# Skewness and kurtosis relationship marketing

### Skewness and Kurtosis: Assessment in the Returns Distribution | eVestment

measures the combined impact of “pure” and skewness-kurtosis risk on the mean of .. the puzzling intertemporal relation between the market risk premium and. or co-kurtosis with the market is priced; historical returns data are typically . centrated positions in skewed securities, and resulting in a negative relation be. When returns fall outside of a normal distribution, the distribution exhibits skewness or kurtosis. Skewness is known as the third “moment” of a return distribution.

### Keep Skewness In Perspective

In addition, some investment vehicles, such as hedge funds, also exhibit negative skewness. Kurtosis Kurtosis measures the degree to which exceptional values, those much larger or much smaller than the average, occur more frequently high kurtosis or less frequently low kurtosis than in a normal bell shaped distribution. In other words, more values are closer to the average than would be found in a normal distribution, and tails are thinner.

To ensure sufficient liquidity, a stock had to have at least 80 daily transactions. The average number of intraday transactions per day for a stock was more than 1, The authors used data from the Center for Research and Security Prices database to obtain the daily returns of each company in order to calculate weekly returns. The authors aggregated daily realized moments to obtain weekly realized volatility, skewness and kurtosis measures for more than 2 million firm-week observations.

They then sorted stocks into deciles based on the current-week realized moment and computed the subsequent one-week return of a trading strategy that buys the portfolio of stocks with a high realized moment—volatility, skewness or kurtosis—and sells the portfolio of stocks with a low realized moment.

Realized volatility increases from 19 percent for the first decile to percent for the highest decile. A positive relationship exists between realized volatility and historical skewness. Realized skewness has a negative relationship with realized volatility reflecting that stocks with big drops in price are more volatile and realized kurtosis shows an increasing pattern through the volatility deciles. Over time, realized volatility tends to be consistently highest for firms with small market caps, low book-to-market ratios and high market betas.

Firms with a high degree of asymmetry, either positive or negative, are small, highly illiquid and followed by fewer analysts. In addition, the number of intraday transactions for these firms is lower. When sorting on realized volatility, the resulting portfolio return differences are not statistically significant. When sorting by realized skewness, the long stocks with low skewnessshort stocks with high skewness and value-weighted portfolio produced an average weekly return of 24 basis points with a t-statistic of 3.

Realized skewness was highly significant in explaining the cross section of returns after controlling for all the factors the authors examined, including realized volatility and kurtosis, firm size, book-to-market ratios, market beta, historical skewness, the number of analysts that follow a firm, idiosyncratic volatility and illiquidity as well as a few others.

When idiosyncratic volatility increases, low-skewness stocks are compensated with higher returns while high-skewness stocks are compensated with lower returns.

**What is Skewness?**

This pattern is stronger for small stocks. Across deciles, the average kurtosis ranged from about 4 to roughly The estimates for the Carhart four-factor alpha are smaller and less statistically significant compared with those for the raw returns. So, a number of studies have tested higher order CAPM model for developed stock markets, but there has been little work in the emerging stock markets.

They found that CAPM is not working in the market. They concluded that the invalidity of CAPM in the market is because of finding nonlinear relationship between risk and return and not finding beta as a complete measure of risk. To the best of our knowledge, no research has been done to measure the technical efficiency of companies listed in the Bangladesh stock market by using the risk factors which are derived from higher moment CAPM.

## Assessing Skewness and Kurtosis in the Returns Distribution

According to Berger and Humphrey [ 13 ], many of the researchers used either parametric approach: SFA or nonparametric approach: Data Envelopment Analysis DEA for investigating the technical efficiency of financial institutions, for example, banking industry [ 14 — 18 ] and insurance industry [ 1920 ]. The reason of using SFA was that it has the advantage of dealing with stochastic noise, allowing for statistical tests of hypotheses concerning production structure and degree of inefficiency.

The reason of not using DEA was that DEA does not impose any assumptions about production functional form and also does not take into account random errors; hence, the efficiency estimates may be biased if the production process is largely characterized by stochastic elements [ 21 ].

SFA employs a composed error model in which inefficiencies are assumed to follow an asymmetric distribution, usually the half-normal or the truncated-normal, while random errors are assumed to follow a symmetric distribution, usually the standard normal [ 22 ]. Most past studies used the half-normal or the truncated-normal distribution as assumption about inefficiency effects model because of the ease of estimation and interpretation [ 23 ].

- The relationships between unsystematic risk, skewness and stock returns during up and down markets
- There was a problem providing the content you requested
- Economics Research International

Application of different distributions, like gamma and exponential, can also be significant sometimes [ 24 — 26 ]. Materials and Methods 2. In fact, when most of the world stock markets declined during the last global financial crisis instock prices in DSE market experienced a continuous rise [ 27 ]. The reasons behind this were that DSE was isolated from the global financial markets and Bangladesh Bank BB took prompt actions to safeguard the banks and other financial institutions from the crisis.

That is why DSE has significant implications for the performance of financial sector, and even the economy as a whole [ 28 ]. The data which was collected from DSE market belongs to 71 nonfinancial companies for the period of — Recently, the DSE market included 22 categories of companies, of which the following 10 categories were covered in this analysis: Market return market capitalization, book to market ratio, and market value were taken as the independent variables.

We also introduced the co-skewness and co-kurtosis terms as independent variables in the final analysis of SFA, as we know that one of the main objectives of this study was to check the contribution of co-skewness and co-kurtosis which was derived from H-CAPM for finding the technical efficiency of the studied companies and their respective groups in the DSE market.

In our analysis, the following model [ 32 ] was used where efficiency effects were separated from stochastic element.

This model was preferred because in this study no explanatory variables were associated with technical inefficiency effects.