close version of it does. In an otherwise frictionless market, if asset supplies vary randomly over time and agents possess finite lives, a closed-end mutual fund's stock price may not track its net asset value. Furthermore, the analysis provides a number of conditions under which these discrepancies will lead to the existence of systematic discounts for the mutual fund's shares. In addition, the model provides predictions regarding the correlation between current closed-end fund discounts and current changes in stock prices and future changes in corporate productivity. As the analysis shows, the same parameter values that lead to systematic discounts also lead to other fund price characteristics that resemble many of the results found within empirical studies.

RPF-275* "Edgeworth Binomial Trees"

Mark Rubinstein. November 1997.

Available in PowerPoint .pps format only. Use Notes View.

This paper develops a simple technique for valuing European and American derivatives with underlying asset risk-neutral returns which depart from lognormal in terms of prespecified non-zero skewness and greater-than-three kurtosis. Instead of specifying the entire risk-neutral distribution by the riskless return and volatility (as in the Black-Scholes case), this distribution is specified by its third and fourth central moments as well. An Edgeworth expansion is used to transform a standard binomial density into a unimodal standardized discrete density -- evaluated at equally-spaced points -- with approximately the prespecified skewness and kurtosis. This density is in turn adjusted to have a mean equal to the riskless return (adjusted for the payout return, if any) and to a prespecified volatility. European derivatives are then easily valued by using this risk-neutral density to weight their possible payoffs.

European options with earlier maturities, American and exotic options can be valued in a consistent manner by using the method of implied binomial trees. These trees are particularly well-suited for this since they are generated from arbitrary discrete expiration-date risk-neutral probabilities -- precisely what is provided by the Edgeworth expansion.

The paper ends by translating several examples of alternative risk-neutral distributions into option prices and then into Black-Scholes implied volatility smiles. Implied trees are used to determine smiles for otherwise identical shorter-maturing options and future smiles for the original options conditional on knowing the future underlying asset price.

RPF-274-Rev* "Derivatives Performance Attribution."

Mark Rubinstein. Revised May 1998.

Downloadable in PowerPoint .pps format only. Use Notes View.

Abstract: This paper shows how to decompose the dollar profit earned from an option into two basic components: 1) mispricing of the option relative to the asset at the time of purchase, and 2) profit from subsequent fortuitous changes or mispricing of the underlying asset. This separation hinges on measuring the "true relative value" of the option from its realized payoff. The payoff from any one option has a huge standard error about this value which can be reduced by averaging the payoff from several independent option positions. It appears from simulations that 95% reductions in standard errors can be further achieved by using the payoff of a dynamic replicating portfolio as a Monte Carlo control variate. In addition, it is shown that these low standard errors are robust to discrete rather than continuous dynamic replication and to the likely degree of misspecification of the benchmark formula used to implement the replication.

The first basic component, the option mispricing profit, can be further decomposed into profit due to superior estimation of the volatility (volatility profit) and profit from using a superior option valuation formula (formula profit). In order to make this decomposition reliably, the benchmark formula used for the attribution needs to be similar to the formula implicitly used by the market to price options. If so, then simulation indicates that this further decomposition can be achieved with low standard errors.

The second basic component can be further decomposed into profit from a forward contract on the underlying asset (asset profit) and what I term pure option profit. The asset profit indicates whether or not the investor was skillful by buying or selling options on mispriced underlying assets. However, asset profit could also simply be just compensation for bearing risk -- a distinction beyond the scope of this paper. Although simulation indicates that the attribution procedure gives an unbiased allocation of the option profit to this source, its standard error is large -- a feature common with attempts by others to measure performance of assets.

RPF-273 "Profits and Position Control: A Week of FX Dealing."

Richard K. Lyons. October 1997.

(available as Word/Windows document only)

This paper examines foreign exchange trading at the dealer level. The dealer we track averages $100,000 in profits per day on volume of $1 billion per day (or one basis point). The half-life of the dealer's position is only ten minutes, providing strong support for inventory models. A methodological innovation allows us to identify his speculative position over time. This speculative position determines the share of profits deriving from speculation versus intermediation: intermediation is much more important.

RPF-272* "Bank Risk Management: Theory."

David H. Pyle. July 1997.

(available as Word/Windows document only)

This paper discusses why risk management is needed. It outlines some of the theoretical underpinnings of contemporary bank risk management, with an emphasis on market and credit risks.

RPF-271 "International Portfolio Investment Flows."

Michael J. Brennan. and H. Henry Cao. February 1997.

This paper develops a model of international equity portfolio investment flows based on differences in informational endowments between foreign and domestic investors. It is shown that when domestic investors possess a cumulative informati on advantage over foreign investors about their domestic market, investors tend to purchase foreign assets in periods when the return on foreign assets is high and to sell when the return is low. The implications of the model are tested using data on US equity portfolio flows.

RPF-270* "Is There Private Information in the FX Market? The Tokyo Experiment."

Takatoshi Ito. and Richard K. Lyons and Michael T. Melvin. January 1997.

It is a common view that private information in the foreign exchange market does not exist. We provide evidence against this view. The evidence comes from the introduction of trading in Tokyo over the lunch-hour. Lunch return variance do ubles with the introduction of trading, which cannot be due to public information since the flow of public information did not change with the trading rules. Having eliminated public information as the cause, we exploit the volatility pattern over the wh ole day to discriminate between the two alternatives: private information and pricing errors. Three key results support the predictions of private-information models. First, the volatility U-shape flattens: greater revelation over lunch leaves a smaller share for the morning and afternoon. Second, the U-shape tilts upward, an implication of information whose private value is transitory. Finally, the morning exhibits a clear U-shape when Tokyo closes over lunch, and it disappears when trading is introd uced.

RPF-269* "Are Investors Reluctant to Realize Their Losses?"

Terrance Odean. November 1996.

IAbstract: test the disposition effect, the tendency of investors to hold losing investments too long and sell winning investments too soon, by analyzing trading records for 10,000 accounts at a large discount brokerage house. These investors demonstrate a strong preference for realizing winners rather than losers. Their behavior does not appear to be motivated by a desire to rebalance portfolios, or to avoid the higher trading costs of low price stocks. Nor is it justified by subsequent portfolio performance. For taxable investments it is non-optimal and leads to lower after-tax returns. Tax-motivated selling is most evident in December.

RPF-268* "A Theory of Corporate Capital Structure and Investment."

Miguel Cantillo Simon

Abstract: This article describes how financial disruptions affect investment in a general equilibrium economy. I show that in a world with differentiated lenders, the most efficient will become financial intermediaries; their preeminence will nonetheless be limited by frictions with depositors. Because of these frictions, cash rich companies prefer to tap the bond market directly, while moderately endowed firms borrow from intermediaries, and cash poor companies are unable to borrow at all. The aggregation of this model produces an economy with intuitive features: investment falls whenever the risk free rate rises, or when the financial health of firms and intermediaries deteriorates.

RPF-267 "Options and Expectations"

Hayne E. Leland

Who should buy options (ordinary or "exotic"), and who should sell? Buyers and sellers must differ from the average investor, who will not undertake options positions. We develop a simple binomial model to characterize the expectations (relative to the average or consensus) which must be held by investors to justify buying or selling various types of derivatives, or following dynamic strategies which generate similar payoffs. European option sellers must believe markets are more mean-reverting than average; option buyers must believe they are more mean-averting. The probabilities of ordinary option buyers and sellers are path independent and their expected return process must be a martingale. Path-dependent options or dynamic strategies imply probabilities which are path dependent. "Asian" derivative purchasers must believe the expected return to the underlying asset decreases through time. Lookback purchasers believe the opposite.

RPF-266* "Volume, Volatility, Price and Profit When All Traders Are Above Average"

Terrance Odean

This paper looks at three market models in which investors are rational in all respects except that they are overconfident about the precision of their private information. A substantial literature in cognitive psychology establishes that people usually are overconfident and, specifically, that they are overconfident about the precision of their knowledge. Overconfidence affects expected trading volume, volatility of prices, market depth, price quality, expected profits, and expected utility. The three models demonstrate how the effects of overconfidence depend on who is overconfident. The paper also examines the consequences for markets when traders systematically underweight their prior information.

RPF-265* "Recovering Risk Aversion from Option Prices and Realized Returns"

Jens Carsten Jackwerth

A well-known relationship exists between aggregate subjective and risk-neutral probability distributions and utility functions. Previously, only subjective probabilities could be estimated with some degree of accuracy from historical data. Now, using the convenient method developed by Jackwerth and Rubinstein (1996), we can also estimate risk-neutral probabilities reliably. For the first time, we empirically derive stable utility functions implied by stock returns and option prices. These implied utility functions dramatically change shapes around the 1987 crash and t hereafter exhibit convexity and increasing risk aversion across parts of the wealth dimension. A simulated trading strategy based on analyzing the utility functions mean-variance dominates holding the market.

RPF-264* "Generalized Binomial Trees"

Jens Carsten Jackwerth

In a novel approach, standard and implied binomial trees are completely specified in terms of two basic inputs: the ending nodal probability distribution and a linear weight function which governs the stochastic process resulting in that distribution. Several key economic principles, such as no interior arbitrage, are intuitively related to these basic inputs. A simple and computationally efficient three-step algorithm, common to all binomial trees, is found. Noting that the currently used linear weight function is unnecessarily restrictive, a binomial tree even more versatile is introduced, the generalized binomial tree. Applications to recovering the stochastic process implied in (European, American, or exotic) options of several times-to-expiration are developed.

RPF-263-rev.* "Beyond Mean-Variance: Performance Measurement of Portfolios Using Options or Dynamic Strategies."

Hayne E. Leland

Current investment performance analysis is based on the CAPM, using "alpha" or Sharpe Ratios. But the validity of this analysis rests on the validity of the CAPM, which assumes either normally distributed returns, or mean-variance preferences. Either assumption is suspect: even if asset returns were normally distributed, the returns of options or dynamic strategies (including market timing) would not be. And investors distinguish upside from downside risks, implying skewness preference. We consider a Black-Scholes/Merton world, in which the market portfolio follows a diffusion process with constant drift and volatility. In this world, the market portfolio is mean-variance inefficient and the CAPM alpha will systematically mismeasure the value added by investment managers. The problem is particularly severe for portfolios using options or dynamic strategies. We show how a simple modification of the CAPM beta can lead to correct risk measurement, and the alphas of all fairly-priced options and/or dynamic strategies will be zero in the Black-Scholes/Merton world.

This paper has been written for the Fischer Black Commemorative Issue of the The Journal of Portfolio Management.

RPF-262.* "Implied Binomial Trees: Generalizations and Empirical Tests."

Jens Carsten Jackwerth

Efficient generalizations for Rubinstein's (1994) implied binomial tree are presented which allow for varying path-probabilities and incorporate information from times other than the end of the tree. The three generalizations involve deformation of the time scale, arbitrary transition probability weights, and jumps. Two empirical tests compare the performance of implied binomial trees, the Black-Scholes model, and the CEV model. In the first test, all models are fitted to observed longer term option prices, used to price shorter term options, and pricing errors are assessed. In a second test, the term structure of at-the-money volatilities is assumed known. All models are adapted to incorporate this information and pricing errors are recomputed.

A postscript version of this paper is available from http://haas.berkeley.edu/~jackwert .

RPF-261* "Optimal Asset Rebalancing in the Presence of Transactions Costs."

Hayne E. Leland. Rev. August 1996.

We examine the optimal trading strategy for an investment fund which wishes to maintain assets two assets in fixed proportions, e.g. 60/40 in stocks and bonds. transactions costs are assumed to be proportional to the amount of each asset traded. We show that the optimal policy involves a band about the target stock proportion. As long as the actual stock/bond ratio remains inside this band, no trading should occur. If the ratio goes outside the band, trading should be undertaken to move the ratio to the nearest edge of the band. We compute the optimal band and resulting annual turnover and tracking error of the optimal policy, as a function of transactions costs, asset volatility, the target asset mix, and other parameters. We show how changes in transactions costs and other parameters affect the size of the no-trade band, turnover, and tracking error. Compared to a quarterly rebalancing strategy, an example demonstrates that the optimal strategy can reduce turnover by almost 50 percent.

RPF-260* "Stock Price Volatility in a Multiple Security Overlapping Generations Model."

Matthew Spiegel.

A number of empirical studies have reached the conclusion that stock price volatility cannot be fully explained within the standard dividend discount model. This paper proposes a resolution based upon a model that contains both a random supply of risky assets and finitely lived agents who trade in a multiple security environment. As the analysis shows where exist 2k equilibria when K securities trade. The low volatility equilibria have properties analogous to those found in the infinitely lived agent models of Campbell and Kyle (1991) and Wang (1993, 1994). In contrast, the high volatility equilibria have very different characteristics. Within the high volatility equilibria very large price variances can be generated with very small supply shocks. Using previously established empirical results the model can reconcile the data with supply shocks that are less than 10% as large as observed dividend shocks. The multiple security analysis also shows that within the economy some securities may trade under high volatility conditions, while others trade in low volatility conditions. Switching the economy from a high to a low volatility equilibrium for any single security may be very difficult. Depending upon the variance-covariance structure of the economy, an equilibrium change may require simultaneous control over the trading environment of every single security in the economy.

RPF -259 "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads."

Hayne E. Leland and Klaus Bjerre Toft

This paper examines the optimal capital structure of a firm which can choose both the amount and maturity of its debt. Bankruptcy is determined endogenously rather than by the imposition of a positive net worth condition or by a cash flow constraint. The results extend Leland's [1994] closed-form results to a much richer class of possible debt structures and permits study of the optimal maturity of debt as well as the optimal amount of debt. The model generates predictions of leverage, credit spreads, default rates, and writedowns which accord quite closely with historical averages. While short term debt does not exploit tax benefits as completely as long term debt, it is more likely to provide incentive compatibility between debtholders and equityholders. The agency costs of "asset substitution" are minimized when the firm uses shorter term debt. The tax advantage of debt must be balanced against bankruptcy and agency costs in determining the optimal maturity of the capital structure. The model predicts differently shaped term structures of credit spreads for different levels of risk. These term structures are similar to that found empirically by Sarig and Warga [1989]. The model has important implications for bond portfolio management. In general, Macaulay duration dramatically overstates true duration of risky debt, which may be negative for "junk" bonds. Furthermore, the "convexity" of bond prices can become "concavity."

RPF-258. "Imperfect Competition in Securities Markets with Diversely Informed Traders."

H. Henry Cao

November 1995

We show that the infinite regression problem in models with differentially informed traders can be solved using a fixed point method which we use to derive the dynamic equilibrium in a multi-auction model with diversely informed traders. We find that when the informed traders' signals are not perfectly correlated, their private information will be revealed to the market gradually so that the market is only semi- strong form efficient and not strong-form efficient. Market depth in the continuous auction model initially increases with time but decreases to zero at the end. Our results are in contrast to the results of Holden and Subrahmanyam (1992) and Foster and Viswanathan (1993) (HS-FV) who showed that when auctions occur frequently and informed traders have perfect information, the information is revealed to the market almost immediately. However, when the correlation in the private signals goes to 1, our model converges to the HS-FV model.

257. "The Efficacy of Insider Trading Regulation."

Matthew Spiegel and Avanidhar Subrahmanyam

October 1995

Regulatory authorities often lack a "smoking gun" (i.e., hard evidence such as a note or a memorandum) when prosecuting individuals for illegal insider trading. As a result, many insider trading cases depend solely on circumstantial evidence, which is usually obtained by associating trades with "unusual" price moves. However, insiders with the most accurate information (the ones most likely to possess "material, non-public" information) are the ones best able to modify their trading strategy in response to prosecution strategies based on price moves. This is a major obstacle to the efficacy of insider trading regulation. Thus, if legislation discourages strategic insiders with relatively precise information from trading, then in all likelihood any investor who is prosecuted will possess only the weakest (most imprecise) information. Stratetgic behavior by insiders in response to insider trading regulations can thereby lead to a situation where the pool of prosecuted traders contains a large fraction of innocent individuals (i.e., individuals with relatively poor information).

RPF-256REV.* "How Do Firms Choose Their Lenders? Theory and Evidence."

Miguel Cantillo and Julian Wright

(October 1995 )Revised February 2000

This article investigates which companies finance themselves through intermediaries and which borrow directly from arm's length investors. Our empirical results show that large companies with abundant cash and collateral tap credit markets directly; these markets cater to safe and profitable industries, and are most active when riskless rates or intermediary earnings are low. We show that determinants of lender selection sharpen during investment downturns and that there are substantial asymmetries in the way firms enter and exit capital markets. These results support a theoretical framework where intermediaries have better reorganizational skills but a higher opportunity cost of capital than bondholders.

255. "A Theory of Corporate Capital Structure and Investment."

Miguel Cantillo

October 1995

This paper develops a costly state verification (CSV) model which describes how financial fluctuations affect real activity in a general equilibrium setting. In an economy with differentiated lenders, the most efficient will become intermediaries (e.g. banks). Intermediation generally creates frictions which prevent banks from dominating the debt markets. In this model, firms with abundant funds avoid intermediaries, and tap the credit markets directly. Meanwhile, firms with moderate resources borrow from intermediaries. The aggregation of this model produces an economy with appealing features: aggregate investment drops with a rise in the riskless rate, and a deterioration of bank or corporate health.

RPF-254*. "The Rise and Fall of Bank Control in the United States: 1890-1920."

Miguel Cantillo

October 1995

This paper sketches the evolution in the governance structures of railroad and industrial firms in the United States between 1850 and 1914. I describe how the largest of these companies became controlled by salaried executives, and with no board member willing to oversee or to veto manager actions. Initially, railroads and industrial firms were tightly controlled by a small number of shareholders. The link of ownership and control was changed by massive corporate restructuring in the 1890s and 1900s. The newly reorganized firms were controlled by banks such as J.P. Morgan, which took board positions to ensure adequate financial returns for themselves and for their clients. The final stage of corporate governance began in the 1910s as a public policy reaction to bank control. This reaction resulted in an almost complete disappearance of active institutional investors from boards of directors. Using stock market data from 1914, I find that this political reaction destroyed about 6 percent of the equity value of bank controlled firms. By the late 1920s, all the elements that define contemporary governance structures in the United States were in place and running their logical course.

RPF-253.* "A Spatial Model of Housing Returns and Neighborhood Substitutability."

William N. Goetzmann and Matthew Spiegel

September 1995

This paper presents a new spatial model for analyzing return indices for infrequently traded assets, and applies it to housing data. Within many asset classes, particularly real estate, one expects there to exist a spatial correlation in deviations from the index due to omitted explanatory variables in the econometric model. This error structure can be useful in estimating location-specific would normally make this impossible, the use of spatial and factor correlations provides sufficient information to estimate zip code level returns. We use these indices to examine the degree to which housing market participants in one major metropolitan statistical area view neighborhoods as substitutes. Using distance defined in terms of geographical proximity, median household income, average educational attainment and racial composition, we find that median household income is the salient variable explaining covariance of neighborhood housing returns. Racial composition and educational attainment, while significant are much less influential and geographical proximity is nearly meaningless. Our methodology has applications to a range of infrequently traded assets, including bonds, commercial real estate and collectibles. The approach may be viewed as an extension of "non-parametric" spatial correlation models. In the non-parametric approach a distance function and decay rate are exogenously specified. In a spatial model one estimates the distance metric and uses statistical rules to obtain the resulting decay rates. The results of our analysis of housing substitutability in the San Francisco Bay area have implications for estimates of the covariance of housing returns within metropolitan areas. In particular, low covariances imply gains to diversification for lenders, equity-holders and tax authorities.

RPF-252.* "Pricing Mortgage-Backed Securities in a Multifactor Interest Rate Environment: A Multivariate Density Estimation Approach."

Jacob Boudoukh, Matthew Richardson, Richard Stanton, and Robert F. Whitelaw

May 1995

This paper develops a nonparametric, model-free approach to the pricing of mortgage-backed securities (MBS), using multivariate density estimation (MDE) procedures to investigate the relation between MBS prices and interest rates. While the usual methods for valuing MBSs are highly dependent on specific assumptions about interest rates and prepayments, this method will yield consistent results without requiring such assumptions. The MDE estimation suggests that weekly MBS prices from January 1987 to May 1994 can be well described as a function of the level and slope of the term structure. We analyze how this functionaries across MBSs with different coupons and investigate the sensitivity of prices to the two factors. As an application, we sue the estimated relation to hedge the interest rate risk of MBSs. These hedging results compare favorably with other commonly used hedging methods.

RPF-251.* "Mortgage Choice: What's the Point?"

Richard Stanton and Nancy Wallace

May 1995

This paper develops a general equilibrium model of mortgage lending, combining self-selection theory with option pricing. We construct a separating equilibrium, in which borrowers offer a menu of prepayable, fixed rate mortgage contracts, differing in their tradeoff between coupon rate and points (prepaid interest). Borrowers select the optimal contract from the menu, revealing their mobility via their choice of loan, and lenders make zero profit on each loan taken out. This equilibrium can only exist if borrowers face frictions, such as refinancing costs. This provides a possible explanation for the prepayment options that are embedded in mortgage contracts, despite the significant deadweight costs associated with refinancing. We also show that the recent proliferation of loans with many different horizons represents an alternative means of persuading borrowers to self-select, with lower deadweight costs. Finally, our model suggests that the menu of contracts available at the time of origination should be an important predictor of future prepayment. Most commonly used prepayment models, which do not take this into account, are therefore misspecified, leading to errors in pricing and hedging mortgages and mortgage-backed securities.

250. "Implied Probability Distributions: Empirical Analysis."

Jens Carsten Jackwerth and Mark Rubinstein

June 1995

An earlier article, "Implied Binomial Trees," introduced a theoretical model for implying the stochastic process of an underlying asset price from the prices of associated options. This sequel provides details concerning application of the model to the full record of S&P; 500 index options transactions from April 2, 1986 through December 31, 1993. Most prominently, it introduces a revised optimization technique for estimating expiration-date risk-neutral probability distributions which is probably theoretically superior and definitely orders of magnitude faster than the approaches outlined in the antecedent paper. This method maximizes the smoothness of the distribution while at the same time insuring that multimodalities are not unrealistically strong. With the exception of the lower left-hand tail of the distribution, alternative optimization specifications typically produce approximately the same implied distributions. Considerable care is taken to specify such parameters as interest rates, dividends, and synchronous index levels, as well as to filter for general arbitrage violations and to use time aggregation to correct for unrealistic persistent jaggedness of implied volatility smiles. The resulting implied probability distributions exhibit changes in skewness as time-to-expiration approaches which are consistent with theoretical predictions. While time patterns of skewness and kurtosis exhibit a discontinuity across the divide of the 1987 market crash, they remain remarkably stable on either side of the divide. Moreover, since the crash, the risk-neutral probability of a four standard deviation decline in the S&P; index (-46 percent over a year) is 100 times more likely than would appear to be the case under the assumption of lognormality.

249. "A Variable Reduction Technique for Pricing Average-Rate Options."

Hua He and Akihiko Takahashi

May 1995

Average-rate options, commonly known as Asian options, are contingent claims whose payoffs depend on the arithmetic average of some underlying index over a fixed time horizon. This paper proposes a new valuation technique, called the variable reduction technique, for average rate options. This method transforms the valuation problem of an average-rate option into an evaluation of a conditional expectation that is determined by a one-dimensional Markov process (as opposed to a two-dimensional Markov process). This variable reduction technique works directly with the arithmetic average and does not encounter approximation errors when volatility of the underlying is relatively large. Further, reducing the dimensionality by one makes pricing more efficient in terms of computing time. The variable reduction technique is applied in a simple Black-Scholes' economy in which there is one risky asset and one riskless bond. The paper also discusses application of the technique to average-rate options where the underlying index is an interest rate. Numerical comparisons of different methods are also presented.

248. "Double Lookbacks."

Hua He, William P. Keirstead, and Joachim Rebholz

May 1995

A new class of options, double lookbacks, where the payoffs depend on the maximum and/or minimum prices of one or two traded assets is introduced and analyzed. This class of double lookbacks includes calls and puts with the underlying being the difference between the maximum and minimum prices of one asset over a certain period, and calls or puts with the underlying being the difference between the maximum prices of two correlated assets over a certain period. Analytical expressions of the joint probability distribution of the maximum and minimum values of two correlated geometric Brownian motions are derived and used in the valuation of double lookbacks. Numerical results are shown, and prices of double lookbacks are compared to those of standard lookbacks on a single asset.

247. "Anatomy of an ARM: Index Dynamics and Adjustable Rate Mortgage Valuation." (Related topics)

Richard Stanton and Nancy Wallace

April 1995

This paper analyzes the dynamics of the commonly used indices for Adjustable Rate Mortgages, and systematically compares the effects of their time series properties on adjustable rate mortgage prepayment and value. Our ARM valuation methodology allows us simultaneously to capture the effects of the dynamics of the index, discrete coupon adjustment, and caps and floors. It allows us either to calculate an optimal prepayment strategy for mortgage holders, or to use an empirical prepayment function. We find that the dynamics of the ARM indices, including both their average levels and their speeds of adjustment to interest rate shocks, introduce significant variation in the value of the prepayment option across ARMs. Valuation methodologies that ignore the time series properties of the index with respect to current rates will therefore systematically misprice adjustable rate mortgages.

246. "Effects of Competition on Bidder Returns."

Sankar De, Mark Fedenia, and Alexander J. Triantis

April 1995

This study offers several new perspectives on the effects of competition in takeover contests on bidder returns. Using a more extensive database than existing studies and employing several different measures of success in a takeover, we find that success in competitive acquisitions decreases shareholder wealth relative to failure and also relative to success in observed single-bidder takeovers. Further, we consider and test a number of hypotheses regarding bidder returns, including hypotheses suggested by the preemptive bidding theory. In general, our results indicate lack of support for the predictions of preemptive bidding theory and for the hypotheses linking the method of payment and the observed level of competition. We also test hypotheses relating to returns across the multiple events in a multiple-bid contest that competition among bidders generates. The results of these tests underscore the importance of timing as well as success of a bid to the bidder's subsequent performance.

245. "On Revelation of Private Information in Stock Market Economies."

Marcus Berliant and Sankar De

April 1995

The notion that an agent in a given market can infer from the market price the (non-price) information received by other agents, as embodied in the existing studies of revealing rational expectations equilibrium, requires that the agent know the correct functional relationship between the non-price information of all agents and the resulting equilibrium price. This condition is usually restrictive and unsuitable as a description of reality. In this paper we show that this condition is also unnecessary in a stock market economy where producers or firms use their private information in their own optimization programs,k which include stock purchases. Interestingly, this result does not extend to the case of consumers with private information.

244. "Optimal Cash Management for Investment Funds."

Hayne Leland and Gregory Connor

March 1995

We consider the question of how much cash should be held by an investment fund for transactions purposes. Cash is needed to meet redemptions and rights offerings; it is generated by dividends and contributions. It is assumed the cumulative cash flow follows a random walk, perhaps with a drift. If transactions costs were zero, it would be optimal to keep zero cash balances, since cash reduces expected return and adds to tracking error. But keeping cash balances at zero would be very expensive in the presence of transactions costs, since random walks have infinite variation. The optimal cash policy requires a no trade interval [*]. If cash balances are within this interval, no transfers between cash and portfolio securities takes place. If cash falls beneath zero, securities should be sold to return the cash balance to zero. If cash exceeds L*, cash should be invested in the portfolio to reduce the cash balance to L*. We derive closed form solutions for L*, and show how this responds to changes in transactions costs and other parameters of cash flows and portfolio returns. Finally, a closed form estimate of expected turnover associated with optimal strategies is derived.

243. "Foreign Exchange Volume: Sound and Fury Signifying Nothing?."

Richard K. Lyons

January 1995

This paper examines whether currency trading volume is informative, and under what circumstances. Specifically, we use transactions data to test whether trades occurring when trading intensity is high are more informative -- dollar for dollar -- than trades occurring when intensity is low. Theory admits both possibilities, depending primarily on the posited information structure. We present what we call a hot-potato model of currency trading, which explains why low-intensity trades might be more informative. In the model, the wave of inventory-management trading among dealers following innovations in order flow generates an inverse relationship between intensity and information content. Empirically, low-intensity trades are more informative, supporting the hot-potato hypothesis.

242. "Explaining Forward Exchange Bias. . .Intraday."

Richard K. Lyons and Andrew K. Rose

January 1995

Intraday interest rates are zero. Consequently, a foreign exchange dealer can short a vulnerable currency in the morning, close this position in the afternoon, and never face an interest cost. This tactic might seem especially attractive in times of crisis, since it suggests an immunity to the central bank's interest rate defense. In equilibrium, however, buyers of the vulnerable currency must be compensated on average with an intraday capital gain as long as no devaluation occurs. That is, currencies under attack should typically appreciate intraday. Using data on intraday exchange rate changes within the EMS, we find this prediction is borne out.

241. "On the Accounting Valuation of Employee Stock Options."

Mark Rubinstein

December 1994

In its exposure draft, "Accounting for Stock-based Compensation," FASB proposes that either the Black-Scholes or binomial option pricing model be used to expense employee stock options, and that the value of these options be measured on their grant date with typically modest ex-post adjustment. This brings the accounting profession squarely up against the Scylla of imposing too narrow a set of rules that will force many firms to misstate considerably the value of their stock options and the Charybdis of granting considerable latitude which will increase non-comparability across financial statements of otherwise similar firms. This, of course, is a common tradeoff afflicting many rules for external financial accounting. It is not my intention to take a position on this issue, but merely to point out the inherent dangers in navigating between these twin perils. To examine this question, this paper develops a binomial valuation model which simultaneously takes into consideration the most significant differences between standard call options and employee stock options: longer maturity, delayed vesting, forfeiture, non-transferability, dilution, and taxes. The final model requires 16 input variables: stock price on grant date, stock volatility, stock payout rate, stock expected return, interest rate, option striking price, option years-to-expiration, option years-to-vesting, expected employee forfeiture rate, minimum and maximum forfeiture rate multipliers, employee's non-option wealth per owned option, employee's risk aversion, employee's tax rate, percentage dilution, and number of steps in the binomial tree. Many of these variables are difficult to estimate. Indeed, a firm seeking to overvalue its option might report values almost double those reported by an otherwise similar firm seeking to undervalue its options. The alternatives of expensing minimum (zero-volatility) option values, whether at grant or vesting date, can easily be gamed by slightly redefining employee stock option contracts, and therefore would not accomplish FASB's goals. As an alternative, FASB could give more careful consideration to exercise date accounting, under which an expense is recognized at the time of exercise equal to the exercise value of the option. This would achieve the long sought external accounting goal of realizing stock options as compensation, while at the same time minimizing the potential for the revised accounting rules to motivate gaming behavior or non-comparable statements.

240. "Bond Prices, Yield Spreads, and Optimal Capital Structure with Default Risk."

Hayne Leland

November 1994

This paper examines the value of debt subject to default risk in a continuous time framework. By considering debt with regular principal repayments (e.g. through a sinking fund), we are able to examine bonds with arbitrary maturity while retaining a time-homogeneous environment. This extends Leland's [1994] earlier closed-form results to a much richer class of possible debt structures. We examine the term structure of yield spreads and find that a rise in interest rates will reduce yield spreads of current debt issues. It may tilt the term structure as well. Duration is also affected by default risk. The traditional Macaulay duration measure overstates effective duration, which for junk bonds may even be negative. While short term debt does not exploit tax benefits as completely as does long term debt, it is more likely to provide incentive compatibility between debt holders and equity holders. The agency costs of asset substitution are minimized when firms use shorter term debt. Optimal capital structure depends upon debt maturity. Optimal leverage ratios are smaller, and maximal firm values are less, when short term debt is used. The yield spread at the optimal leverage ratio increases with debt maturity.

239. "Gains from Diversifying into Real Estate: Three Decades of Portfolio Returns Based on the Dynamic Investment Model."

Robert R. Grauer and Nils H. Hakansson

October 1994

This paper compares the investment policies and returns for portfolios of stocks and bonds with and without up to three categories of real estate. Both a domestic and a global setting are examined, with and without the possibility of leverage. The portfolios were generated via the dynamic investment model on the basis of the empirical probability assessment approach applied to past (joint) realizations of returns, both with and without correction for smoothing in the real estate data series. Our principal findings are: 1) the gains from adding real estate on a semi-passive (equal-weighted) basis to portfolios of either U.S. or global financial assets were relatively modest; in contrast, 2) the gains from adding real estate to the universe of U.S. financial assets under an active strategy were rather large (in some cases highly statistically significant), especially for the very risk-averse strategies; 3) the gains from adding (U.S.) real estate to a universe of global financial assets under an active strategy were mixed, although generally favorable for the highly risk- averse strategies; 4) correcting for second-moment smoothing in the real estate returns series had a relatively small impact for the more risk-tolerant strategies; and 5) there was some evidence that de-smoothing resulted in improved probability estimates.

238. "Options on Leveraged Equity with Default Risk."

Klaus Bjerre Toft

July 1994

In this paper, I derive option pricing formulas for call and put options written on leveraged equity in an economy with corporate taxes and bankruptcy costs. The firm can be forced into bankruptcy by breaching a net-worth covenant, or it may declare bankruptcy when it is optimal for equity holders to do so. Consequently, option values and sensitivities depend on structural variables such as the corporate tax rate, the firm's coupon payments, and the firm value at which bankruptcy is declared. The derived formulas for calls and puts on equity with default risk simplify to Black-Scholes type formulas for down-and-out barrier options if bankruptcy is declared as soon as the value of the firm's assets equals the after-tax value of the promised coupon payments on the debt. If the capital structure contains no debt, the pricing results simplify to Black-Scholes formulas for call and put options. The model developed in this paper relates implied Black-Scholes volatility for equity options to structural characteristics such as leverage and the debt's protective covenants. Options priced by the proposed model are characterized by Black-Scholes implied volatilities which are decreasing in striking price. Moreover, equity options on firms with protected debt have more pronounced volatility skews than options on firms with unprotected debt. Finally, I show how to evaluate the term structure of default spreads for corporate interest-only strips.

237. "Exact Formulas for Expected Hedging Error and Transactions Costs in Option Replication."

Klaus Bjerre Toft

July 1994

In this paper, I derive exact formulas for expected hedging error and transactions costs in option replication for the Black-Scholes economy with exogenously fixed trading points. I derive the formulas using two different volatilities which allow the hedger to use a transactions costs adjusted volatility to determine the hedge portfolio. The expected hedging error is written in an easily recognized form. The four terms in the expectation can be interpreted as terms from Black and Scholes' (1973) formula with adjusted parameters. This interpretation holds for all future hedging periods even though the expectation is conditional on the stock price at the time of the hedging scheme's initiation. I also derive an approximation of the expected transactions costs. This approximation has a simple interpretation: for each of the future hedging periods, the approximate expected transactions costs incurred at the end of each hedging period are proportional to the option's gamma with adjusted parameters, multiplied by the squared expected value of the underlying asset. For the risk neutral economy with no volatility adjustment, I show that present values of the approximate expected transactions costs are identical for each of the future hedging intervals. Moreover, I illustrate that the approximation to the expected transactions costs is accurate except for hedging periods close to the maturity of the contingent claim. Here, the exact expectation tends to be larger than the approximation, even though the expectation is taken only with knowledge of the initial stock price. Finally, I derive an approximation of the variance of the hedging scheme's cash-flow (the hedging error minus the transactions costs) for each of the future hedging periods. This approximation facilitates evaluation of the tradeoff between cost and variance of the replication strategy.

236. "Dynamic Aggregation and Computation of Equilibria in Finite-Dimensional Economies with Incomplete Financial Markets."

Domenico Cuoco and Hua HŠ

June 1994

This paper constructs a representative agent supporting the equilibrium allocation in event-tree economies with time-additive preferences and possibly incomplete securities markets. If the equilibrium allocation is Pareto optimal, this construction gives the usual linear welfare function. Otherwise, the representative agent's utility function is state-dependent, even when individual agents have state-independent utilities and homogeneous beliefs. The existence of a representative agent allows us to provide a characterization of equilibria which does not rely on the derivation of the agents' intertemporal demand functions for consumption and investment. More specifically, it allows us to transform the dynamic general equilibrium problem into a static one, and is therefore especially well suited for numerical computation of equilibria in economies with incomplete financial markets.

235. "Market Structure and Liquidity on the Tokyo Stock Exchange."

Bruce N. Lehmann and David M. Modest

March 1994

Most equity market mechanisms have designated market makers who provide continuous liquidity. This is not the case on one of the largest and most active stock markets in the world: the Tokyo Stock Exchange (TSE). Its designated intermediaries are merely order clerks called saitori, who log limit orders in a public limit order book and match incoming market orders against them in accordance with strict rules based on price, time, and size priority. On the TSE, orders from the investor public, not from designated market makers, bridge temporal fluctuations in the demand for liquidity. In this paper, we study the chui and tokubetsu kehai (warning and special quote) mechanisms of the TSE. Since no designated market ;maker stands ready to absorb transient order flow variation, these procedures provide for flagging possibly transient order imbalances and for routinely halting trade to attract orders when particular kinds of order imbalances occur. Such mechanisms always trade the benefits of attracting more liquidity to the marketplace against the cost of impeding the price discovery process and the immediacy of execution. We establish several facts about the impact of these mechanisms on market liquidity. Investors seldom trip the trading halt mechanisms of the TSE and, when they do, they usually execute all or part of their order at the warning quote, a price known in advance. Traders are more likely to trigger indicative quote dissemination and temporary trading halts when the market is relatively volatile, particularly around the morning open and after delayed opens. The volume of trade is similar when orders do and do not result in trading halts, an economically sensible result since the ex ante limit order books should be identical. Substantially larger trades and special quote trading halts (which provide for price discovery through orderly quote changes), a result that is also intuitively plausible. What is perhaps surprising is not that these result accord with intuition but rather that they conform to it so well.

234. "Trading and Liquidity on the Tokyo Stock Exchange: A Bird's Eye View."

Bruce N. Lehmann and David M. Modest

April 1994

The trading mechanism for equities on the Tokyo Stock Exchange (TSE) stands in sharp contrast to the primary mechanisms used to trade stocks in the United States. In the U.S., exchange-designated specialists have affirmative obligations to provide continuous liquidity to the market. Specialists offer simultaneous and tight quotes to both buy and sell and supply sufficient liquidity to limit the magnitude of price changes between consecutive transactions. In contradistinction, the TSE has no exchange-designated liquidity suppliers. Instead, liquidity is provided through a public limit order book and liquidity is organized through restrictions on maximum price changes between trades which serve to slow down trading. In this paper, we examine the efficacy of the TSE's trading mechanisms at providing liquidity. Our analysis is based on a complete record of transactions and best-bid and best-offer quotes for most stocks in the First Section of the TSE over a period of 26 months. We study the size of the bid-ask spread and its cross- sectional and intertemporal stability; intertemporal patterns in returns, volatility, volume, trade size, and the frequency of trades; and market depth based on the response of quotes to trades and the frequency of trading halts and warning quotes.

233. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure."

Hayne E. Leland

January 1994

This paper examines corporate debt values and capital structure in a unified analytical framework. It derives closed form results for the value of long-term risky debt and yield spreads, and for optimal capital structure, when firm asset value follows a diffusion process with constant volatility. Debt values and optimal leverage are explicitly linked to firm risk, taxes, bankruptcy costs, riskfree interest rates, payout rates, and bond covenants. The results elucidate the different behavior of junk bonds vs. investment grade bonds, and aspects of asset substitution, debt repurchase, and debt renegotiation.

232. "Implied Binomial Trees."

Mark Rubinstein

January 1994

Despite its success, the Black-Scholes formula has become increasingly unreliable over time in the very markets where one would expect it to be most accurate. In addition, attempts by financial economists to extract probabilistic information from option prices have been puny in comparison to what is clearly possible. This paper develops a new method for inferring risk-neutral probabilities (or state- contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and hence consistent with all the observed option prices). If specified exogenously, the model can also accommodate local interest rates and underlying asset payout rates which are general functions of the concurrent underlying asset price and time. In a 200 step lattice, for example, there are a total of 60,301 unknowns: 40,200 potentially different move sizes, 20,100 potentially different move probabilities, and 1 interest rate to be determined from 60,301 independent equations, many of which are non-linear in the unknowns. Despite this, a backwards recursive solution procedure exists which is only slightly more time-consuming than for a standard binomial tree with given constant move sizes and move probabilities. Moreover, closed-form expressions exist for the values and hedging parameters of European options maturing with or before the end of the tree. The tree can also be used to value and hedge American and several types of exotic options. Interpreted in terms of continuous-time diffusion processes, the model here assumes that the drift and local volatility are at most functions of the underlying asset price and time. But instead of beginning with a parameterization of these functions (as in previous research), the model derives these functions endogenously to fit current option prices. As a result, it can be thought of as an attempt to exhaust the potential for single state-variable path-independent diffusion processes to rectify problems with the Black- Scholes formula that arise in practice.

231. "Optimal Transparency in a Dealership Market with an Application to Foreign Exchange."

Richard K. Lyons

September 1993

This paper addresses the issue of optimal transparency in a multiple-dealer market. In particular, we examine the question: Would risk-averse dealers prefer ex-ante that signed order flow were observable? We answer this question with the solution to a mechanism design problem. The resulting incentive-efficient mechanism is one in which signed order flow is not observable. Rather, dealers prefer a slower pace of price discovery because it induces additional risk-sharing. Specifically, slower price discovery permits additional trading with customers prior to revelation; this reduces the variance of unavoidable position disturbances, thereby reducing the marketmaking risk inherent in price discovery. We then apply the framework to the spot foreign exchange market in order to understand better the current degree of transparency in that market.

230. "Tests of Microstructural Hypotheses in the Foreign Exchange Market."

Richard K. Lyons

August 1993

This paper introduces a three-part transactions dataset to test various microstructural hypotheses about the spot foreign exchange market. In particular, we test for effects of trading volume on quoted prices through the two channels stressed in the literature: the information channel and the inventory-control channel. We find that trades have both a strong information effect and a strong inventory-control effect, providing support for both strands of microstructure theory. The bulk of equity-market studies also find an information effect; however, these studies typically interpret this as evidence of inside information. Since there are no insiders in the foreign exchange market, this finding suggests a broader conception of the information environment, at least in this context.

229. "The Economic Functions of Derivatives: An Academician's Point of View."

David Pyle

July 1993

The question of the economic functions of derivatives has been widely discussed in the financial economics literature. In this paper, I focus on the sources of economic efficiency gains from the use of derivatives. These sources include helping to complete capital markets, lowering transaction costs, and reducing agency costs. Many of these functions can be obtained by using primary securities so an important question is what characteristics of derivatives account for their enhanced efficiency and utility relative to the assets that underlie them. Three characteristics are identified and discussed: 1) the dependence of derivative value on changes in the value of underlying assets, 2) the positive dependence of some derivative values on asset volatility, and 3) the non-linear payoffs provided by some derivatives.

228. "Differential Information and Dynamic Behavior of Stock Trading Volume."

Hua He and Jiang Wang

May 1993

We develop a multi-period model of stock trading in which investors receive differential information concerning the underlying value of the stock. Investors trade competitively in the market based on their own private information and the information revealed by the market clearing prices as well as other public news. By showing that the hierarchy of expectations (i.e., forecasting the forecasts of others) is a closed system, we resolve the infinite regress problem that is common to intertemporal models with differential information and derive a rational expectations equilibrium. We analyze the dynamic behavior of equilibrium trading volume. In particular, we examine how trading volume is related to the information flow to the market and how investors' trading reveals their private information.

227. "The U.S. Savings and Loan Crisis."

David H. Pyle

April 1993

226. "Long-Term Debt Value, Bond Covenants, and Optimal Capital Structure."

Hayne Leland

February 1993

225. "Liquidation Costs and Risk-Based Bank Capital."

Helena M. Mullins and David H. Pyle

January 1993.

Bank capital rules which do not recognize audit costs, liquidation costs and portfolio diversification can seriously underestimate actuarially fair capital requirements. If depositors do not have access to low cost alternatives, the effect of higher requirements can be imposed on them. Otherwise, they need absorb only costs associated with minimum-risk, minimum-cost assets. If borrowers have direct access to financial markets or can borrow from uninsured, less highly levered institutions, insured banks facing a fair risk-based capital requirement and fixed premium cannot attract them. A schedule of required capital and insurance premium pairs would allow banks to retain investment flexibility.

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Updated 8/7/01 Questions or praise: Patt Bagdon
Institute of Business and Economic Research, University of California, Berkeley