Optimal consumption and investment with liquid and illiquid assets

I consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio that consists of one bond, one liquid risky asset (no transaction costs), and one illiquid risky asset (proportional transaction costs). I fully characterize the optimal consumption and trading strategies in terms of the solution of the free boundary ordinary differential equation (ODE) with an integral constraint. I find an explicit characterization of model parameters for the well‐posedness of the problem, and show that the problem is well posed if and only if there exists a shadow price process. Finally, I describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset.     

When do investors forgive entrepreneurs for lying?

A growing literature suggests that some entrepreneurs lie to investors in order to improve the likelihood of acquiring resources needed for firm survival and growth. We propose a framework outlining the conditions that may enable an investor who has been told a lie by an entrepreneur to respond with forgiveness rather than by withdrawing from the relationship. Integrating the literatures on evolutionary psychology, forgiveness, and stakeholder theory we argue that investor's appraisals of expected relationship value and expected exploitation risk are the key antecedents to an investor's decision to forgive an entrepreneur's lie.     

The role of the temporary component in spot prices in the revision of expected future spot prices: Evidence from index futures quotes

It is frequently argued that foreign investors have extrapolative expectations due to their informational disadvantages. That is, in the absence of other sources of information, foreigners revise their expectations on the future price of a domestic stock more in line with its current price change than do domestic investors. In this study, we analytically show that foreigners might respond more to a price change because they pay relatively less attention to a temporary component in price—i.e. because they are more well‐informed. We confirm this hypothesis with a simple yet powerful test that is designed by the identification schemes arising directly from the nature of a temporary component and by the access to a direct measure of the investor's expectation, namely, the quote for futures contracts. After controlling for the temporary component effect and using the lead–lag relationship between the spot and futures markets, we show that foreign investors are indeed most well‐informed, whereas domestic individuals are at the other end with the most extrapolative expectations. Finally, domestic institutions are largely indistinguishable from foreigners but are noticeably different from domestic individuals.     

INDIFFERENCE VALUATION OF MORTGAGE‐BACKED SECURITIES IN THE PRESENCE OF PREPAYMENT RISK

We present a utility‐based methodology for the valuation and the risk management of mortgage‐backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded prepayment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools.     

Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework

This paper formulates a utility indifference pricing model for investors trading in a discrete time financial market under nondominated model uncertainty. Investor preferences are described by possibly random utility functions defined on the positive axis. We prove that when the investors's absolute risk aversion tends to infinity, the multiple‐priors utility indifference prices of a contingent claim converge to its multiple‐priors superreplication price. We also revisit the notion of certainty equivalent for multiple‐priors and establish its relation with risk aversion.     

INVESTING WITH LIQUID AND ILLIQUID ASSETS

We find optimal trading policies for long‐term investors with constant relative risk aversion and constant investment opportunities, which include one safe asset, liquid risky assets, and an illiquid risky asset trading with proportional costs. Access to liquid assets creates a diversification motive, which reduces illiquid trading, and a hedging motive, which both reduces illiquid trading and increases liquid trading. A further tempering effect depresses the liquid asset's weight when the illiquid asset's weight is close to ideal, to keep it near that level by reducing its volatility. Multiple liquid assets lead to portfolio separation in four funds: the safe asset, the myopic portfolio, the illiquid asset, and its hedging portfolio.     

China's segmented stock market: An application of the conditional international capital asset pricing model

China's segmented stock market provides an opportunity to study conditional international asset pricing from multiple viewpoints—domestic and foreign. We use the multivariate GARCH-M framework of De Santis and Gérard [De Santis, G., and Gérard, B., 1998. How big is the premium for currency risk? Journal of Financial Economics 49, pp. 375–412.], but add conditional local specific risk and find global, local, and currency risk to be priced and time-varying in Chinese markets, suggesting mild segmentation for developing country markets. The time-varying price of currency risk indicates that the strict currency restrictions in China do not sufficiently reduce currency risk to stabilize the price of currency risk. We also find that the price of local risk in the Chinese A stock market is non-time-varying relative to the developed market, but time-varying relative to the emerging market. This finding implies that the Chinese A stock market is more comparable to a developed market than an emerging market. However, results on Chinese B shares show the opposite relationship: from a foreign investor's perspective, Chinese B shares are better categorized as being emerging than developed. This is further supported by an Engle–Granger cointegration test.     

STATIC FUND SEPARATION OF LONG‐TERM INVESTMENTS

This paper proves a class of static fund separation theorems, valid for investors with a long horizon and constant relative risk aversion, and with stochastic investment opportunities. An optimal portfolio decomposes as a constant mix of a few preference‐free funds, which are common to all investors. The weight in each fund is a constant that may depend on an investor's risk aversion, but not on the state variable, which changes over time. Vice versa, the composition of each fund may depend on the state, but not on the risk aversion, since a fund appears in the portfolios of different investors. We prove these results for two classes of models with a single state variable, and several assets with constant correlations with the state. In the linear class, the state is an Ornstein–Uhlenbeck process, risk premia are affine in the state, while volatilities and the interest rate are constant. In the square root class, the state follows a square root diffusion, expected returns and the interest rate are affine in the state, while volatilities are linear in the square root of the state.     

LIQUIDATION OF AN INDIVISIBLE ASSET WITH INDEPENDENT INVESTMENT

We provide an extension of the explicit solution of a mixed optimal stopping–optimal stochastic control problem introduced by Henderson and Hobson. The problem examines whether the optimal investment problem on a local martingale financial market is affected by the optimal liquidation of an independent indivisible asset. The indivisible asset process is defined by a homogeneous scalar stochastic differential equation, and the investor's preferences are defined by a general expected utility function. The value function is obtained in explicit form, and we prove the existence of an optimal stopping–investment strategy characterized as the limit of an explicit maximizing strategy. Our approach is based on the standard dynamic programming approach.     

Nonlinear price impact and portfolio choice

In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long‐term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square‐root impact law and, as extreme cases, linear impact and proportional transaction costs.     

Dividend policy and capital structure of a defaultable firm

Default risk significantly affects the corporate policies of a firm. We develop a model in which a limited liability entity subject to default at an exponential random time jointly sets its dividend policy and capital structure to maximize the expected lifetime utility from consumption of risk‐averse equity investors. We give a complete characterization of the solution to the singular stochastic control problem. The optimal policy involves paying dividends to keep the ratio of firm's equity value to investors' wealth below a critical threshold. Dividend payout acts as a precautionary channel to transfer wealth from the firm to investors for mitigation of losses in the event of default. Higher the default risk, more aggressively the firm leverages and pays dividends.     

A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements

This paper examines optimal consumption and investment choices and the cost of hedging contingent claims in the presence of margin requirements or, more generally, of nonlinear wealth dynamics and constraints on the portfolio policies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities' price process and the investor's preferences. As an illustration, explicit solutions are provided for an agent with ‘logarithmic’ utility. A PDE characterization of the cost of hedging a nonnegative path‐independent European contingent claim is also provided.     

PARADIGM DEPLETION,KNOWLEDGE PRODUCTION AND RESEARCH EFFORT: CONSIDERING THOMAS KUHN'S IDEAS

This paper deals in a Stackelberg differential game with Kuhn (1962) ideas of paradigm depletion and resiliency. Paradigm is considered as potential knowledge, as a stock of ideas that can be harvested to produce science. The results are: (i) paradigm depletion can be optimal, (ii) the optimal editor's shadow price of potential knowledge must be non‐positive, if it is positive, the editor is a keeper of the orthodoxy rather than a scientist, (iii) editor's and/or researcher's impatience is bad for science, and (iv) in equilibrium editor's behavior does not matter for research effort, while only editor's behavior matter for the paradigm.     

Perceived risks and choices in entrepreneurs' new venture decisions

Though risk plays a central role in most entrepreneurial decision making, little empirical research has explicitly examined how the elements of risk, risk perceptions, and entrepreneurs' propensities to take risks influence choices among potentially risky entrepreneurial ventures. This experimental study asked a sample of entrepreneurs leading America's fastest growing firms to make choices among a series of hypothetical new ventures. The results indicate that such choices are influenced by the risks inherent in the new ventures, as evidenced by the pattern of outcomes anticipated in each venture, the entrepreneurs' differing perceptions of those risks, and differences in their personal propensities to take risks.The subjects in our sample of entrepreneurs tended not to choose ventures having a high degree of variability in their pattern of anticipated outcomes. This avoidance of outcome variability suggests that the sensitivity analyses commonly prescribed for examining new venture attractiveness may inhibit risk taking, and may deter potential investors from investing in their firms. New approaches to assessing and presenting new venture risk, other than the traditional best case/expected case/worst case approach, may be advisable, as well as sufficiently through market research to provide evidence of the degree to which market acceptance is likely for the venture's products or services.We also found an effect of differences in risk propensities among entrepreneurs on their new venture choices. This effect suggests not only that entrepreneurs should be wary of any biases they bring to their new venture decisions, but that prospective investors should consider the degree to which entrepreneurs in whom they choose to invest are well-matched to the investors' own risk-taking propensities.Finally, while our sample of entrepreneurs tended to shun high levels of variability in their new venture choices, they appeared willing to accept a considerable degree of hazard, or possible downside, in their new venture choices, presumably in pursuit of potentially significant gains. Entrepreneurs are advised to seek a clear understanding of the downside entailed in their proposed ventures, and develop strategies to mitigate the likelihood of adverse outcomes. Thus they will not jeopardize chances for near term success and attracting support of investors and others in later stages of the venture or in subsequent ventures.Our research did not attempt to examine how our subjects' choices would have played out in terms of performance, but the apparent biases which entrepreneurs' risk propensities bring to their assessment of proposed new ventures is a potentially important issue that merits further scrutiny. On one hand, such biases may lead to patterns of suboptimal decisions. On the other hand, our results suggest that investors should entrust their new venture investments to entrepreneurs whose risk propensities (and perhaps other personal characteristics) best match the needs of both the opportunity at hand and the investor's objectives. As many venture capitalists attest, the management of a proposed new venture should lie at the heart of their investment decision.     

Take the money or run? Investors' ethical reputation and entrepreneurs' willingness to partner

Drawing on the multi-principal–agent perspective, this research models the influence of venture capitalists' reputation for ethical behavior on entrepreneurs' willingness to partner decisions. We test our model using a two-study design. Study one, a conjoint experiment, revealed that explicit knowledge of past unethical behavior negatively affects entrepreneurs' willingness to partner. Interaction effects revealed that factors previously shown to influence the entrepreneurs' evaluations—investor value-add and investment track record—become largely contingent upon and often subjugated by investors' ethical reputation. Study two, a traditional between-subjects scenario experiment, revealed that when entrepreneurs develop their own perceptions about the ethicality of an investor's prior behaviors, the ethical dimension remains highly influential. Further, we find that as the consequences of rejecting funding become more severe (e.g., possible bankruptcy), entrepreneurs become increasingly willing to partner with unethical investors. We also find that high fear of failure entrepreneurs are less willing to partner with unethical investors than their low fear of failure counterparts.     

Optimal partial hedging of options with small transaction costs

This study uses asymptotic analysis to derive optimal hedging strategies for option portfolios hedged using an imperfectly correlated hedging asset with small fixed and/or proportional transaction costs, obtaining explicit formulae in special cases. This is of use when it is impractical to hedge using the underlying asset itself. The hedging strategy holds a position in the hedging asset whose value lies between two bounds, which are independent of the hedging asset's current value. For low absolute correlation between hedging and hedged assets, highly risk‐averse investors and large portfolios, hedging strategies and option values differ significantly from their perfect market equivalents. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 31:855–897, 2011     

INDIFFERENCE PRICES AND IMPLIED VOLATILITIES

We consider a general local‐stochastic volatility model and an investor with exponential utility. For a European‐style contingent claim, whose payoff may depend on either a traded or nontraded asset, we derive an explicit approximation for both the buyer's and seller's indifference prices. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surfaces. For European claims on a nontraded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indifference price and implied volatility approximations in two examples.     

PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME

We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T] and can trade continuously at a traditional exchange (the “primary venue”) and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multidimensional Poisson process. We characterize the costs of trading by a linear‐quadratic functional which incorporates both the price impact costs of trading at the primary exchange and the market risk of the position. The solution of the cost minimization problem is characterized by a matrix differential equation with singular boundary condition; by means of stochastic control theory, we provide a verification argument. If a single‐asset position is to be liquidated, the investor slowly trades out of her position at the primary venue, with the remainder being placed in the dark pool at any point in time. For multi‐asset liquidations this is generally not the case; for example, it can be optimal to oversize orders in the dark pool in order to turn a poorly balanced portfolio into a portfolio bearing less risk.     

ASSET PRICE BUBBLES IN INCOMPLETE MARKETS*

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset's market and fundamental price, we characterize all possible price bubbles in an incomplete market satisfying the “no free lunch with vanishing risk (NFLVR)” and “no dominance” assumptions. We show that the two leading models for bubbles as either charges or as strict local martingales, respectively, are equivalent. We propose a new theory for bubble birth that involves a nontrivial modification of the classical martingale pricing framework. This modification involves the market exhibiting different local martingale measures across time—a possibility not previously explored within the classical theory. Finally, we investigate the pricing of derivative securities in the presence of asset price bubbles, and we show that: (i) European put options can have no bubbles; (ii) European call options and discounted forward prices have bubbles whose magnitudes are related to the asset's price bubble; (iii) with no dividends, American call options are not exercised early; (iv) European put‐call parity in market prices must always hold, regardless of bubbles; and (v) futures price bubbles can exist and they are independent of the underlying asset's price bubble. Many of these results stand in contrast to those of the classical theory. We propose, but do not implement, some new tests for the existence of asset price bubbles using derivative securities.     

Is Firm‐specific Return Variation a Measure of Information Efficiency?

The issue of whether firm‐specific return variation measures the private information reflected in stock returns or trading noise is controversial. Using a firm's geographic proximity to its investors as a proxy for a firm's private information, we investigate the relation between firm‐specific return variation and price informativeness. We find that firms located in metropolitan areas experience higher firm‐specific return variation and that holdings and trading by local institutional investors positively affect firm‐specific return variation. These findings suggest that higher firm‐specific return variation is indicative of more informative stock prices.