Skewness Preference,Risk Taking and Expected Utility Maximisation

Available empirical evidence suggests that skewness preference plays an important role in understanding asset pricing and gambling. This paper establishes a skewness-comparability condition on probability distributions that is necessary and sufficient for any decision-maker's preferences over the distributions to depend on their means, variances, and third moments only. Under the condition, an Expected Utility maximizer's preferences for a larger mean, a smaller variance, and a larger third moment are shown to parallel, respectively, his preferences for a first-degree stochastic dominant improvement, a mean-preserving contraction, and a downside risk decrease and are characterized in terms of the von Neumann-Morgenstern utility function in exactly the same way. By showing that all Bernoulli distributions are mutually skewness comparable, we further show that in the wide range of economic models where these distributions are used individuals’ decisions under risk can be understood as trade-offs between mean, variance, and skewness. Our results on skewness-inducing transformations of random variables can also be applied to analyze the effects of progressive tax reforms on the incentive to make risky investments.     

Model Misspecification and Underdiversification

In this paper, we study intertemporal portfolio choice when an investor accounts explicitly for model misspecification. We develop a framework that allows for ambiguity about not just the joint distribution of returns for all stocks in the portfolio, but also for different levels of ambiguity for the marginal distribution of returns for any subset of these stocks. We find that when the overall ambiguity about the joint distribution of returns is high, then small differences in ambiguity for the marginal return distribution will result in a portfolio that is significantly underdiversified relative to the standard mean‐variance portfolio.     

Price Convexity and Skewness

This paper develops a model in which investors who are prohibited from short selling agree to disagree on the precision of a publicly observed signal. The model implies that the equilibrium price is a convex function of the public signal. The model predicts that (1) the stock price reacts more to good news than to bad news; (2) the skewness of stock returns is positively correlated with contemporaneous returns, but negatively correlated with lagged returns; (3) short sale constraints increase rather than decrease skewness; and (4) disagreement about information precision increases skewness. Empirical tests conducted find supportive evidence for all these predictions.     

Skewness and Stock Option Prices

Abstract

In the classical Black-Scholes model, the logarithm of the stock price has a normal distribution, which excludes skewness. In this paper we consider models that allow for skewness. We propose an option-pricing formula that contains a linear adjustment to the Black-Scholes formula. This approximation is derived in the shifted Poisson model, which is a complete market model in which the exact option price has some undesirable features. The same formula is obtained in some incomplete market models in which it is assumed that the price of an option is defined by the Esscher method. For a European call option, the adjustment for skewness can be positive or negative, depending on the strike price.     

上市公司偏好、政府策略选择与会计信息失真均衡

上市公司会计信息失真可分为治理性失真、竞争性失真和干预性失真三大类.模型均衡表明,寡占博弈下的竞争性失真由真假会计信息市场信息产品边际净收益决定,与干预性、企业性因素无关,而干预性失真则由政府干预策略选择、干预强度、企业偏好和会计信息产品边际净收益等企业性、市场性和干预性三大因素决定.三大因素不对称地影响上市公司和市场的会计信息均衡,并通过改变干预性失真均衡而改变上市公司和市场会计信息绝对和相对均衡,以调节上市公司和市场的会计信息质量.实际市场信息失真主要是竞争性失真和干预性失真叠加的结果.     

Utility and the Skewness of Return in Gambling

This paper demonstrates that the intuitively appealing argument based on the postulated trade-off between expected return, variance and skewness of return of a risk-averse gambler does not provide an explanation of observed betting behaviour. It is shown how the expected utility of a representative gambler faced with a single-prized outcome event can be expressed in terms of the mean and variance of return, the mean and skewness of return or, generally, of the mean and any other single moment of return: and the standard practice of taking a Taylor series expansion/approximation of the expected utility involving moments of return is usually incorrect. Previous analyses have suggested that a punter will accept a lower mean return for higher skewness and this work seems to have involved invalid expansions of the utility function. The upshot is that with certain utility functions which have been used in a number of studies, any analysis based on expansion and estimation of the derivatives of the utility function may be valid only for data based on odds-on favourites and not for longshots.     

Interest Rate Skewness and Biased Beliefs

Conditional skewness of Treasury yields is an important indicator of the risks to the macroeconomic outlook. Positive skewness signals upside risk to interest rates during periods of accommodative monetary policy and an upward-sloping yield curve, and vice versa. Skewness has substantial predictive power for future bond excess returns, high-frequency interest rate changes around Federal Open Market Committee announcements, and survey forecast errors for interest rates. The estimated expectational errors, or biases in beliefs, are quantitatively important for statistical bond risk premia. These findings are consistent with a heterogeneous-beliefs model in which one of the agents is wrong about consumption growth.     

On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation

Recent studies in the empirical finance literature have reportedevidence of two types of asymmetries in the joint distributionof stock returns. The first is skewness in the distributionof individual stock returns. The second is an asymmetry in thedependence between stocks: stock returns appear to be more highlycorrelated during market downturns than during market upturns.In this article we examine the economic and statistical significanceof these asymmetries for asset allocation decisions in an out-of-samplesetting. We consider the problem of a constant relative riskaversion (CRRA) investor allocating wealth between the risk-freeasset, a small-cap portfolio, and a large-cap portfolio. Weuse models that can capture time-varying moments up to the fourthorder, and we use copula theory to construct models of the time-varyingdependence structure that allow for different dependence duringbear markets than bull markets. The importance of these twoasymmetries for asset allocation is assessed by comparing theperformance of a portfolio based on a normal distribution modelwith a portfolio based on a more flexible distribution model.For investors with no short-sales constraints, we find thatknowledge of higher moments and asymmetric dependence leadsto gains that are economically significant and statisticallysignificant in some cases. For short sales-constrained investorsthe gains are limited.     

What's in Your 403(b)? Academic Retirement Plans and the Costs of Underdiversification

Sponsors of defined contribution retirement plans typically limit the investment choices of plan participants to a small number of investment managers and a limited number of investment vehicles. Such restrictions may limit excessive risk-taking by participants but also may preclude opportunities for efficient diversification. Many college and university 403 (b) plans have restricted investment choices to the retirement annuities offered by TIAA-CREF, the current manager of over half of all 403(b) contributions. Using 10 years of historical data, we study the efficiency of this TIAA-CREF opportunity set relative to a larger set that includes several standard index funds. Extrapolations must be interpreted -with caution. Assuming optimal rebalancing, depending on loss aversion and diversification constraints, the historical sample of returns implies that over a 20-year remaining work life, an employee -with an expanded menu that includes standard index funds could gain over 40% in terminal wealth compared to one who is restricted to TIAA-CREF retirement annuities. Even when a naive diversification strategy of equally weighting (1/n) all available funds is used, the expandedmenu outperforms the restricted portfolio by more than 25% over20years. These differences generally are significant at conventional levels based on parametric and nonparametric testing and do not appear to result from idiosyncratic market performance durinz the sample period.     

Ex Ante Skewness and Expected Stock Returns

We use option prices to estimate ex ante higher moments of the underlying individual securities’ risk‐neutral returns distribution. We find that individual securities’ risk‐neutral volatility, skewness, and kurtosis are strongly related to future returns. Specifically, we find a negative (positive) relation between ex ante volatility (kurtosis) and subsequent returns in the cross‐section, and more ex ante negatively (positively) skewed returns yield subsequent higher (lower) returns. We analyze the extent to which these returns relations represent compensation for risk and find evidence that, even after controlling for differences in co‐moments, individual securities’ skewness matters.     

Variance Spillover and Skewness in Financial Asset Returns

Bond and stock returns have been observed in the literature to exhibit unconditional skewness and temporal persistence in conditional skewness. We demonstrate that observed persistence in conditional third central moments can be due to the spillover of conditional variance dynamics. The confounding of true skewness and a variance spillover effect is problematic for financial modeling. Using market data, we empirically demonstrate that a simple standardization approach removes the variance‐induced skewness persistence. An important implication is that more parsimonious return and asset pricing models result if skewness persistence need not be modeled.     

Conglomerate Investment,Skewness, and the CEO Long‐Shot Bias

Do behavioral biases of executives matter for corporate investment decisions? Using segment‐level capital allocation in multisegment firms (“conglomerates”) as a laboratory, we show that capital expenditure is increasing in the expected skewness of segment returns. Conglomerates invest more in high‐skewness segments than matched stand‐alone firms, and trade at a discount, which indicates overinvestment that is detrimental to shareholder wealth. Using geographical variation in gambling norms, we find that the skewness‐investment relation is particularly pronounced when CEOs are likely to find long shots attractive. Our findings suggest that CEOs allocate capital with a long‐shot bias.     

Skewness of Returns, Capital Adequacy, and Mortgage Lending

We calibrate a simulation model of credit value-at-risk for mortgage lending to UK experience. Simulations to capture the skewness of returns that might arise in the context of a financial crisis suggest that the IRB calculations of the new Basel Accord can substantially understate prudential capital adequacy. The same model shows that raising capital requirements has only a small impact on bank funding costs. We conclude that Pillar 2 supervisory review should increase capital requirements above IRB levels for secured bank assets—those whose returns can potentially fall furthest, relative to other, normally “riskier” assets, in extreme outcomes. JEL classification: G21, G28, R31. Presented at the December 2003 conference at the University of Tor Vegata, Rome. We are grateful for comments from William Lang, Mario Onarato, Larry Wall, and from an anonymous referee. All errors and omissions are our own responsibility. “The lady doth protest too much, methinks. The Queen's response to the players in Hamlet, Act 3, scene 2.     

The Analytics of the Intervaling Effect on Skewness and Kurtosis of Stock Returns

This paper analyzes how the skewness and kurtosis of securities' returns are affected by the length of the differencing interval over which returns are measured. Hawawini's previous analysis of this “intervaling effect” on log returns is shown to be incorrect, and the correct effects are derived. While Hawawini only considered log returns, we also derived the intervaling effect on the skewness and kurtosis of “simple” returns. Our results show that the length of differencing interval has very different effects on log and simple returns, but in both cases the effects on the returns' skewness and kurtosis are substantial and also quite tractable. These results also enable us to reconcile some of the contradictory results published earlier on the intervaling effect.     

The Skewness of the Price Change Distribution: A New Touchstone for Sticky Price Models

We present a new way of empirically evaluating various sticky price models that are used to assess the degree of monetary nonneutrality. While menu cost models uniformly predict that price change skewness and dispersion fall with inflation, in the Calvo model, both rise. However, the U.S. Consumer Price Index (CPI) data from the late 1970s onward show that skewness does not fall with inflation, while dispersion does. We present a random menu cost model that, with a menu cost distribution that has a strong Calvo flavor, can match the empirical patterns. The model exhibits much more monetary nonneutrality than existing menu cost models.     

Skewness and Kurtosis Implied by Option Prices: A Correction

Corrado and Su (1996) provide skewness and kurtosis adjustment terms for the Black‐Scholes model, using a Gram‐Charlier expansion of the normal density function. In this note we provide a correction to the expression for the skewness coefficient and illustrate the effect on call option prices of the error found.     

Individuals and Their Local Utility Stocks: Preference for the Familiar

We find individuals are four times more likely to purchase stocks of their local direct utility company as opposed to utility companies operating outside their state of residence. Our tests reveal that individuals do not possess superior or private information about their local utilities. Indeed, individual preference for their local utility stocks seems to be driven by preference for familiar assets, even in the presence of a desire for high dividend yields. In addition, affluence and sophistication do not reduce local bias.     

Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns

This paper utilizes the most flexible skewed generalized t (SGT) distribution for describing petroleum and metal volatilities that are characterized by leptokurtosis and skewness in order to provide better approximations of the reality. The empirical results indicate that the forecasted Value-at-Risk (VaR) obtained using the SGT distribution provides the most accurate out-of-sample forecasts for both the petroleum and metal markets. With regard to the unconditional and conditional coverage tests, the SGT distribution produces the most appropriate VaR estimates in terms of the total number of rejections; this is followed by the nonparametric distribution, generalized error distribution (GED), and finally the normal distribution. Similarly, in the dynamic quantile test, the VaR estimates generated by the SGT and nonparametric distributions perform better than that generated by other distributions. Finally, in the superior predictive test, the SGT distribution has significantly lower capital requirements than the nonparametric distribution for most commodities.