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.     

An examination of predictable risk and return in UK stock returns

This paper examines whether conditional asset pricing models can explain the predictability in UK stock returns using the frameworks of Ferson and Harvey (1999) and Kirby (1998). The paper finds that the domestic Arbitrage Pricing Theory model is able to explain most of the observed time-series predictability in stock returns and tends to perform better than the domestic CAPM in explaining the predictability generated by the predictive instruments. The paper also finds that domestic asset pricing models tends to capture more of the time-series predictability in UK stock returns than international models. However none of the models are able to explain all of the predictability in returns.     

A Discrete‐Time Intertemporal Asset Pricing Model: GE Approach with Recursive Utility

This paper studies the equilibrium characterization of asset pricing in a discrete‐time Lucas exchange economy (Lucas 1978) with the intertemporal recursive utility function of Epstein and Zin (1989). A general formulation of equilibrium asset pricing is presented. It is shown that risk aversion of a certainty equivalent corresponds to risk aversion in the intertemporal asset pricing model. The discrete‐time analogue of Ma's (1993) option pricing formula is derived in an i.i.d. environment, with which we prove an observational nonequivalence theorem in distinguishing the differences of the betweenness recursive utility functions and the expected utility functions. Additionally, when the consumption growth rate follows a first-order Markov process, it is shown that the observational nonequivalence result holds for Kreps–Porteus expected utility. Finally, as by-products, this paper also contains derivations of closed-form formulas for the aggregate equity (with endogenously determined yields), the term structure of interest rates, and European call options on the aggregate equity in a Markov setting.     

Systematic risk in emerging markets: the D-CAPM

There is by now a growing literature arguing against the use of the CAPM to estimate required returns on equity in emerging markets (EMs). One of the characteristics of this model is that it measures risk by beta, which follows from an equilibrium in which investors display mean–variance behavior. In that framework, risk is assessed by the variance of returns, a questionable and restrictive measure of risk. The semivariance of returns is a more plausible measure of risk and can be used to generate an alternative behavioral hypothesis (mean–semivariance behavior), an alternative measure of risk for diversified investors (the downside beta), and an alternative pricing model (the downside CAPM, or D-CAPM for short). The empirical evidence discussed below for the entire Morgan Stanley Capital Indices database of EMs clearly supports the downside beta and the D-CAPM over beta and the CAPM.     

SKEWNESS‐AWARE ASSET ALLOCATION: A NEW THEORETICAL FRAMEWORK AND EMPIRICAL EVIDENCE

This paper presents a new measure of skewness, skewness‐aware deviation, that can be linked to prospective satisficing risk measures and tail risk measures such as Value‐at‐Risk. We show that this measure of skewness arises naturally also when one thinks of maximizing the certainty equivalent for an investor with a negative exponential utility function, thus bringing together the mean‐risk, expected utility, and prospective satisficing measures frameworks for an important class of investor preferences. We generalize the idea of variance and covariance in the new skewness‐aware asset pricing and allocation framework. We show via computational experiments that the proposed approach results in improved and intuitively appealing asset allocation when returns follow real‐world or simulated skewed distributions. We also suggest a skewness‐aware equivalent of the classical Capital Asset Pricing Model beta, and study its consistency with the observed behavior of the stocks traded at the NYSE between 1963 and 2006.     

Market integration in developed and emerging markets: Evidence from the CAPM

Beta, as measured by the Capital Asset Pricing Model (CAPM), is widely used for pricing stocks, determining the cost of capital, and gauging the extent to which markets are integrated. The CAPM model assumes that equilibrium conditions prevail. The choice of which market portfolio to use in the regression – the home country or global index – depends on the level of global market integration. We present several new empirical observations on the pricing of stocks and market integration. We provide guidance on how practitioners should calculate beta on securities in various developed and emerging markets.     

PORTFOLIO SELECTION WITH MONOTONE MEAN-VARIANCE PREFERENCES

We propose a portfolio selection model based on a class of monotone preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to be monotone and are therefore not economically meaningful. The functional associated with this new class of preferences is the best approximation of the mean-variance functional among those which are monotonic. We solve the portfolio selection problem and we derive a monotone version of the capital asset pricing model (CAPM), which has two main features: (i) it is, unlike the standard CAPM model, arbitrage free, (ii) it has empirically testable CAPM-like relations. The monotone CAPM has thus a sounder theoretical foundation than the standard CAPM and a comparable empirical tractability.     

权证发行对标的股票价格风险影响的实证研究

研究权证发行对标的证券价格风险的影响,对研究资本市场的有效性及权证定价等方面具有重要的意义。目前我国已经发行的备兑权证,运用资本资产定价模型(CAPM)和GARCH-M模型,探讨权证的发行时正股的无风险报酬、系统性风险(Beta)和总风险(报酬率波动性)是否有显著影响。实证结果表明,无论是认购权证、认沽权证,还是蝶式权证的发行对正股的无风险报酬、系统性风险的影响基本上均不显著,但对半数以上发行权证的股票的总风险有显著影响。抑制权证市场的投机性,发挥其本身应发挥的价格发现功能、促进股票的流动性、降低股价波动性等的功能,就必须从风险相互对冲的角度,循序渐进地大力发展权证等衍生产品的规模,促进衍生品市场健康、有序地发展。     

Stock pricing in Latin America: The synchronicity effect

This paper investigated whether the stock price synchronicity level (SPSL) is a pricing factor in the Latin American scenario. To do so, the shares with the highest liquidity level listed in the stock exchange in five Latin American (LA) countries (Argentina, Brazil, Chile, Mexico and Peru) were used. The results indicated that the SPSL is associated with a positive premium. This premium was obtained by the CAPM model and by the Fama-French three- and five-factor models. There was evidence that the average SPSL increases in periods of greater turmoil in the financial markets. Moreover, it was found that the SPSLs are not associated monotonically with the efficiency levels of stock prices. Overall, the use of the SPSL factor in asset pricing models reduced the bias in estimating the stock premiums in LA.     

多因素资产定价模型的实证研究

以上海股市417家A股股票为样本,以2000年2月18日至2001年6月8日的周收益率为样本数据,研究股票组合收益与各种因素之间的关系,建立9个单因素模型和6个四因素模型。结果发现:6种风险度量指标对股票组合收益率的解释能力十分微弱,而平均流通市值的自然对数和平均短期(1年)历史收益率对股票组合收益率的解释能力达到76.2％。因此,在上海A股市场,CAPM失去了有效性,资产定价可以由多因素模型决定。     

基于CAPM的人力成本计量模型研究

在人力资本产权理论下,二元资本结构已被考虑了人力资本的三元资本结构所取代,合理计量人力资本成本成为企业管理的迫切要求。本文把人力资本分为五大类型,在类型范围内计量个体人力成本,并对资本资产定价模型(CAPM)进行两个层次的修正,构建了考虑风险因素的人力资本成本计量模型,该模型对现代企业人力资本成本的合理计量具有指导作用。     

TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION

Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance, and support information. No additional restrictions on the type of distribution such as normality is made. The investor’s utility is modeled as a piecewise‐linear concave function. We derive exact and approximate optimal trading strategies for a robust (maximin) expected utility model, where the investor maximizes his worst‐case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Extensions of the model to capture asymmetry using partitioned statistics information and box‐type uncertainty in the mean and covariance matrix are provided. Using the optimized certainty equivalent framework, we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst‐case risk under distributional ambiguity. New closed‐form results for the worst‐case optimized certainty equivalent risk measures and optimal portfolios are provided for two‐ and three‐piece utility functions. For more complicated utility functions, computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.     

Dynamically consistent alpha‐maxmin expected utility

The alpha‐maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of alpha. In this paper, we derive a recursive, dynamically consistent version of the alpha‐maxmin model. In the continuous‐time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level. We study the properties of the utility function and provide an Arrow–Pratt approximation of the static and dynamic certainty equivalent. We then derive a consumption‐based capital asset pricing formula and study the implications for derivative valuation under indifference pricing.     

An intertemporal capital asset pricing model under heterogeneous beliefs

An intertemporal CAMP under heterogeneous beliefs is derived. It is shown that an asset's risk consists of three components: the market consensus of volatility risk, the market consensus of the risk induced by changes in the investment opportunity set, and risk associated with uncertain shifts in investor's subjective expectations. The multiperiod market price of risk with heterogeneous beliefs defines a new structure of market risk that captures contemporaneous changes in investors' subjective expectations and the dynamics of the investment opportunity set. The investors' demand for risky assets also is examined under heterogeneous belief. In addition, the model derived provides a generalized version of other CAPM's, such as the classical CAPM, Merton's intertemporal CAPM, and Bredeen's consumption-based CAPM.     

Computational aspects of robust optimized certainty equivalents and option pricing

Accounting for model uncertainty in risk management and option pricing leads to infinite‐dimensional optimization problems that are both analytically and numerically intractable. In this article, we study when this hurdle can be overcome for the so‐called optimized certainty equivalent (OCE) risk measure—including the average value‐at‐risk as a special case. First, we focus on the case where the uncertainty is modeled by a nonlinear expectation that penalizes distributions that are “far” in terms of optimal‐transport distance (e.g. Wasserstein distance) from a given baseline distribution. It turns out that the computation of the robust OCE reduces to a finite‐dimensional problem, which in some cases can even be solved explicitly. This principle also applies to the shortfall risk measure as well as for the pricing of European options. Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions. Finally, we give conditions on the latter set under which the robust average value‐at‐risk is a tail risk measure.     

资本资产定价扩展模型理论及其发展趋势

组合投资理论自从马柯维茨1952年建立以来,一直在迅速发展,特别是夏普(1962)、林特尔(1965)和摩森(1966)提出并发展了资本资产定价模型(CAPM)后,使纯粹的理论研究有机会应用于实际证券分析当中。但是,CAPM忽略了许多因素的影响,使CAPM理论与实际存在难以弥合的距离。为此,对CAPM进行修正和补充就成为后来学者研究的重点。     

EQUILIBRIUM ASSET AND OPTION PRICING UNDER JUMP DIFFUSION

This paper develops an equilibrium asset and option pricing model in a production economy under jump diffusion. The model provides analytical formulas for an equity premium and a more general pricing kernel that links the physical and risk‐neutral densities. The model explains the two empirical phenomena of the negative variance risk premium and implied volatility smirk if market crashes are expected. Model estimation with the S&P 500 index from 1985 to 2005 shows that jump size is indeed negative and the risk aversion coefficient has a reasonable value when taking the jump into account.     

A BENCHMARK APPROACH TO FINANCE

This paper derives a unified framework for portfolio optimization, derivative pricing, financial modeling, and risk measurement. It is based on the natural assumption that investors prefer more rather than less, in the sense that given two portfolios with the same diffusion coefficient value, the one with the higher drift is preferred. Each such investor is shown to hold an efficient portfolio in the sense of Markowitz with units in the market portfolio and the savings account. The market portfolio of investable wealth is shown to equal a combination of the growth optimal portfolio (GOP) and the savings account. In this setup the capital asset pricing model follows without the use of expected utility functions, Markovianity, or equilibrium assumptions. The expected increase of the discounted value of the GOP is shown to coincide with the expected increase of its discounted underlying value. The discounted GOP has the dynamics of a time transformed squared Bessel process of dimension four. The time transformation is given by the discounted underlying value of the GOP. The squared volatility of the GOP equals the discounted GOP drift, when expressed in units of the discounted GOP. Risk-neutral derivative pricing and actuarial pricing are generalized by the fair pricing concept, which uses the GOP as numeraire and the real-world probability measure as pricing measure. An equivalent risk-neutral martingale measure does not exist under the derived minimal market model.     

Pricing collateralized derivatives with an arbitrary numeraire

Since the 2008 crisis collateralized derivatives have become commonplace in the market. There have been many papers in recent years on pricing collateralized derivatives but the topic has been surrounded by confusion with debate focusing on whether or not a risk‐free rate needs to be assumed. In addition, as pointed out by Bielecki and Rutkowski, several authors do not pay enough attention to the pricing measure they are working in when setting up their models. The contribution of this paper is to show the pricing formula for a collateralized derivative can be derived under the usual assumptions of an arbitrage‐free economy starting from any equivalent martingale measure and associated numeraire.     

Derivatives pricing with liquidity risk

This paper develops a novel, general derivative pricing model which introduces a liquidity risk factor. The model variants we outline offer a sufficient degree of flexibility so as to enable the valuation of various types of derivative classes including futures, American options, and mortgage backed security options, whereas existing derivative models can only price liquidity risk in European derivatives. We validate the model with oil and gold futures data and compare it to a classical benchmark model void of any liquidity risk. We find that our model is significantly more accurate than the classical model for pricing both oil and gold contracts.