Financial Intermediation and the Costs of Trading in an Opaque Market

Municipal bonds trade in opaque, decentralized broker-dealermarkets in which price information is costly to gather. We analyzea database of trades between broker-dealers and customers inmunicipal bonds. These data were only released to the publicwith a lag; the market was opaque. Dealers earn lower averagemarkups on larger trades, even though dealers bear a higherrisk of losses with larger trades. We estimate a bargainingmodel and compute measures of dealer’s bargaining power.Dealers exercise substantial market power. Our measures of marketpower decrease in trade size and increase in the complexityof the trade for the dealer. (JEL G0, G24)     

Options and Bubbles

The Black-Scholes-Merton option valuation method involves derivingand solving a partial differential equation (PDE). But thismethod can generate multiple values for an option. We providenew solutions for the Cox-Ingersoll-Ross (CIR) term structuremodel, the constant elasticity of variance (CEV) model, andthe Heston stochastic volatility model. Multiple solutions reflectasset pricing bubbles, dominated investments, and (possiblyinfeasible) arbitrages. We provide conditions to rule out bubbleson underlying prices. If they are not satisfied, put-call paritymight not hold, American calls have no optimal exercise policy,and lookback calls have infinite value. We clarify a longstandingconjecture of Cox, Ingersoll, and Ross. (JEL G12 and G13)     

Agency and Optimal Investment Dynamics

Agency problems limit firms’ access to capital markets,curbing investment. Firms and investors seek contractual waysto mitigate these problems. What are the implications for investment?We present a theory of a firm’s investment dynamics inthe presence of agency problems and optimal long-term financialcontracts. We derive results relating firms’ investmentdecisions, current and past cash flows, firm size, capital structure,and dividends. Among the results, optimal investment is increasingin current and past cash flow; and optimal investment is positivelyserially correlated over time (after controlling for investmentopportunities). These results hold for a range of agency problems.(JEL G30, G31, G32, G35, D82, D86, D92)     

The dynamics of portfolio management contracts

We consider the multiperiod relationship between a client anda portfolio manager and the resulting problem of motivatinga manager of unknown ability to acquire valuable information.We explore the contractual form and the optimal retention policyof the client and find that the optimal initial set of contractsfeatures a smaller performance based fee component paid to themanager than in a first-best contract, and the contract choiceelicits only partial information about the manager. As a result,ex post performance measurement is critical to future recontracting.In general, managers are retained only if the returns on theirportfolio exceed the benchmark by an appropriate amount.     

Price Informativeness and Investment Sensitivity to Stock Price

The article shows that two measures of the amount of privateinformation in stock price—price nonsynchronicity andprobability of informed trading (PIN)—have a strong positiveeffect on the sensitivity of corporate investment to stock price.Moreover, the effect is robust to the inclusion of controlsfor managerial information and for other information-relatedvariables. The results suggest that firm managers learn fromthe private information in stock price about their own firms’fundamentals and incorporate this information in the corporateinvestment decisions. We relate our findings to an alternativeexplanation for the investment-to-price sensitivity, namelythat it is generated by capital constraints, and show that boththe learning channel and the alternative channel contributeto this sensitivity. (JEL G14, G31)     

Optimal Equity Stakes and Corporate Control

I show that firms may optimally sell blocks of their own equityto other firms in anticipation of future corporate control activity.In the model, a target and one potential acquirer, who may alsobe an alliance partner, can negotiate before synergy valuesare learned. I find that equity implements an optimal mechanism,allowing the partners to extract surplus from outside bidderswho may arrive later. The stake is limited by the outsiders'willingness to investigate. The results imply that corporatecontrol may motivate an equity sale even when no takeover activityis apparent at the time or occurs ex post.     

Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain

We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states. Partial observation means that only the prices are observable. For the investors objective of maximizing the expected utility of the terminal wealth we derive an explicit representation of the optimal trading strategy in terms of the unnormalized filter of the drift process, using HMM filtering results and Malliavin calculus. The optimal strategy can be determined numerically and parameters can be estimated using the EM algorithm. The results are applied to historical prices.Received: March 2004, Mathematics Subject Classification (2000): 91B28, 60G44JEL Classification: G11Supported by NSERC under research grant 88051 and NCE grant 30354.     

The Pooling and Tranching of Securities: A Model of Informed Intermediation

I show that when an issuer has superior information about thevalue of its assets, it is better off selling assets separatelyrather than as a pool due to the information destruction effectof pooling. If, however, the issuer can create a derivativesecurity that is collateralized by the assets, pooling and "tranching"may be optimal. If the residual risk of each asset is not highlycorrelated, tranching allows the issuer to exploit the riskdiversification effect of pooling to create a low-risk and highlyliquid security. In contrast, for an uninformed seller, purepooling reduces underpricing and is preferred to separate assetsales. These results lead to a dynamic model of financial intermediation:originators sell pools of assets, some of which are purchasedby informed intermediaries who then further pool and tranchethem. Pooling and tranching allow intermediaries to leveragetheir capital more efficiently, enhancing the returns to theirprivate information.     

Accounting information,disclosure, and expected utility: Do investors really abhor uncertainty?

Investors are said to “abhor uncertainty,” but if there were no uncertainty they could earn only the risk‐free rate. A fundamental result in the analytical accounting literature shows that investors buying into a CARA‐normal CAPM market pay lower asset prices, gain higher ex‐ante expected returns, and obtain higher expected utility, when the market payoff has higher variance. New investors obtain similar “welfare” gains from risk under a log/power utility CAPM. These results do not imply that investors “abhor information.” To realize investors' ex‐ante expectations, the subjective probability distributions representing market expectations must be accurate. Greater payoff risk can add to investors' expected utility, but higher ex‐post(realized) utility comes from better information and more accurate ex‐ante expectations. An important implication for accounting is that greater disclosure can have the simultaneous effects of (i) exposing more fully or perceptibly firms' payoff uncertainty, thereby increasing new investors' expected utility, and (ii) improving market estimates of firms' payoff parameters (means, variances, covariances), thereby giving investors a better chance of realizing their expectations. Paradoxically, better information can be valuable to new investors by exposing more fully and more accurately the risk in firms' business operations and results–new investors maximizing expected utility want both more risk and better information.     

Perpetual American options in incomplete markets: the infinitely divisible case

We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.     

The design of an optimal insurance contract for irreplaceable commodities

This paper discusses optimal insurance contract for irreplaceable commodities. To describe the dual impacts on individuals when a loss occurs to the insured irreplaceable commodities, we use a state-dependent and bivariate utility function, which includes both the monetary wealth and sentimental value as two arguments. We show that over (full, partial) insurance is optimal when a decrease in sentimental value will increase (not change, decrease, respectively) the marginal utility of monetary wealth. Moreover, a non-zero deductible exists even without administration costs. Furthermore, we demonstrate that a positive fixed reimbursement is optimal if (1) the premium is actuarially fair, (2) the monetary loss is a constant, and (3) the utility function is additively separable and the marginal utility of money is higher in the loss state than in the no-loss state. We also characterize comparative statics of fixed-reimbursement insurance under an additively separable preference assumption. JEL Classification G22 · D86 The author acknowledge funding from National Science Council in Taiwan (NSC93-2416-H-130-020).     

Managerial responses to incentives: Control of firm risk, derivative pricing implications, and outside wealth management

We model a firm’s value process controlled by a manager maximizing expected utility from restricted shares and employee stock options. The manager also controls allocation of his outside wealth, which allows partially hedging of his exposure to firm risk. Managerial control increases the expected time to exercise for his employee stock options. It also reduces the gap between his certainty equivalent and the firm’s Fair Value for his compensation, but that gap remains substantial. Managerial control also causes traded options to exhibit an implied volatility smile. With costly control the same basic patterns remain, but the manager’s risk-taking is dampened.     

The Book-to-Market and Size Effects in a General Asset Pricing Model: Evidence from Seven National Markets

The positive relation of returns with Book-to-Market ratio (BE/ME)and their negative relation withMarket Value(MVE) remains strongunder a general stochastic discount function (SDF) that doesnot depend on a specific asset pricing model and avoids potentiallyserious simultaneity biases inherent in the Fama and Frenchthree-factor model. However, we find that SDF_s that includethe equivalent of the HML portfolio do not span all asset sub-spaces,even with additional conditioning information. Finally, macroand financial variables we introduce to the pricing functionsdo not offer an alternative explanation of the BE/ME effect.JEL Classification codes: G10, G12, G15, G30.     

Optimal exercise of executive stock options and implications for firm cost

This paper conducts a comprehensive study of the optimal exercise policy for an executive stock option and its implications for option cost, average life, and alternative valuation concepts. The paper is the first to provide analytical results for an executive with general concave utility. Wealthier or less risk-averse executives exercise later and create greater option cost. However, option cost can decline with volatility. We show when there exists a single exercise boundary, yet demonstrate the possibility of a split continuation region. We also show that, for constant relative risk averse utility, the option value does not converge to the Black and Scholes value as the correlation between the stock and the market portfolio converges to one. We compare our model's option cost with the modified Black and Scholes approximation typically used in practice and show that the approximation error can be large or small, positive or negative, depending on firm characteristics.     

Optimal insurance under maxmin expected utility

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the maxmin expected utility model of Gilboa and Schmeidler (J. Math. Econ. 18:141–153, 1989), whereas the insurer is a (risk-averse or risk-neutral) expected-utility maximiser. We characterise optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, of marginal utility of wealth, of belief heterogeneity, as well as of ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how a singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Rényi ambiguity set.

     

Why Does Implied Risk Aversion Smile?

Implied risk aversion estimates reported in the literature arestrongly U-shaped. This article explores different potentialexplanations for these "smile" patterns: (i) preference aggregation,both with and without stochastic volatility and jumps in returns,(ii) misestimation of investors’ beliefs caused by stochasticvolatility, jumps, or a Peso problem, and (iii) heterogeneousbeliefs. The results reveal that preference aggregation andmisestimation of investors’ beliefs caused by stochasticvolatility and jumps are unlikely to be the explanation forthe smile. Although a Peso problem can account for the smile,the required probability of a market crash is unrealisticallylarge. Heterogeneous beliefs cause sizable distortions in impliedrisk aversion, but the degree of heterogeneity required to explainthe smile is implausibly large. (JEL: G12, G13)     

The Impact of Regret on the Demand for Insurance

We examine optimal insurance purchase decisions of individuals that exhibit behavior consistent with Regret Theory. Our model incorporates a utility function that assigns a disutility to outcomes that are ex post suboptimal, and predicts that individuals with regret‐theoretical preferences adjust away from the extremes of full insurance and no insurance coverage. This prediction holds for both coinsurance and deductible contracts, and can explain the frequently observed preferences for low deductibles in markets for personal insurance.     

Household Portfolio Diversification: A Case for Rank-Dependent Preferences

The proliferation of novel preference theories in financialeconomics is hampered by a lack of non-experimental evidenceand by the theories’ additional complexity which has notbeen shown to be critical in applications. In this article Ipresent arguments in support of preferences with rank dependency.Using the Survey of Consumer Finances data, I document two widespreadpatterns inconsistent with expected utility: (i) many householdssimultaneously invest in well-deversified funds and in poorly-diversifiedportfolios of stocks; and (ii) some households with substantialsavings do not invest anything in equities. I show that portfoliochoice models with rank-dependent preferences, plausibly parameterizedand under fully rational assumptions, are quantitatively consistentwith the observed diversification. These results call for furtherefforts to integrate the models of rank-dependent preferencesin portfolio theory and asset pricing.     

Option Coskewness and Capital Asset Pricing

This article shows how the market coskewness model of Rubinstein(1973) and Kraus and Litzenberger (1976) is altered when a nonredundantcall option is optimally traded. Owing to the option’snonredundancy, the economy’s stochastic discount factor(SDF) depends not only on the market return and the square ofthe market return but also on the option return, the squareof the option return, and the product of the market and optionreturns. This leads to an asset pricing model in which the expectedreturn on any risky asset depends explicitly on the asset’scoskewness with option returns. The empirical results show thatthe option coskewness model outperforms several competing benchmarkmodels. Furthermore, option coskewness captures some of thesame risks as the Fama–French factors small minus big(SMB) and high minus low (HML). These results suggest that thefactors that drive the pricing of nonredundant options are alsoimportant for pricing risky equities.(JEL G11, G12, D61)