# Questions tagged [kurtosis]

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109 views

### How much is considered as a fat tail for a ratio variable based on kurtosis?

I have two variables as below: inventory turnover (multiple to 100 already) and inventory day. And I have the kurtosis as below: I do not know how to judge if there is any "fat-tail kurtosis&...
92 views

### Skewness and Kurtosis in GARCH vs Heston

GARCH(1,1) In discrete time, we can model returns as follows \begin{align} r_t &= \mu + \sigma_t\epsilon_t\\ \sigma_t^2 &= \omega + \alpha \epsilon_{t-1}^2 + \beta\sigma_{t-1}^2 \end{align} ...
89 views

### Correctly simulating BEKK series to model asset returns

I am trying to create financial data as close as possible to that of asset returns. Using the R code I can collect some stock data and compute the return: ...
41 views

### Skewness and kurtosis measures when full distribution is not available

I have asked this question here, but did not get any answer. I was wondering if anybody knows a method of deriving skewness and kurtosis measures from different quantiles, mean, and/or variance. I do ...
137 views

### Relationship mean variance efficiency and skewness of the return distribution?

I am wondering what the relationship is between skewness, kurtosis and mean variance efficiency is. Is it correct that particular investors are willing to give up mean variance efficiency in return ...
530 views

### Why assume stock returns are normally distributed instead of just adjusting the kurtosis?

Most standard models assume stock returns are normally distributed even though everyone agrees that real-world returns have fat tails. We've all heard stories of hedge funds that went bankrupt cause ...
310 views

### Annualization of higher-order co-moments (coskewness and cokurtosis arrays)

I'm developing a dynamic portfolio optimization procedure based on the implementation of the Modified sharpe ratio. The mentioned ratio depends, among other factors, on the skewness and kurtosis of ...
245 views

### Rationale for describing kurtosis as "peakedness"?

Despite plenty of evidence to the contrary, many quantitative finance sources of information, including teaching resources such as CFA prep, persist in defining kurtosis as a measure of "peakedness." ...
29 views

### Why Jarque - Bera values are so high? Is this normal? [closed]

Please advise whether the following is a normal occurrence: In the above table I have Autocorrelation at lag1, LB, Skew, Kurt and JB test. I have noticed that whenever the value of Kurt increases, ...
313 views

359 views

### how to compute daily skewness of S&P daily return timeseries under no other more high - frequency time series?

As we all know , return time series marked features: fat tail or negative skewness and peakedness. For a similar problem of variance computation, we can compute variance by garch model and other ...
111 views

### Optimize an equity portfolio for the four central moments: problem formulation

Basically i am confused as to which formula to use for portfolio skew and kurtosis and how to use the same in the optimization problem. I would also like to know the options available regarding the ...
12k views

### How to annualize skewness and kurtosis based on daily returns

I'm trying to annualize the four moments based on a string of daily returns (continuously compounded) for 11 years. The formulas for the annualization of the mean and the standard deviation I did ...
8k views

### Skewness and Kurtosis under aggregation

Returns possess non-zero skewness and excess kurtosis. If these assets are temporally aggregated both will disappear due to the law of large numbers. To be exact, if we assume IID returns skewness ...
1k views

### Derivation of portfolio skewness and portfolio kurtosis

Where can I find derivation of formula for portfolio skewness and kurtosis? I can find formulas everywhere, but not their derivations? For example, the portfolio variance formula, \$\sigma_P = w^\top \...
1k views

### Distribution for High Kurtosis

Can you please advise which distribution to follow when your skewness is 0.28 and Kurtosis value is 51. Since it's leptokurtic and positively skewed I would like to fit distribution and also wanted to ...
6k views

### Calculating Portfolio Skewness & Kurtosis

I need to calculate the skewness and kurtosis of 2 asset portfolio, can someone please help me with the formulas and definition of terms? Thank you. I have been using the matrices method and I am not ...