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"On Adaptive Tail Index Estimation for Financial Return
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.
"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
"Return-Volume Dependence and Extremes in International
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.
"On the Relation Between Binomial and Trinomial Option Pricing
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.
"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,
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.
and Return Dynamics of New Ventures."
Jonathan B. Berk, Richard C. Green and Vasant Naik. September
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.
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
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.
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
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
"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
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
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.
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
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
RPF-273 "Profits and Position Control:
A Week of FX Dealing."
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.
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
"Is There Private Information in the FX Market? The Tokyo
Takatoshi Ito. and Richard K. Lyons and Michael T. Melvin.
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.
"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
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.
"Volume, Volatility, Price and Profit When All Traders Are
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
"Recovering Risk Aversion from Option Prices and Realized
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
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
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.
"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
"Optimal Asset Rebalancing in the Presence of Transactions
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.
"Stock Price Volatility in a Multiple Security Overlapping
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
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  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 . 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
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
Matthew Spiegel and Avanidhar Subrahmanyam
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
RPF-256REV.* "How Do Firms Choose Their Lenders?
Theory and Evidence."
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
255. "A Theory of Corporate Capital
Structure and Investment."
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
"The Rise and Fall of Bank Control in the United States:
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.
"A Spatial Model of Housing Returns and Neighborhood Substitutability."
William N. Goetzmann and Matthew Spiegel
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
"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
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.
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.
Probability Distributions: Empirical Analysis."
Jens Carsten Jackwerth and Mark Rubinstein
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
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
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
247. "Anatomy of an ARM: Index
Dynamics and Adjustable Rate Mortgage Valuation." (Related
Richard Stanton and Nancy Wallace
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
Sankar De, Mark Fedenia, and Alexander J. Triantis
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
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
Hayne Leland and Gregory Connor
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
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
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."
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."
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 
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
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
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
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
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
236. "Dynamic Aggregation and Computation
of Equilibria in Finite-Dimensional Economies with Incomplete
Domenico Cuoco and Hua H
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
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
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
233. "Corporate Debt Value, Bond
Covenants, and Optimal Capital Structure."
Hayne E. Leland
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
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
231. "Optimal Transparency in a
Dealership Market with an Application to Foreign Exchange."
Richard K. Lyons
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
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."
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
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
227. "The U.S. Savings and Loan
David H. Pyle
226. "Long-Term Debt Value, Bond
Covenants, and Optimal Capital Structure."
225. "Liquidation Costs and Risk-Based
Helena M. Mullins and David H. Pyle
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.