The impact of downside risk on risk-adjusted performance of mutual funds in the Euronext markets

Many performance measures, such as the classic Sharpe ratio have difficulty in evaluating the performance of mutual funds with skewed return distributions. Common causes for skewness are the use of options in the portfolio or superior market timing skills of the portfolio manager. In this article we examine to what extent downside risk and the upside potential ratio can be used to evaluate skewed return distributions. In order to accomplish this goal, we first show the relation between the risk preferences of the investor and the risk- adjusted performance measure. We conclude that it is difficult to interpret differences in the outcomes of risk-adjusted performance measures exclusively as differences in forecasting skills of portfolio managers. We illustrate this with an example of a simulation study of a protective put strategy. We show that the Sharpe ratio leads to incorrect conclusions in the case of protective put strategies. On the other hand, the upside potential ratio leads to correct conclusions. Finally, we apply downside risk and the upside potential ratio in the process of selecting a mutual fund from a sample of mutual funds in the Euronext stock markets. The rankings appear similar, which can be attributed to the absence of significant skewness in the sample. However, find that the remaining differences can be quite significant for individual fund managers, and that these differences can be attributed to skewness. Therefore, we prefer to use the UPR as an alternative to the Sharpe ratio, as it gives a more adequate evaluation of the use of options and forecasting skills.Downside risk, mutual funds, performance measurement, risk preference, asymmetric return distributions

On the Empirical Importance of the Conditional Skewness Assumption in Modelling the Relationship Between Risk and Return

The main goal of this paper is an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal CAPM model we built a general sampling model suitable in analysing such a relationship. The most important feature of our assumptions is that the skewness of the conditional distribution of returns is used as an alternative source of relation between risk and return. This general specification relates to GARCH-In-Mean model. In order to make conditional distribution of financial returns skewed we considered a constructive approach based on the inverse probability integral transformation. In particular, we apply the hidden truncation mechanism, two equivalent approaches of the inverse scale factors, order statistics concept, Beta and Bernstein distribution transformations, and also the constructive method. Based on the daily excess returns on the Warsaw Stock Exchange Index we checked the empirical importance of the conditional skewness assumption on the relation between risk and return on the Warsaw Stock Market. We present posterior probabilities of all competing specifications as well as the posterior analysis of positive sign of the tested relationship.Comment: Presented at 3-rd Symposium on Socio- and Econophysics, FENS2007, Wroclaw 22-24 November 200

Cross-sectional return predictability: the predictive power of return asymmetry, skewness and tail risk

This thesis attempts to investigate the cross-sectional predictive power of return asymmetry, skewness and tail risk. It mainly consists of three empirical chapters on the relation between predictive patterns of the return distribution and expected stock returns. In the first empirical chapter, I adopt a measure of asymmetry, originally proposed by Patil et al. (2012), which can be employed to characterise the shape of the entire distribution of asset returns instead of skewness. Empirical evidence on the relation between asset returns and the skewness of the return distribution is mixed. As skewness is primarily influenced by the tail behaviour of the return distribution, it is possible for two distributions with identical skewness to have quite different asymmetry. I will examine the relationship between this new measure and stock returns. My empirical analysis indicates that stocks with high return asymmetry exhibit low expected returns. The negative relation between return asymmetry and expected returns persists after I control for size, book-to-market, momentum, short-term return reversals, liquidity, idiosyncratic volatility and various skewness factors. My results are consistent with the findings from theoretical models such as those of Brunnermeier et al. (2007) and Barberis and Huang (2008). In the second empirical chapter, I examine the default risk and financial crisis explanations for the market skewness risk effect and find that the effect is stronger among stocks with large size, high growth, and low default risk. This suggests that the positive skewness preference theory only holds for safe stocks. Moreover, the effect of market skewness risk on stock returns interacts with default risk significantly. Market skewness risk has explanatory power for stock returns only during the periods of good economic conditions. Additionally, the market skewness risk effect is not persistent. After the financial crisis of 2007-2008, the strong effect disappears. In the last empirical chapter, I know that investors sometimes underweight the tail event. I then try to figure out this situation by examining the default risk and financial crisis explanations for the tail risk effect. I find that market size, book-to-market ratio, and default risk have large impact on the tail risk effect. Moreover, tail risk only has explanatory power for stock returns during the periods of good economic conditions. The results suggest that when investors hold stocks with small size, low growth, and high default risk, the tail risk tends to be ignored. The tail risk effect is not persistent. The significant tail risk effect also disappear after the financial crisis of 2007-2008

Risk-Neutral Skewness, Informed Trading, and the Cross Section of Stock Returns

AbstractIn this article, we use volatility surface data from options contracts to document a strong, robust, and positive cross-sectional relation between risk-neutral skewness (RNS) and subsequent stock returns. The differential return between high- and low-RNS stocks amounts to 0.17% per week. Preannouncement RNS is positively related to earnings announcement returns, and the positive RNS&ndash;return relation is more pronounced for other nonscheduled news releases. This suggests that it is informed trading that drives the positive relation between RNS and subsequent stock returns. We also find that RNS contains incremental information beyond trading signals captured by option-implied volatility and volume.</jats:p

An approach to measuring The relation between risk and return. Bayesian analysis for WIG Data

The main goal of this paper is an application of Bayesian inference in testing the relation between risk and return of the financial time series. On the basis of the Intertemporal CAl’M model, proposed by Merton (1973), we built a general sampling model suitable in analysing such relationship. The most important feature of our model assumptions is that the possible skewness of conditional distribution of returns is used as an alternative source of relation between risk and return. Thus, pure statistical feature of the sampling model is equipped with economic interpretation. This general specification relates to GARCH-In-Mean model proposed by Osiewalski and Pipień (2000). In order to make conditional distribution of financial returns skewed we considered a constructive approach based on the inverse probability integral transformation. In particular, we apply the hidden truncation mechanism, two approaches based on the inverse scale factors in the positive and the negative orthant, order statistics concept, Beta distribution transformation, Bernstein density transformation and the method recently proposed by Ferreira and Steel (2006). Based on the daily excess returns of WIG index we checked the total impact of conditional skewness assumption on the relation between return and risk on the Warsaw Stock Market. Posterior inference about skewness mechanisms confirmed positive and decisively significant relationship between expected return and risk. The greatest data support, as measured by the posterior probability value, receives model with conditional skewness based on the Beta distribution transformation with two free parameters

Essays on the Skewness of Firm Fundamentals and Stock Returns

This dissertation investigates whether the skewness of firm fundamentals is informative about future firm performance and stock return. We present two distinct preference-free theoretical models of firm fundamentals, both of which imply a positive relation between the skewness of firm fundamentals and expected stock return. Consistent with this implication, we show empirically that the skewness measures of firm fundamentals positively predicts cross-sectional stock returns. Further supporting both models, we find that higher fundamental skewness implies not only higher future firm growth option but also higher future firm profitability. Our results cannot be explained by existing risk factors and return predictors including the levels of firm fundamentals and the skewness of stock returns.Business Administratio

Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns

Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month(MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX generally subsumes or reverses the puzzling negative relation between returns and idiosyncratic volatility recently documented in Ang et al. (2006, 2008)

Black-Litterman Asset Allocation under Hidden Truncation Distribution

In this paper, we study the Black-Litterman (BL) asset allocation model (Black and Litterman, 1990) under the hidden truncation skew-normal distribution (Arnold and Beaver, 2000). In particular, when returns are assumed to follow this skew normal distribution, we show that the posterior returns, after incorporating views, are also skew normal. By using Simaan three moments risk model (Simaan, 1993), we could then obtain the optimal portfolio. Empirical data show that the optimal portfolio obtained this way has less risk compared to an optimal portfolio of the classical BL model and that they become more negatively skewed as the expected returns of portfolios increase, which suggests that the investors trade a negative skewness for a higher expected return. We also observe a negative relation between portfolio volatility and portfolio skewness. This observation suggests that investors may be making a trade-off, opting for lower volatility in exchange for higher skewness, or vice versa. This trade-off indicates that stocks with significant price declines tend to exhibit increased volatility.Comment: 45 page

Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns

Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month (MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX reverses the puzzling negative relation between returns and idiosyncratic volatility recently documented in Ang et al. (2006, 2008).

Three essays on modeling stock returns: empirical analysis of the residual distribution, risk-return relation, and stock-bond dynamic correlation

This dissertation studies the following issues: the presence of non-normal distribution features and the significance of higher order moments, the tradeoff between risk and return, and the dynamic conditional correlation between stock returns and bond returns. These issues are structured into three essays.Essay #1 tackles the non-normal features by employing the exponential generalized beta distribution of the second kind (EGB2) to model 30 Dow Jones industrial stock returns. The evidence suggests that the model with the EGB2 distribution assumption is capable of taking care of stock return characteristics, including fat tails, peakedness (leptokurtosis), skewness, clustered conditional variance, and leverage effect, therefore, is capable of making a good prediction on the happenings of extreme values. The goodness of fit statistic provides supporting evidence in favor of the EGB2 distribution in modeling stock returns. Evidence also suggests that the leverage effect is diminished when higher order moments are considered.Essay #2 examines the risk-return relation by applying high frequency data of 30 Dow Jones industrial stocks. I find some supportive evidence in favor of the positive relation between the expected excess return and expected risk. However, this positive relation is not revealed for all 30 stocks using a standard weighted least squares regression (WLS) method. Using a quantile regression method, I find that the risk-return relation evolves from negative to positive as the returns’ quantile increases. This essay also finds interesting evidence that the intraday skewness coefficient explains a great deal of the variation in the excess returns.Essay #3 mainly focuses on the analysis of the time-varying correlations between stock and bond returns using the asymmetric dynamic conditional correlation (ADCC) model (Cappiello et al., 2004). The estimated coefficients show some volatile behavior and display some degree of persistence over time. Testing the asymmetric dynamic correlations by using a set of macroeconomic information, I find that the federal funds rate, the relative volatility between the stock and bond markets, the yield spread, and oil price shocks are the significant factors for the coefficients’ time varying.Ph.D., Finance -- Drexel University, 200