The role of varying risk attitudes in an auction with a buyout option

Summary. An auction with a buyout option is modelled. Such an option allows a bidder to purchase the item being auctioned at a pre-specified buyout price, instead of attempting to obtain the item through the traditional auction procedure. This analysis is motivated by internet auctions where such options are present. If all auction participants are risk neutral, the seller will choose a buyout price high enough so that the option is never exercised. However, a risk averse seller facing risk neutral bidders will choose a price low enough so that the option is exercised with positive probability. Further, if bidders are risk neutral and the seller is risk averse, this option may result in a Pareto improvement compared to a sealed bid second price auction.Received: 3 December 2002, Revised: 28 September 2004, JEL Classification Numbers: D44, L86, D8. Correspondence to: Timothy MathewsWe would like to thank Yair Tauman, Thomas Jeitschko, Pradeep Dubey, Konstantinos Serfes, Abraham Neyman, Qihong Liu, and an anonymous referee, as well as participants of the 2001 Canadian Economic Association Conference and the 2001 Stony Brook International Conference on Game Theory. This paper is based upon Chapter Two of Mathews doctoral dissertation.     

EQUIVALENT OPTION PRICE WITH SUPPLY UNCERTAINTY

This paper compares two ex ante measures of the benefits of a project with supply uncertainty: compensating option price, the willingness to pay for a project, and equivalent option price, the willingness to accept to forego a project. The paper shows that compensating option price does not generally rank three or more projects correctly, even when the projects only impose a change in a single good. Equivalent option price, like equivalent variation with certain outcomes, always ranks three or more projects correctly. This paper also presents a method to empirically estimate equivalent option price using estimates of the benefits of certain changes. This approach is practically important so that the same study results can be used to estimate equivalent option price even as new projects are developed or as changes occur in the scientific information regarding the probabilities of various project outcomes. An application of the empirical method estimates the benefits of a policy to improve air and water quality when there is uncertainty about the effectiveness of the policy.     

Currency Options and Export-Flexible Firms

This paper examines the production and hedging decisions of a globally competitive firm under exchange rate uncertainty. The firm is risk averse and possesses export flexibility in that it can distribute its output to either the domestic market or a foreign market after observing the realized spot exchange rate. To hedge against its exchange rate risk exposure, the firm can trade fairly priced currency call options of an arbitrary strike price. We show that both the separation and the full‐hedging results hold if the strike price of the currency call options is set equal to the ratio of the domestic and foreign selling prices. Otherwise, neither result holds. Specifically, we show that the optimal level of output is always less than that of an otherwise identical firm that is risk neutral. Furthermore, an under‐hedge (over‐hedge) is optimal whenever the strike price of the currency call options is below (above) the ratio of the domestic and foreign selling prices.     

An experimental study of the impact of competition for Other People’s Money: the portfolio manager market

In this paper we experimentally investigate the impact that competing for funds has on the risk-taking behavior of laboratory portfolio managers compensated through an option-like scheme according to which the manager receives (most of) the compensation only for returns in excess of pre-specified strike price. We find that such a competitive environment and contractual arrangement lead, both in theory and in the lab, to inefficient risk taking behavior on the part of portfolio managers. We then study various policy interventions, obtained by manipulating various aspects of the competitive environment and the contractual arrangement, e.g., the Transparency of the contracts offered, the Risk Sharing component in the contract linking portfolio managers to investors, etc. While all these interventions would induce portfolio managers, at equilibrium, to efficiently invest funds in safe assets, we find that, in the lab, Transparency is most effective in incentivising managers to do so. Finally, we document a behavioral “Other People’s Money” effect in the lab, where portfolio managers tend to invest the funds of their investors in a more risky manner than their Own Money, even when it is not in either the investors’ or the managers’ interest to do so.     

Option implied beta and option return

We study the information content of option-implied betas for future equity option returns, using data on the S&P 500 index options and all of the component stock options. We find a significantly strong relation between option-implied betas and option returns cross-sectional. The paper presents evidence that call (put) option returns increase (decrease) with the option-implied betas of the underlying stock. A trading strategy of buying high (low) implied beta call (put) option portfolio and selling low (high) implied beta call (put) option portfolio generates a statistically and economically significant return. Our results are robustly persistent even after controlling for various cross-sectional effects and are not explained by the risk factors in asset pricing.     

A risk index to model uncertain portfolio investment with options

This paper models the portfolio investment performance with options by using a risk index, which is defined as the average loss below the risk-free interest rate. Using a risk-free interest rate as the uniform reference rate for all portfolios, the risk index offers an easier-to-compare loss value than the value-at-risk return, where portfolio specific references are used to calculate the average losses. Besides, uncertainty theory is used in the paper to derive the portfolio decision when stock prices are subject to experts' estimations. By analytical computation and empirical analysis, we find that portfolios considering options generate better return than the ones without options. The empirical analysis reveals that the options can effectively hedge the risk, and the call option with a higher exercise price offers higher return per unit of option premium. Furthermore, our proposed model produces higher expected return in most cases than the model where the risk is measured by the chance of the total return failing to reach the threshold level of return.     

The effects of abandonment options on operating leverage and forward hedging

This paper examines the behavior of the competitive firm under output price uncertainty when the firm is endowed with an abandonment option and has access to a forward market for its output. When the realized output price is less than its marginal cost, the firm optimally exercises its abandonment option and ceases production. The firm lets its abandonment option extinguish, thereby producing up to its capacity, only when the realized output price exceeds its marginal cost. The ex post exercising of the abandonment option as such convexifies the firm's ex ante profit with respect to the random output price. We show that neither the separation theorem nor the full-hedging theorem holds in the presence of the abandonment option. The firm under-hedges its output price risk exposure in the forward market wherein the forward price contains a nonpositive risk premium. When the set of hedging instruments is expanded to include options, we show that both the separation and full-hedging theorems are restored. We further show that the firm prefers options to forwards for hedging purposes when both types of contracts are fairly priced.     

Strategic use of futures and options by commodity processors

The impacts of input–output price relationships on end-users' demands for positions in futures and options are analyzed using a mean-variance portfolio model and applied to price risk management in the bread manufacturing industry. A production relationship was assumed between the input and resultant output, and correlation between the input and output prices were introduced into the portfolio model. The optimal hedge ratio can be either positive or negative depending upon the relationship between the input and output price standard deviation adjusted for production technology and input–output price correlation. Introduction of a call option into the portfolio (in addition to the futures) does not change the hedging demand for futures; however, the speculative component changes. The results show that the addition of input–output linear production and price correlation relationships would not justify a hedging role for options unless there is bias in the futures and/or options markets.     

Price bounds on bond options,swaptions, caps,and floors assuming only nonnegative interest rates

This paper derives bounds on the prices of European and American bond options, caps, floors, and European swaptions assuming only absence of arbitrage and nonnegative interest rates. The bounds are considerably tighter than Merton's bounds on stock option prices, especially for options on short-term bonds or swaps and short-term caps and floors. For American bond options, it is important to distinguish between options on the quoted (“clean”) bond price and options on the actual (“dirty”) bond price. For example, it is shown that it may be optimal to exercise an American call on the quoted bond price early even if the underlying bond makes no payments in the remaining life of the option.     

Why banks should keep secrets

Summary. We show that it is sometimes efficient for a bank to commit to a policy that keeps information about its risky assets private. Our model, based upon Diamond-Dybvig (1983), has the feature that banks acquire information about their risky assets before depositors acquire it. A bank has the option of using contracts where the middle-period return on deposits is contingent on this information, but by doing so it must also reveal the information. We derive the conditions on depositors preferences and banking technology for which a bank would prefer to keep information secret even though it must then use a non-contingent deposit contract.Received: 5 November 2002, Revised: 19 December 2004, JEL Classification Numbers: D8, G21, G28.I would like to thank an anonymous referee, Sudipto Bhattacharya, Ed Green, Chandra Kanodia, Andy McLennan, Arijit Mukherji, Bradley Ruffle, Neil Wallace, Warren Weber, and especially Nobu Kiyotaki for useful comments and suggestions.     

Do lucky CEOs avoid innovation?

Stock options are one of the most widely used equity-based compensation mechanisms to mitigate misalignment between managers’ and shareholders’ interests. And yet, it is sometimes suspiciously used as a method of extracting shareholders’ wealth to managers (Bebchuk et al., 2009). The typical ways to do so is using opportunistic timing such as backdating, spring-loading, etc. As shown in Bebchuk et al. (2010), opportunistic timing of option grants increases the incidence of lucky grants, or stock option grants that CEOs receive when the price is abnormally low. We investigate whether lucky grants to CEOs impact firm innovations and, by extension, long-term growth. Using patent citations as a proxy variable for innovation (Kogan et al., 2017), we find that innovation decreases if CEOs received lucky grant in the previous year. The results imply that lucky grants may reduce the incentive for CEOs to invest in risky, long-term projects and negatively affect fir innovation.     

A SMOOTH AMBIGUITY MODEL OF THE COMPETITIVE FIRM

This paper examines the optimal production decision of the competitive firm under price uncertainty when the firm's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second‐order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price risk. Ambiguity preferences are modeled by the (second‐order) expectation of a concave transformation of the (first‐order) expected utility of profit conditional on each plausible subjective distribution of the price risk. Within this framework, we derive necessary and sufficient conditions under which the ambiguity‐averse firm optimally produces less in response either to the introduction of ambiguity or to greater ambiguity aversion when ambiguity prevails. In the case that the price risk is binary, we show that ambiguity and greater ambiguity aversion always adversely affect the firm's production decision.     

Pigouvian pricing and stochastic evolutionary implementation

We study the implementation of efficient behavior in settings with externalities. A planner would like to ensure that a group of agents make socially optimal choices, but he only has limited information about the agents’ preferences, and can only distinguish individual agents through the actions they choose. We describe the agents’ behavior using a stochastic evolutionary model, assuming that their choice probabilities are given by the logit choice rule. We prove that there is a simple price scheme with the following property: regardless of the realization of preferences, a group of agents subjected to the price scheme will spend the vast majority of time in the long run behaving efficiently. The price scheme defines a game that may possess multiple equilibria, but we are able to obtain a unique and efficient selection from this set because of the stochastic nature of the agents’ choice rule. We conclude by comparing the performance of our price scheme with that of VCG mechanisms.     

Option-implied preferences adjustments, density forecasts, and the equity risk premium

The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two-lognormals and several alternative risk adjustments. Our results show that, between October 1996 and March 2000, we can reject the hypothesis that the risk-neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at 4- and 8-week horizons. When forecasting through risk-adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. We show that risk adjustments based on a power specification for the stochastic discount factor—which is the approach used so far in the literature that derives the objective density function from option prices- generates an excessive volatility of risk premia. We use alternative risk adjustments and find that the forecasting performance of the distribution improves slightly in some cases when risk aversion is allowed to be time-varying. Finally, from October 1996 to December 2004, the ex-ante risk premium perceived by investors and that are embedded in option prices is between 12 and 18% higher than the premium required to compensate the same investors for the realised volatility in stock market returns.      

Options and sunspots in a simple monetary economy

Summary. We study sunspot immunity in a dynamic monetary economy in which consumers are allowed to trade put and call option contracts on the general price level. We define the concept of strong sunspot immunity to characterize economies that have no sunspot equilibria regardless of the number of extrinsic states and their probabilities of occurrence. We show that a small number of option contracts can make an economy strongly sunspot immune. In addition, we demonstrate how asset re-trading opportunities, and the associated capital gains and losses, reduce the number of options needed for this result to obtain. Received: August 13, 1996; revised version: January 20, 1997     

Currency hedging with options and futures

This paper examines the optimal hedging decision of a competitive exporting firm which faces concurrently hedgeable exchange rate risk and non-hedgeable price risk. We show that the hedging role of currency options is due to two distinct sources of non-linearity: (i) the multiplicative nature of the price and exchange rate risk; and (ii) the marginal utility function of the firm. In particular, we show that a long put option position is optimal when the price risk is negatively correlated with the exchange rate risk and/or the firm is prudent.     

Past experience of uncertainty affects risk aversion

In an experiment with more than 500 participants we study how past experience of uncertainty (imperfect knowledge of the state space) affects risk preferences. Participants in our experiment choose between a sure outcome and a lottery in 32 periods. All treatments are exactly identical in periods 17–32 but differ in periods 1–16. In the early periods of the risk treatment there is perfect information about the lottery; in the ambiguity Treatment participants perfectly know the outcome space but not the associated probabilities; in the unawareness treatment participants have imperfect knowledge about both outcomes and probabilities. We observe strong treatment effects on behavior in periods 17–32. In particular, participants who have been exposed to an environment with very imperfect knowledge of the state space subsequently choose lotteries with high (low) variance less (more) often compared to other participants. Estimating individual risk attitudes from choices in periods 17–32 we find that the distribution of risk attitude parameters across our treatments can be ranked in terms of first order stochastic dominance. Our results show how exposure to environments with different degrees of uncertainty can affect individuals’ subsequent risk-taking behavior.     

The Impact of Power Distance and Uncertainty Avoidance on Real Options Exercise: Potential for Suboptimal Time Delays and Value Destruction

Real options (RO) valuation has been promoted as a way to evaluate investment opportunities and make investment decisions that takes into account the value of managerial flexibility in the face of uncertainty. Although RO enjoys a substantial body of literature considering its application and suitability in different situations, the impact of national culture on the application of RO has received little attention. Values embedded in national culture affect the behavior of managers. In particular, these values play a role in how managers frame information, communicate, and make decisions, directly and indirectly affecting behavior through cultural layers such as organizational culture. National culture, therefore, can systematically affect the application of RO, potentially leading to suboptimal outcomes. In this article, we hypothesize how 2 particularly relevant dimensions of culture, power distance and uncertainty avoidance, affect RO exercise, and estimate the magnitude suboptimality of these effects using a model we develop for the case of a put option. Our estimates suggest RO may not always be a superior valuation approach to net present value for national cultures with certain characteristics.     

Stock options and managerial optimal contracts

Summary. In this paper we are concerned with the performance of stock option contracts in the provision of managerial incentives. In our simple framework, we restrict the space of contracts available to the principal to those conformed by a fixed payment and a call option on the firms stock. As compared to the fixed payment and the option grant, we find that the strike price plays an intermediate role in the provision of insurance and incentives. We also develop some methods for the calibration of a standard principal-agent model based upon observed CEO earnings schedules and the volatility of the firms value in the stock market. These methods are useful to address some important issues such as the performance of stock option contracts, the degree of risk aversion compatible with current earnings profiles and the sensitivity of compensation to changes in firms characteristics.Received: 9 April 2003, Revised: 13 September 2004, JEL Classification Numbers: C6, D83. Correspondence to: Manuel S. SantosWe have benefitted from helpful discussions with Marco Celentani, Hector Chade, Alejandro Manelli and Ed Schlee. We are especially grateful to an anonymous referee for very detailed comments.     

Option moneyness and price disagreements

This article investigates price disagreements between actual and options-implied futures prices by considering option moneyness. Out-of-the-money (OTM) options trading induces price disagreements more frequently than at-the-money (ATM) options trading. Examining price adjustments to eliminate disagreements, we find that the futures (options) market tends to move less (more) for OTM option disagreements than ATM option disagreements, suggesting that the price dynamics of OTM options are less informative and noisier than that of ATM options.