Preference For Positive Skewness Research Articles

Corporate Insider Trading and Return Skewness

Corporate insider trades predict idiosyncratic return skewness. CEO purchases are followed by an increase and CEO sales by a decrease in idiosyncratic skewness. The evidence suggests that this effect is driven by personal preferences rather than behavioral biases such as overconfidence. Our findings are consistent with the interpretation that CEOs, who are generally considered to be underdiversified, optimize their holdings by taking a preference for positive skewness into account. We observe particularly robust results for CEO sales, which substantiates the less common notion that insider sales can be informative for investors.

Cumulative prospect theory and mean–variance analysis: a rigorous comparison

We propose a numerical optimization approach that can be used to solve portfolio selection problems including several assets and involving objective functions from cumulative prospect theory (CPT). Implementing the suggested algorithm, we compare asset allocations that are derived for CPT based on two different methods: maximizing CPT along the mean–variance efficient frontier so that simple mean–variance algorithms can be used, and maximizing CPT without this restriction. According to the theoretical literature, with normally distributed returns and unlimited short sales, these two approaches lead to the same optimal solutions. We find that for empirical finite discrete distributions obtained via sampling and subsequent clustering from a normal distribution, the difference between the two approaches remains negligible even if short sales are restricted. However, if standard asset allocation data for pension funds is considered, the difference is considerable. Moreover, for certain types of derivatives, such as call options, the restriction of asset allocations to the mean–variance efficient frontier produces sizable losses in various respects, including decreases in expected returns and expected utility. We are able to explain these differences by CPT’s preference for positive skewness, which is not accounted for by optimizing CPT along the mean–variance efficient frontier.

Insurance Choice Under Third Degree Stochastic Dominance

In this paper, we investigate the insurance choice of a risk-averse insured with a positive skewness preference, where the insurance premium is calculated by a general mean-variance principle. The proposed class of premium principles is quite general in the sense that it includes the expected value principle, variance related principles and mean value principle as special cases. When the indemnity is assumed to be increasing and concave in the loss, we show that the expected utility of the insured's final wealth can be improved by purchasing a dual change-loss insurance policy. It is further sub-optimal to a quota-share insurance contract for the expected value premium principle and variance related premium principles. However, the quota-share insurance often is not an optimal choice for mean value premium principle.

Probability Weighting and Asset Prices: Evidence from Mergers and Acquisitions

For mergers and acquisitions with a small failure probability, the average decline in target stock price if the deal fails is much larger than any increase that accompanies deal success. Probability weighting implies that the deal failure probability of such target stocks will be overweighted, leading them to be undervalued. I test whether investors are averse to holding such stocks and find strong supporting evidence. Target stocks with lower ex-ante failure probability yield positive abnormal returns, but other targets do not generate significant abnormal returns. A trading strategy that buys target stocks with low ex-ante failure probability and sells short target stocks with high ex-ante failure probability delivers around 1% abnormal return per month. These abnormal returns are not subsumed by a preference for positive skewness under traditional (expected) utility models; in fact, target stocks with lower ex-ante failure probability have lower betas, lower volatilities, and lower downside risk. I also find that profits from the strategy are significantly higher when arbitrage is more difficult.

Probability Weighting and Asset Prices: Evidence from Mergers and Acquisitions

For mergers and acquisitions with a small failure probability, the average decline in target stock price if the deal fails is much larger than any increase that accompanies deal success. Probability weighting implies that the deal failure probability of such target stocks will be overweighted, leading them to be undervalued. I test whether investors are averse to holding such stocks and find strong supporting evidence. Target stocks with lower ex-ante failure probability yield positive abnormal returns, but other targets do not generate significant abnormal returns. A trading strategy that buys target stocks with low ex-ante failure probability and sells short target stocks with high ex-ante failure probability delivers around 1% abnormal return per month. These abnormal returns are not subsumed by a preference for positive skewness under traditional (expected) utility models; in fact, target stocks with lower ex-ante failure probability have lower betas, lower volatilities, and lower downside risk. I also find that profits from the strategy are significantly higher when arbitrage is more difficult.

Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?

AbstractWe investigate the pricing of risk-neutral skewness in the stock options market by creating skewness assets comprised of two option positions (one long and one short) and a position in the underlying stock. The assets are created such that exposure to changes in the underlying stock price (delta), and exposure to changes in implied volatility (vega) are removed, isolating the effect of skewness. We find a strong negative relation between risk-neutral skewness and the skewness asset returns, consistent with a positive skewness preference. The returns are not explained by well-known market, size, book-to-market, momentum, short-term reversal, volatility, or option market factors.

Aggregate investor preferences and beliefs in stock market: A stochastic dominance analysis

Abstract This paper analyzes whether the market portfolio is efficiently related to benchmark portfolios formed on size, value, momentum and reversal with various utility theories by using stochastic dominance criteria. The results support the prospect theory including assumption of loss aversion at monthly and yearly horizons, which indicates the market utility is S-shaped, and steeper for losses than for gains. And, the findings do not provide convincing evidence for positive skewness preference. Therefore, it should probe into asset pricing model and financial puzzles by prospect theory preferences. It may thus be difficult for the market to benefit from the asset through its features on skewness or other higher order central moment. We also develop several bootstrap procedures with favorable properties in statistical size and power for testing stochastic dominance efficiency.

Skewness Preference in Financial Markets

Studies on the importance of skewness for investors find a negative relation between the risk premium and skewness, implying preference for positive skewness. Hedge funds (or money managers in general), however, acting as agents, may have preference for negative skewness as it would mean frequent returns and thus bonuses and more importantly survival at the job. I study skewness preferences of hedge funds and small, retail investors. I find a negative relation between the risk premium and a robust skewness measure for an index of small-cap stocks and one of the oldest closed-end funds, both of which tend to have a higher proportion of retail ownership, suggesting preference for positive skewness. For a hedge fund index, on the other hand, I find a positive relation, suggesting preference for negative skewness. In time periods when skewness is positive, hedge funds have a stronger preference for negative skewness, indicative of their strong aversion to skewness. These results suggest that skewness preference in financial markets need not always be for positive skewness, which seems to be the general consensus in the literature, once the agency problem and survival and compensation motives of money managers are recognized.

Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?

We investigate the pricing of risk-neutral skewness in the stock options market by creating skewness assets comprised of two option positions (one long and one short) and a position in the underlying stock. The assets are created such that exposure to changes in the underlying stock price (delta), and exposure to changes in implied volatility (vega) are removed, isolating the effect of skewness. We find a strong negative relation between risk-neutral skewness and the skewness asset returns, consistent with a positive skewness preference. The returns are not explained by well-known market, size, book-to-market, momentum, short-term reversal, volatility, or option market factors.

Preference for Positive Skewness and Expected Stock Returns

This paper investigates the role of skewness preference in cross-sectional pricing of NYSE, AMEX, and NASDAQ stocks over the long sample period of January 1926-December 2005 as well as two subsamples. Portfolio-level analyses and the firm-level cross-sectional regressions indicate a negative and significant relation between total skewness and expected stock returns. After controlling for size, book-to-market, momentum, liquidity, and idiosyncratic volatility, the negative relation between total skewness and expected returns remains economically and statistically significant. These results hold for the NYSE stocks, after screening for size, price, and liquidity, and they are also robust across different sample periods. We decompose total skewness into idiosyncratic and systematic components and find a significantly negative relation between idiosyncratic skewness and the cross-section of expected returns, whereas there is no evidence for a significant link between systematic skewness and average stock returns.

Skewness in individual stocks at different investment horizons

This paper examines the (a)symmetry of several individual stock returns at different investment horizons: daily, weekly and monthly. While some asymmetries are observed in daily returns, they disappear almost completely in weekly and monthly returns. The explanation for this fact lies in the convergence to normality that takes place when the investment horizon increases. These features allow one to question several financial models; in particular, they question the preference for positive skewness as a factor for investments in stock markets.

Skewness preference, mean-variance and the demand for put options

This paper compares the mean–variance and the mean–variance–skewness approaches to modelling expected utility. Attention is focused on a problem encountered in risk management: determining the optimal demand for a put option hedging the return on an asset with a negatively skewed return distribution. It is demonstrated theoretically that incorporating positive skewness preference into the decision-maker's objective function typically produces a reduction in the demand for put options when compared with the mean–variance solution. A state-dependent example is provided to illustrate how a mean–variance–skewness objective can result in a significant reduction in the optimal amount of crop insurance demanded when compared with the mean–variance solution. Copyright © 1999 John Wiley & Sons, Ltd.

Why a Decision Maker May Prefer a Seemingly Unfair Gamble

It is generally believed that risk-averse managers will not accept unfair gambles and therefore may not have the incentive to invest in high-risk projects, products or technology. This paper argues that this is not necessarily so. Rational, risk-averse managers with sufficient preference for positive skewness may undertake projects with payoff distributions that are unfair gambles. Furthermore, the minimum required payoff is shown to be less for managers with preference for positive skewness than otherwise. Thus, a risk-averse manager with preference for positive skewness may accept potentially innovative high-risk projects that are rejected by those without such preference.

Skewness, sampling risk, and the importance of diversification

Recent papers have extended portfolio theory to include skewness along with mean return and variance to explain security preferences. Because the positive skewness typically present in individual assets such as stocks and call options is rapidly reduced through diversification, several authors have suggested that a preference for positive skewness can lead to antidiversification as investors attempt to capture the greatest amount of positive skew. These analyses ignore the sampling risk (the probability that the skewness of a particular portfolio of size n will be near its expected value) that exists when less than fully diversified portfolios are held. This analysis presents skewness statistics for three security populations over three market periods to illustrate the relationship between sampling risk and diversification. Small portfolios of stocks or call options are shown to possess greater expected skewness than larger portfolios for each sample period examined, but small portfolios also exhibit the greatest sampling risk for skewness. Depending upon an investor's skewness preference, some diversification in these assets appears appropriate to increase the confidence regarding the actual skewness that will be observed for a particular portfolio chosen. Expected skewness for covered call portfolios is negative for all portfolio sizes and sample periods and declines as portfolio size inreases. The elimination of sampling risk and the reduction of negative expected skewness can be accomplished through complete diversification in these assets.

On the Distributional Conditions for a Consumption‐oriented Three Moment CAPM

ABSTRACTIn this paper, we develop sufficient conditions on probability distributions for a three moment (mean, variance, and skewness) consumption‐oriented capital asset pricing model (CAPM) to price correctly a subset of assets. The assumptions that individuals in an allocationally efficient capital market have identical probability beliefs and monotone increasing strictly concave utility functions displaying nonincreasing absolute risk aversion imply an aggregate preference function that exhibits preference for expected return, aversion to variance of return, and preference for positive skewness. For otherwise arbitrary preferences, we show that quadratic characteristic lines are sufficient for a subset of assets to be priced according to a three moment consumption‐oriented CAPM.