What is Leptokurtic and Platykurtic?

Leptokurtic: More values in the distribution tails and more values close to the mean (i.e. sharply peaked with heavy tails) Platykurtic: Fewer values in the tails and fewer values close to the mean (i.e. the curve has a flat peak and has more dispersed scores with lighter tails).

Are stock returns Leptokurtic?

The daily stock returns at Macedonian Stock Exchange (MSE) are characterized by high volatility and non-Gaussian behaviors as well as they are extremely leptokurtic. The analysis of MSE time series stock returns determine volatility clustering and high kurtosis.

Why does Leptokurtic have fatter tails?

Leptokurtic (Kurtosis > 3): Distribution is longer, tails are fatter. Peak is higher and sharper than Mesokurtic, which means that data are heavy-tailed or profusion of outliers. The reason for this is because the extreme values are less than that of the normal distribution.

What is Leptokurtic Mesokurtic and Platykurtic distribution and its properties?

Distributions may be described as mesokurtic, platykurtic, or leptokurtic. Mesokurtic distributions have a kurtosis of zero, meaning that the probability of extreme, rare, or outlier data is zero or close to zero. In contrast, a leptokurtic distribution has fatter tails.

What kurtosis means?

Kurtosis is a measure of the combined weight of a distribution’s tails relative to the center of the distribution. When a set of approximately normal data is graphed via a histogram, it shows a bell peak and most data within three standard deviations (plus or minus) of the mean.

What does positively skewed mean?

Understanding Skewness These taperings are known as “tails.” Negative skew refers to a longer or fatter tail on the left side of the distribution, while positive skew refers to a longer or fatter tail on the right. The mean of positively skewed data will be greater than the median.

What does kurtosis mean for stocks?

Kurtosis is a statistical measure that is used to describe the size of the tails on a distribution. Excess kurtosis helps determine how much risk is involved in a specific investment.

What does a kurtosis of 3 mean?

Kurtosis is a measure of the combined sizes of the two tails. If the kurtosis is greater than 3, then the dataset has heavier tails than a normal distribution (more in the tails). If the kurtosis is less than 3, then the dataset has lighter tails than a normal distribution (less in the tails).

What is the difference between skew and kurtosis?

Skewness is a measure of symmetry, or more precisely, the lack of symmetry. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers.

Is high kurtosis good or bad?

Kurtosis is only useful when used in conjunction with standard deviation. It is possible that an investment might have a high kurtosis (bad), but the overall standard deviation is low (good). Conversely, one might see an investment with a low kurtosis (good), but the overall standard deviation is high (bad).

How kurtosis is calculated?

x̅ is the mean and n is the sample size, as usual. m4 is called the fourth moment of the data set. m2 is the variance, the square of the standard deviation. The kurtosis can also be computed as a4 = the average value of z4, where z is the familiar z-score, z = (x−x̅)/σ.

Which is the best definition of leptokurtic?

Definition of leptokurtic 1 of a frequency distribution curve : being more peaked than the corresponding normal distribution curve 2 of a frequency distribution : being more concentrated about the mean than the corresponding normal distribution

How are leptokurtic distributions different from normal distributions?

Leptokurtic distributions are statistical distributions with kurtosis over three. It is one of three major categories found in kurtosis analysis. Its other two counterparts are mesokurtic and platykurtic. Leptokurtic distributions are distributions with kurtosis larger than that of a normal distribution.

Which is a heavier tail platykurtic or leptokurtic?

In general, leptokurtic distributions have heavier tails or a higher probability of extreme outlier values when compared to mesokurtic or platykurtic distributions.

Are there any return series that are leptokurtic?

The returns data are non-normal, and, except for the Auto index, Metal index and, to some extent, the Telecom index, return distributions are quite significantly leptokurtic. Also, virtually all return series are negatively skewed to some degree. If you want to impress your friends, the technical term is ” leptokurtic .”