Questions tagged [kurtosis]

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Is there a modified Bachelier's futures spread option model with adjustments for skew and kurtosis?

I'm looking at pricing a very large deal and while the distribution is kind of "normal," there's quiet a bit of skew and kurtosis that isn't being considered when I use the normal Bachelier'...
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1 answer
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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&...
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129 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} ...
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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: ...
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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 ...
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1 vote
2 answers
161 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 ...
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  • 171
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1 answer
621 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 ...
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4 votes
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428 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 ...
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1 vote
3 answers
258 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." ...
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1 vote
0 answers
32 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, ...
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1 answer
380 views

Kurtosis in GARCH

In a GARCH(1,1) model $$ x_t = \sigma_tz_t$$ $$\sigma_{t+1}^2=a_0 + a_1x_t^2 + b_1\sigma_t^2$$ the kurtosis (when it exists) can be shown to be equal to $$ \kappa_x = \kappa_z \frac{1-(a_1+b_1)^2}...
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How to estimate option implied skewness and kurtosis in R

Suppose that i have data that for each day i have more than one option, either put or call. I.E. I have more than 20 put options and 20 call options for each specific day. What is the way to estimate ...
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3 votes
0 answers
298 views

Annualization of coskewness and cokurtosis

I am constructing a mean-variance-skewness-kurtosis portfolio based on monthly data with a holding period of one year. Meucci describes how to annualize higher order moments in general, but not how to ...
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-1 votes
3 answers
161 views

Is there a stochastic equation which can model returns according to its four moments?

The normal stochastic equation only models mean and standard deviation. For now, I'm randomly picking returns from a historical CDF of the returns. I'd like to have some flexibility when it comes to ...
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Interpretation of Skew and Kurtoisis - strategy backtesting

I am working on my dissertation and i would like to provide a nice interpretation of two tables which i will present below. I have 10 portfolio buckets which i sort on 6 different attributes. One of ...
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2 votes
1 answer
449 views

How do I get Value-at-Risk for a GED distribution in R?

I need to calculate parametric Value-at-Risk using a GARCH model assuming a GED distribution. How can calculate it in R? thank you
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1 vote
1 answer
206 views

Higher moments arbitrage

Is there concrete evidence that statistical arbitrage (historical vs. implied) on higher moments, specifically skewness and kurtosis, can be (significantly) done? Working from this source, the author ...
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2 votes
2 answers
913 views

High values of skewness and kurtosis of realized protfolio returns

I am investigating some asset allocation strategies and I am wondering about the results I obtain. I am working on monthly and weekly data of the same stock indices (SP500, FTSE 100 etc). And when I ...
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3 votes
0 answers
284 views

Risk Neutral Variance Gamma

In the risk neutral version of the Variance Gamma model the stock dynamics are $$S_T=S_0 e^{ (r-q+\omega)t + X(t;\sigma,\nu,\theta)}$$ with $$\omega=\frac{1}{\nu}\ln\left(1-\theta \nu - \frac{\...
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1 vote
1 answer
370 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 ...
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3 votes
0 answers
119 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 ...
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7 votes
1 answer
13k 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 ...
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22 votes
1 answer
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 ...
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5 votes
2 answers
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 \...
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3 votes
2 answers
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 ...
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7 votes
2 answers
7k 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 ...
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17 votes
3 answers
2k views

What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?

Is there any relationship between the risk aversion coefficient in an individual's utility function (commonly used in portfolio optimization) and the preference for higher moments such as skewness and ...
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5 votes
0 answers
213 views

Benefits of Diversification and Rebalancing with negatively skewed leptokurtic return distribution?

I am missing tools to investigate this issue. I am trying to solve this question here. What kind of issues should you acknowledge over the naive diversification/rebalancing with normal distribution? ...
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