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Questions tagged [kurtosis]

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2answers
78 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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1answer
92 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 ...
3
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0answers
57 views

Annualization of higher order Co-moments

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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3answers
171 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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0answers
28 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, ...
4
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1answer
215 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}...
4
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0answers
466 views

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 ...
3
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0answers
246 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 ...
-1
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3answers
139 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 ...
1
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0answers
98 views

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 ...
2
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1answer
318 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
1
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1answer
145 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 ...
0
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2answers
594 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 ...
3
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0answers
219 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{\...
1
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1answer
341 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 ...
2
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0answers
88 views

I want to optimize an equity portfolio for the four central moments can anyone help me with the 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 ...
5
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1answer
9k 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 ...
18
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1answer
6k 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 ...
1
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1answer
748 views

derivation of formula for portfolio skewness and 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 is well known and I ...
3
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2answers
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 ...
6
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2answers
5k 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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3answers
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 ...