Not knowing the competition: evidence and implications for auction design

In a government auction program where first-price auctions generate significantly higher revenue than English auctions, I document evidence that bidders are uncertain about the number of auction entrants. Motivated by additional data evidence, I estimate a structural model of auctions in which rivals' participation is stochastic, allowing for bidders' risk aversion and asymmetry. Counterfactual simulations reveal that bidders' uncertainty about the number of entrants, combined with risk aversion, substantially softens the revenue impact of low competition in first-price auctions. This explains the observed revenue patterns and uncovers an empirically important reason for sellers to favor first-price auctions over English auctions.     

Age‐Dependent Increasing Risk Aversion and the Equity Premium Puzzle

We introduce a new preference structure—age‐dependent increasing risk aversion (IRA)—in a three‐period overlapping generations model with borrowing constraints, and examine the behavior of equity premium in this framework. We find that IRA preferences generate results that are more consistent with U.S. data for the equity premium, level of savings and portfolio shares, without assuming unreasonable levels of risk aversion. We find that the relative difference between the two risk aversions (how much more risk‐averse old agents are relative to the middle‐aged) matters more than the average risk aversion in the economy (how much more risk‐averse both cohorts are). Our findings are robust with respect to a number of model generalizations.     

Auctions with ex post uncertainty

Uncertainty about ex post realized values is an inherent component in many auction environments. In this article, we develop a structural framework to analyze auction data subject to ex post uncertainty as a pure risk. We consider a low‐price sealed‐bid auction model with heterogeneous bidders' preferences and ex post uncertainty. The uncertainty can be common to all bidders or idiosyncratic. We derive the model restrictions and study nonparametric and semiparametric identification of the model primitives under exogenous and endogenous participation. We then develop multistep nonparametric and semiparametric estimation procedures in both cases.     

Risk aversion, intertemporal substitution, and the aggregate investment-uncertainty relationship

We analyze the role of risk aversion and intertemporal substitution in a simple dynamic general equilibrium model of investment and savings. Our main finding is that risk aversion cannot by itself explain a negative relationship between aggregate investment and aggregate uncertainty, as the effect of increased uncertainty on investment also depends on the intertemporal elasticity of substitution. In particular, the relationship between aggregate investment and aggregate uncertainty is positive even if agents are very risk averse, as long as the elasticity of intertemporal substitution is low. A negative investment-uncertainty relationship requires that the relative risk aversion and the elasticity of intertemporal substitution are both relatively high or both relatively low. We also show that the implications of our model are consistent with the available empirical evidence.     

Optimal Life-Cycle Asset Allocation: Understanding the Empirical Evidence

We show that a life‐cycle model with realistically calibrated uninsurable labor income risk and moderate risk aversion can simultaneously match stock market participation rates and asset allocation decisions conditional on participation. The key ingredients of the model are Epstein–Zin preferences, a fixed stock market entry cost, and moderate heterogeneity in risk aversion. Households with low risk aversion smooth earnings shocks with a small buffer stock of assets, and consequently most of them (optimally) never invest in equities. Therefore, the marginal stockholders are (endogenously) more risk averse, and as a result they do not invest their portfolios fully in stocks.     

Risk aversion and the yield of corporate debt

This paper develops a model to estimate the implied default probability of corporate bonds. The model explicitly considers the risk averse behavior of investors to provide a more precise framework for estimating the implied default probability. A Kalman filter method is used to estimate time-varying risk premium associated with the investor's risk aversion. The results of nonlinear regressions indicate that previous risk-neutrality models consistently overestimate the implied default rates of corporate bonds. The results also suggest that investors may have been adequately compensated for investment in risky bonds.     

Liquidity Risk and the Dynamics of Arbitrage Capital

We develop a continuous‐time model of liquidity provision in which hedgers can trade multiple risky assets with arbitrageurs. Arbitrageurs have constant relative risk‐aversion (CRRA) utility, while hedgers' asset demand is independent of wealth. An increase in hedgers' risk aversion can make arbitrageurs endogenously more risk‐averse. Because arbitrageurs generate endogenous risk, an increase in their wealth or a reduction in their CRRA coefficient can raise risk premia despite Sharpe ratios declining. Arbitrageur wealth is a priced risk factor because assets held by arbitrageurs offer high expected returns but suffer the most when wealth drops. Aggregate illiquidity, which declines in wealth, captures that factor.     

Strategic design under uncertain evaluations: structural analysis of design‐build auctions

I investigate firms' competition over price and product design under uncertain design evaluations in the context of Design‐Build (DB) auctions. Reviewers' design evaluations contain uncertainty from a bidder's perspective, leading luck to dampen differences in the firms' chances of winning. I model bidders' behavior and show semiparametric identification of the model primitives. Uncertain design evaluations increase the expected price of design quality and exacerbate an auctioneer's uncertainty in auction outcomes. These effects are mostly due to changes in bidding strategies. Bid ranking swaps due to uncertain evaluations account for a small share of these effects.     

Information feedback in first price auctions

I apply the notion of a self‐confirming equilibrium (SCE) to study how feedback in first price auctions influences bidders' perceptions about their strategic environment, and consequently their bidding behavior. In a private values setting, revealing the two highest bids at the end of each auction is sufficient for bidders to have correct beliefs (justifying the assumption of Nash equilibrium). In contrast, in every symmetric SCE of a symmetric, affiliated, private values model, bidding strategies and revenue are (weakly) higher if only the highest bid is revealed. I also consider interdependent valuations and discuss implications for the empirical auction literature.     

The Winner's Curse and Bidder Competition in Acquisitions: Evidence from Failed Bank Auctions

This study examines the effect of bidder competition in acquisitions. We use predictions from auction theory to test whether acquirers of failed banks overpay (the “winner's curse”) when bidding in FDIC sealed-bid purchase and assumption (P&A) transactions (auctions). The empirical results indicate that winning bids tend to increase as the number of competitors increases, as predicted by theory. We also find that bid levels of all bidders increase with increased competition, which is consistent with bidders' failing to adjust for the winner's curse in a common value auction setting. However, additional tests using winning bids only are consistent with both a common value and a private values model, so this result should be interpreted with caution.     

RULE CHANGES AND UNCERTAINTY IN DISCRIMINATORY AND UNIFORM PRICE AUCTIONS

The auction literature indicates that uncertainty about the value of auctioned goods increases underpricing in discriminatory price auctions. Such uncertainty has a smaller effect on uniform price auctions because the pricing rule aggregates bidders' information. We find that uncertainty resulting from inexperience with an auction mechanism has similar effects. Using initial public offering (IPO) data from Japan and Israel, we find that average underpricing increases temporarily in Japan's discriminatory price auctions after changes in the auction rules, which suggests that bidders reduce their bids in response to uncertainty. Underpricing in Israel's uniform price auctions is not affected by rule changes.     

Optimal Carried Interest: Adverse Selection in Islamic and Conventional Venture Capital and Private-Equity Funds

In an optimal carried interest model with adverse selection, the optimal profit-loss sharing ratio (PSR) explains how the risk aversion of the two parties can affect their bargaining powers by allowing investors to detect the true risk aversion of fund managers and not their true skills. The higher the management fee, the higher is the PSR. Our simulation exercise shows that when the fund manager is more risk averse than the investor for a higher invested capital and weaker expected net profit, the optimal negotiated profit-sharing ratio will be higher.     

Optimal portfolio delegation when parties have different coefficients of risk aversion

We consider the problem of delegated portfolio management when the involved parties are risk-averse. The agent invests the principal's money in the financial market, and in return he receives a compensation which depends on the value that he generates over some period of time. We use a dual approach to explicitly solve the agent's problem analytically and subsequently we use this solution to solve the principal's problem numerically. The interaction between the principal's and the agent's risk aversion and the optimal compensation scheme is studied and, for example, in the case of the more risk averse agent according to common folklore the principal should optimally choose a fee schedule such that the agent's derived risk aversion decreases. We illustrate that this is not always the case.     

Strong Increases in Downside Risk Aversion

A ranking of risk preferences is of economic interest insofar as it leads to unambiguous comparative statics predictions, and for this to be the case, the ranking must be a strict partial ordering. The ranking by greater risk aversion meets this demand at the second order, and yields a variety of well-known predictions concerning the effect of greater risk aversion on demands for insurance and risky assets, among many other applications. There has been less success at the third order, where ranking preferences by aversion to downside risk has not produced a strict partial ordering. The problem is that account has not been taken of the fact that an increase in downside risk aversion must induce changes in risk aversion as well. We propose a definition of stronger downside risk aversion that does yield a strict partial ordering by requiring a nested increase in both second- and third-order risk aversion, so that v is more strongly downside risk averse than u if v is more risk averse and more downside risk averse than u. We demonstrate that v being more strongly downside risk averse than u is characterized by v never liking any change in the probability distribution for y that induces a third-order stochastic dominance deterioration in the distribution for u(y). We apply the definition to obtain intuitive comparative statics predictions in the precautionary saving problem, and relate the definition to alternatives proposed in the literature.     

Information‐Hedging Disclosures and Insider Trading

I model the effect of disclosure on the tradeoff between information risk, liquidity risk, and price risk for a well‐informed, risk‐averse insider. Revealing some information before trading decreases the variability of the insider's information advantage and thus reduces his information risk. Disclosure also lowers adverse selection costs for market makers, which reduces the insider's liquidity risk by increasing his trading flexibility. However, disclosure increases price risk for the insider because the price fully reflects the revealed information. The reduction in information and liquidity risks outweigh the rise in price risk when the insider is less risk averse because a less risk‐averse insider's information‐based motive for trading is stronger than his hedging motive. The opposite relation holds when the insider is more risk averse. Therefore, a less (more) risk‐averse insider experiences an increase (decrease) in welfare when he discloses some information before trading. Cost of capital and policy implications are identified.     

Does knowledge of finance mitigate the gender difference in financial risk-aversion?

We investigate the gender difference in financial risk aversion using a survey of finance professors from universities across the United States. We compare their actual portfolio allocations to that of respondents in the Federal Reserve's Survey of Consumer Finances (SCF). We find that among highly educated individuals, women are significantly more risk averse than men. However, we find that when men and women have both attained a high level of financial education, they are equally likely to invest a significant portion of their portfolio in risky assets, suggesting that financial education mitigates the gender difference in financial risk aversion.     

Convex risk measures based on generalized lower deviation and their applications

Considering the implementability and the properties that a reasonable and realistic risk measure should satisfy, we propose a new class of risk measures based on generalized lower deviation with respect to a chosen benchmark. Besides convexity and monotonicity, our new risk measure can reflect the investor's degree of risk aversion as well as the fat-tail phenomenon of the loss distribution with the help of different benchmarks and weighted functions. Based on the new risk measure, we establish a realistic portfolio selection model taking market frictions into account. To examine the influence of the benchmarks and weighted functions on the optimal portfolio and its performance, we carry out a series of empirical studies in Chinese stock markets. Our in-sample and out-of-sample results show that the new risk measure and the corresponding portfolio selection model can reflect the investor's risk averse attitude and the impact of different trading constraints. Most importantly, with the new risk measure we can obtain an optimal portfolio which is more robust and superior to the optimal portfolios obtained with the traditional expected shortfall risk measures.     

RISK PREFERENCES AND INFORMATION FLOWS IN RACETRACK BETTING MARKETS

Racetrack betting markets provide a unique environment to study risk preferences of investors. In this paper, we define the effects of different risk preferences on the subjective and objective probabilities of winning at racetracks. Our results indicate that up to three groups of bettors participate in these markets: risk loving, risk averse with an entertainment value in their utility functions, and risk averse with superior information or analytical ability. We find that information flows from the tote board concerning the three groups' behavior may be used to earn abnormal and possibly positive returns.     

Heterogeneous Beliefs, Speculation, and the Equity Premium

Agents with heterogeneous beliefs about fundamental growth do not share risks perfectly but instead speculate with each other on the relative accuracy of their models' predictions. They face the risk that market prices move more in line with the trading models of competing agents than with their own. Less risk‐averse agents speculate more aggressively and demand higher risk premiums. My calibrated model generates countercyclical consumption volatility, earnings forecast dispersion, and cross‐sectional consumption dispersion. With a risk aversion coefficient less than one, agents' speculation causes half the observed equity premium and lowers the riskless rate by about 1%.     

The economics of club bidding and value creation

Many acquisitions are conducted by clubs, i.e., coalitions of acquirers that submit a single bid. We present a novel analysis of club bidding where the club creates value by aggregating, at least partially, bidders' values. We show that club formation can lead to higher acquisition prices when the number of bidders is exogenously fixed and large. However, when entry costs require bidders to optimize their participation decisions, club formation acts as an endogenous limit on competition and reduces the target's premium. In contrast, social efficiency with club bidding is always higher. Our findings can reconcile the contradictory evidence on club bidding.